Population Ecology: A Unified Study of Animals and Plants

POPULATION ECOLOGY

A Unijied Study of Animals and Plants

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A Unijied Study of Animals and Plants
MICHAEL BEGON BSC, P ~ D
M A R T I N MORTIMER BSC. P ~ D
DAVID J. THOMPSON BA, DPhil

All of the Department of
Environmental and Evolutionary Biology
The University of Liverpool

THIRD EDITION

Blackwell
Science

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Blackwell ScienceKK Library of Congress
MG KodenmachoBuilding Cataloging-in-PublicatiohData
7-1 0 KodenmachoNihombashi
Chuo-ku,Tokyo 104,Japan Begon, Michael.
Population ecology:a unified study
First published 1981
Reprinted 1982,1983,1985 of animals and plants1
Second edition l 9 8 6
Reprinted 1987,1988,1989,1990,1992,1993 Michael TBheogmonp,sMona.r-tin3rMd eodrt.imer.
Third edition 1996 David J.
Reprinted 1997,1999,2000, 2002
p. cm.
Set by Semantic Graphics,Singapore
Printed and bound in the United Kingdom Includes bibliographicalreferences
by TJ International Ltd, Padstow, Cornwall
(p. ) and index.
The Blackwell Science logo is a
trade mark of Blackwell ScienceLtd, ISBN 0-632-03478-5
registeredat the United Kingdom
Trade Marks Registry 1Population biology. 2 Ecology.

I Mortimer, Martin

I1Thompson,David J. 111Title.

QH352.B43 1996

574.5'248-dc20 95-23676
CIP

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Preface, vii 3.2.1 The basic equations, 52
3.2.2 Incorporation of a range of competition, 54
Part 1:Single-Species Populations 3.2.3 Models for annual plants, 56
3.3 Continuous breeding, 58
Describing populations, 3 3.4 The utility of the equations, 60
3.4.1 Causes of population fluctuations,60
1.l Introduction, 3 3.4.2 The equations as descriptions, 62
1.2 Population processes, 3 3.4.3 'Cobwebbing'-a more general
1.3 The diagrammatic life table, 5
approach, 65
1.3.l General form, 5 3.5 Incorporation of age-specific fecundity and
1.3.2 The common field grasshopper,an annual
mortality, 66
species, 6 3.5.1 The matrix model, 69
1.3.3 Ragwort, a biennial, 7 3.5.2 Using the model, 70
1.3.4 More complex life cycles, 9 3.5.3 A working example: Poa annua, 72
1.3.5 Age and stage: the problems of describing
Part 2: Interspecific Interactions
some plant and animal populations, 10
1.4 Conventional life tables, 13 4 Interspecific competition, 77

1A.1 The cohort life table, 13 4.1 The nature of interspecificinteractions, 77
1A.2 The static life table, 17 4.2 Interspecificcompetition, 78
1.4.3 Resumk, 18 4.3 A field example: granivorous ants, 78
1.5 Some generalizations, 18 4.4 Competition between plant species: experimental
1.6 The modular growth of organisms, 21
1.7 Buried seed banks, 26 approaches, 83
4.4.1 Manipulating density, 83
Intraspecific competition, 28 4.4.2 Manipulating resources, 89
4.5 The ecological niche, 90
2.1 The nature of intraspecific competition, 28 4.6 The Competitive Exclusion Principle, 92
2.2 Three characteristicsof intraspecific 4.7 Competitive exclusion in the field, 92
4.8 Competitive release, 95
competition, 29 4.9 Coexistence: resource partitioning, 95
2.3 Density-dependence:a fourth characteristic, 29 4.10 Character displacement, 98
2.4 Scramble and contest, 31 4.11 Competition: its avoidance or its
2.5 Actual effects of intraspecific competition, 33 non-existence?, 98
4.12 Competition and coexistence in plants, 101
2.5.1 Palmblad's data, 33 4.13 A logistic model of two-species competition, 105
2.5.2 Competition in plants: a deeper look, 37 4.13.1 The model's utility, 107
2.5.3 Individual variability, 42 4.13.2 A test of the model: fruit fly
2.5.4 Self-thinning in plants, 43
2.5.5 Competition in Patella cochlear, 48 competition, 109
2.5.6 Competition in the fruit fly, 50 4.14 Analysis of competition in plants, 110
2.6 Negative competition, 50 4.15 Niche overlap, 112
4.16 Competition and heterogeneity, 1l 4
3 Models of single-species populations, 52

3.1 Introduction, 52
3.2 Populations breeding at discrete intervals, 52

vi CONTENTS

5 Predation, l17 Part 3: Synthesis

Introduction, 117 6 Population regulation, 177
Patterns of abundance, 118
Coevolution, and specialization amongst 6.1 Introduction, 177
predators, 119 6.2 Nicholson's view, l77
5.3.1 One explanation for the degrees of 6.3 Andrewartha and Birch's view, 177
6.4 An example: Thrips imaginis, 178
specialization, 121 6.5 Some general conclusions, 180
5.3.2 Food preference and predator 6.6 A life-table analysis of a Colorado beetle

switching, 122 population, l 8 1
Time and timing, 124 6.6.1 Life-table data, 181
Effects on prey fitness, 125 6.6.2 'Key-factor' analysis, l83
5.5.1 The effects of herbivores on plant 6.6.3 Regulation of the population, 184
fitness, 126 6.6.4 A population model, 185
The effects of predation-rate on predator 6.7 The problem re-emerges, 186
fitness, 131 6.7.1 Life-table analyses, 186
5.6.1 Thresholds, 131 6.7.2 Single-species time series, 188
5.6.2 Food quality, 132 6.7.3 Population regulation in vertebrates, 190
The fu,nctionalresponse of predators to prey 6.8 Population regulation in plants, 191
availability, 133 6.9 Genetic change, 200
5.7.1 The 'type 2' response, 133 6.10 Territoriality, 201
5.7.2 The 'type 1' response, 135 6.11 'Space capture' in plants, 203
5.7.3 Variation in?handling time and searching 6.12 Chaos in ecological systems, 205

efficiency: 'type 3' responses, 136 Beyond population ecology, 210
5.7.4 Switching and 'type 3' responses, 136
Aggregated effects, 137 7.1 Introduction, 210
5.8..1 Parasite-host distributions, l 37 7.2 Metapopulation dynamics, 210
5.8.2 Refuges, 138
5.8.3 Partial refuges: aggregative responses, 139 7.2.1 Metapopulation models, 210
5.8.4 Further responses to patchiness, 140 7.2.2 Examples of metapopulations, 212
5.8.5 'Even' distributions,141 7.2.3 Applications of the metapopulation
5.8.6 Underlying behaviour, 142
5.8.7 'Hide-and-seek', 143 concept, 214
7.3 Community structure, 216
Mutual interference amongst predators, 144
5.9.1 A similar effect amongst parasites, 146 7.3.1 The role of interspecificcompetition, 216
5.10 Interference and pseudo-interference, 146 7.3.2 The role of predation, 217
5.11 Optimal foraging, 148 7.3.3 The role of disturbance, 219
5.12 Resume, 149 7.3.4 The role of instability, 220
5.13 Mathematical models, 149 7.3.5 The role of habitat size and diversity, 222
5.13.1 Host-parasitoid models, 150 7.3.6 Conclusions. 224
5.13.2 Heterogeneity in host-parasitoid
References; 225
interactions, 155
5.13.3 A model of grazing systems, 160 Author index, 239
5.14 'Patterns of abundance' reconsidered, 164
5.15 Harvesting, 165 Organism index, 242
5.15.1 Characteristics of harvested
Subject index, 245
populations, 165
5.l5.2 Harvesting in structured populations, 170
5.15.3 Incorporating population structure:

matrix models of harvesting, 173

This book is intended primarily for students. It is differences between the two. We feel, however, that
designed to describe the present state of population plant and animal populations have had their own,
ecology in terms which can be readily understood by independent ecologistsfor too long, and that, since the
undergraduates with little or no prior knowledge of same fundamental principles apply to both, there is
the subject. We have, however, presented our view, most to be gained at present from a concentration on
rather than some definitive view of the subject, and similarities rather than differences.
consequently, we have tried to provide sufficient
information for everybody (studentand expert alike)to In this third edition, we have retained the basic
disagree with us wherever they think fit. structure of the first two editions; but we have sought
to evolve the text in areas where we feel particular
Population ecology is, to us, the study of the sizes progress has been made and consolidated. We have
(and to a lesser extent the distributions) of plant and looked further at the role of spatial scale in the
animal populations, and of the processes, particularly stability of host-parasitoid and competitive interac-
the biological processes, which determine these sizes. tions and following from this, revisited the role of
As such, it must inevitably be a numerical and density-dependence in population regulation. We
quantitative subject. Nevertheless, we have avoided have addressed the problem of the detection of chaos,
complex mathematics, and we have, wherever poss- buried seeds, herbivory in plants, and introduced a
ible, relegated the mathematical aspects of a topic to major new section on the concept of the metapopula-
the final parts of the section in which that topic is tion. We have also tried further to cement some of the
examined. This will, we hope, make population eco- links between animal and plant populations by paying
logy more generally accessible, and more palatable. attention to descriptive equations common to both.
But this is not to say that the mathematics have been
played down. Rather, we have tried to play up the The book is set out in three parts. The first starts
importanceof real data from the real world: it is these, from the simplest first principles and examines the
and not some mathematical abstraction, which must dynamics and interactions occurring within single-
always be the major and ultimate concern of the species populations. The second part, occupying ap-
population ecologist. proximately half of the book is concerned with
interspecific interactions: interspecific competition
Developing the subject in this way, however, em- and predation. 'Predation', however, is defined very
phasizes that mathematical models do have an essen-
tial role to play. Time and again they crystallize our broadly, and includes the plant-herbivore, host-
understanding of a topic, or actually tell us more parasite, host-parasitoid and prey-predator interac-
about the real world than we can learn directly from tions. The third part of the book synthesizes and
the real world itself. Nature may be the ultimate expands upon the topics from the preceding chapters,
concern of population ecology, but mathematical and does so at three levels: the regulation and
models, laboratory experiments and field experiments determination of population size, the concept of the
and observations can all help to further our under- metapopulation, and the importance of intra- and
standing. inter-population interactions in determining commu-
nity structure.
We have also tried to establish the point implied by
the subtitle: that population ecology is a unified study A number of people read all or most of the
of animals and plants. We are, of course, aware of the manuscript prior to publication of the first edition, and
made generous and helpful suggestions, many of

vii

viii PREFACE

which we have now incorporated. We are deeply faster than at present. Nevertheless, there are few, if
grateful to Professor Tony Bradshaw, Professor J.L. any, populations for which we can claim to fully
Harper, Professor Michael Hassell, Dr Richard Law, comprehend the underlying causes of abundance.
Professor Geoffrey Sagar, Professor Bryan Shorrocks Much remains to be understood, and a great deal
and, most especially, Professor John Lawton. We more remains to be done.
thank Professor Ilkka Hanski and Dr Chris Thomas for
their comments on much of the new material pre- Michael Begon
sented in this third edition. Martin Mortimer
David J. Thompson
Population ecology has come a long way since its
inception, and the rate of progress has never been

Part 1

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Chapter 1

1.1 Introduction Fig. 1.1 Changes in the frequency of three species in a
natural grassland community in the UK over 40 years.
This book provides an introduction to the study of (After Davy & Jeffries,1981.)
populations of animals and plants. Individual species
are products of organic evolution that, in a multitude interactions among species within and between
of differing assemblages, make up the communities of trophic levels.
living organisms that are found on Earth. That these
communities display changes in the relative abun- This chapter is concerned with describing single-
dance of species is evident both from the fossil record species populations and with abstracting the under-
and in the present day. Populations of member species lying demographic features that are common to them
in a community may show a range of dynamic all. With the appropriate description, we may then be
patterns. For instance, over time, populations may able carefully to consider the underlying causes of the
change in size relative to one another; conversely, dynamics of single-species populations.
they may show apparent constancy in size despite the
fact that births and deaths of individual organisms 1.2 Populationprocesses
occur continually within them. Furthermore, indi-
viduals within populations may group together in Although studies of animal and plant populations
differing spatial arrangements which may change with have developed quite separately, these two life forms
time, even though total population size may remain have much in common when examined from a
constant. demographic viewpoint. At the simplest level, plants
are born from seeds just as birds are born from eggs;
Clearly changes in population size in space and and old animals exhibit signs of senility just as old oak
time, even in simple communities, have the potential trees bear dead branches. Moreover, if we were to
to be, and indeed often are, very complex and pose a catalogue the ages of every dandelion plant and every
wealth of ecological questions. For instance in a vole living in a field, we would probably find a range of
grassland community (Fig. 1.1)we may ask 'Which ages in each; and, as time passes, individuals would
processes contributed to a decline in one species either die, or survive to reach the next age group; and
(Festuca ovina) to a quarter of its original abundance, in some age groups, at certain times, individuals
during which time another species appeared (Hiera-
cium pilosella), only to then decline with the subse-
quent increase of a third (Thymus dvucei)?' Or in the
case of Fig. 1.2, 'Why is there an apparent underlying
regularity in the cyclical abundance of the lynx and
snowshoehare?' If we are to understand such patterns
and be able ultimately to predict changes in them,
then our initial focus must be on the individualspecies
themselves and the manner in which populations
respond to internal and external ecological factors.
With this knowledge we may then begin to investigate
questions of species-habitat interrelationships and

4 PART 1: SINGLE-SPECIES POPULATIONS

Fig. 1.2 Changes in abundance of
the lynx Lynx canadensis and the
snowshoe hare Lepus americanus
(after MacLulick, 1%7) in Canada
over 80 years.

would produce offspring of their own. From the change in numbers in a population between two
outset, therefore, it would seem sensible to suggest points in time.

that, even though life forms and stagesof development ,where N, is the population size(numberof individuals)
will differ substantially between species and across
at time t , N, + is the population size one time period
kingdoms (a point taken up in section 1.6) certain
basic population processes are common to all of them. later, at time t + 1,B is the number of new individuals
born between t and t + 1,D is the number of individ-
We can start consideringthese population processes uals which die between t and t + l, and I and E,

by imagining a study of the numbers of voles inhabit- respectively, are the numbers of immigrants and
emigrants during the same period of tirne. One of the
ing a meadow. Let us suppose that the vole numbers simplest ways of envisaging equation 1.1 is as a
increase. We know that there has either been an influx
of voles from adjoining meadows, or young voles have graphical plot of the population size at time t + l
been born, or both of these events have occurred. We
against the size of the population at a previous time t,
have, therefore, pin-pointed two very basic processes where the time interval is one generation. This is
which affect the size of a population: immigration and illustrated in Fig. 1.3. If population size remains static
birth. Conversely, if vole numbers decline, then our over generations, then the population will be repre-
explanation would be that voles must have either died, sented as a stable locus in graphical space on the
diagonal line bisecting the graph. However, if popula-
or simply left the meadow, or both. These processes, tion size changes over generations then a trajectory of
which reduce population numbers, are death and loci may occur away from the equilibrium line. We
emigration. will use this graphical approach to develop models of
single species dynamics later after we have considered
Of course, there is no reason to suggest that all four the ways in which populations can be described.
processes are not occurring simultaneously in the
population and there is therefore a flux of individuals If the population is so large that our study cannot
encompass the whole of it, then this equation must be
within it. If the population declines, then the reason is constructed in terms of densities rather than absolute
simply that death and emigration together have out- numbers. Thus, samples are taken, and N,, for in-
weighed birth and imigration, and vice versa if the stance, becomes 'the number of plants per square
population increases. We can certainly say that birth, metre at time t' or 'the number of insects per leaf'.

death, immigration and emigration are the four fun-
damental demographic parameters in any study of

population dynamics. Moreover, they can be com-
bined in a simple algebraic equation describing the

CHAPTER 1: DESCRIBING POPULATIONS 5

Fig. 1.3 Graphical representation of changes in population Fig. 1.4 A diagrammaticlife table for an idealized higher
,size over plant. F, number of seeds per plant; g, chance of a seed
size Nt+ germinating (0 g S 1); e, chance of a seedling establishing
is plotted text. itself as an adult (06 e 1);p, chance of an adult surviving
gaegnaeinrasttiostnasr.tiEnagcphospuuclcaetsiosinvesipzoepNutl.aStieoen (O a p S l).

Nevertheless, equation 1.1indicates that, at its sim- Mortimer, 1976), which is applied to an idealized
plest, the task of the demographer is to measure these higher plant in Fig. 1.4. The numbers at the start of
four parameters and account for their values-yet the
translation of this into practice is rarely straight- ,each of the stages-seeds, seedlings and adults-are
forward. Almost all species pass through a number of
stages in their life cycle. Insects metamorphose from given in the square boxes. Thus, the Nt + adults alive
eggs to larvae to adults, and some have a pupal stage
as well; plants pass from seeds to seedlings and then to at time t + l are derived from two sources. Some are
photosynthesizing adult plants, and so on. In all such
cases the different stages must be studied individually. the survivors of the Nt adults alive at time t . Their
Also, in reality, the four 'basic' parameters are them- probability of survival(or, equivalently,the proportion
selves often compounded from several other compo- of them that survive) is placed inside a triangle (or
nent processes. Equation 1.1, therefore cannot be arrow)in Fig. 1.4, and denoted by p. So, for instance, if
considered as anything more than a basis upon which
more realistic descriptions can be built. ,Nt is 100and p (the survival-rate)is 0.9, then there are

1.3 The diagrammatic lifetable 100 X 0.9 or 90 survivors contributingto Nt + at time

1.3.1 General form t + l (10 individuals have died; the mortality-rate

The description we require is one which retains the ,(1 -p) between and t + 1is clearly 0.1).
generality of equation 1.1, but can also reflect the The other source of the Nt + adults is 'birth', which
complexities of most actual populations. One such in the present case can be viewed as a multi-stage
description is the diagrammatic life table (Sagar & process involving seed production, seed germination
and the growth and survival of seedlings. The average
number of seeds produced per adult-the average
fecundity of the plant population-is noted by F in
Fig. 1.4 and placed in a diamond. The total number of
seeds produced is, therefore Nt X F. The proportion of
these seeds that actually germinate on average is
denoted by g, which, being essentially a survival-rate,
is placed in an arrow in Fig. 1.4. Multiplying N , X F by
g gives us the number of seedlings which germinate
successfully. The final part of the process is the

6 P A R T 1: SINGLE-SPECIES POPULATIONS

physiological establishment of seedlings as indepen-
dently photosynthesizing adults. The probability of

surviving this very risky phase of plant growth is
denoted by e (once again in an arrow), and the total
number of 'births' is, therefore, N, X F X g X e. The

number in the population at time t + 1is then the sum

of this and the number of surviving adults, N, X p,
We can now substitute the terms from the life table

into our basic equationof population growth (equation
1.1) as follows:

Surviving

& (14
N,,, =N,-N,(l -p)+N,xFxgxe.
v-
Death Birth

There are severalpoints to note about this equation.
The first is that both here and in Fig. 1.4 immigration
and emigrationhave, for simplicity,been ignored, and
our descriptionof how a plant population may change
in size is essentially incomplete. The second is that
'death' has been calculated as the product of N, and
the mortality-rate (1-p)-survival and mortality are
opposite sides of the same coin. The third point is that
birth is quite clearly a complex product of 'birth-
proper' and subsequentsurvival. This is frequentlythe
case: even human 'birth' rates are the product of the
rate at which fertilized eggs implant in the womb and
the rate of prenatal survival.

1.3.2 The common fieId grasshopper, Fig. 1.5 Diagrammatic life table of the field grasshopper
an annual species Charthippusbrunneus. (Population sizes are per 10m2; data
from Richards & WaloK 1954.)
In practice, careful and meticulous field-work is
necessary to build a diagrammatic life table of the type adults survive from one year to the next (p = 0). Ch.
illustrated in Fig. 1.4. Reliable estimates of the transi- brunneus is, therefore, an 'annual' species; each gen-
tion probabilities (p, g and e in Fig. 1.4)are required, eration lasts for just 1 year, and generations are
as well as measurements of the fecundity of adults. discrete, i.e. they do not overlap. It is also clear that
Such data for the common field grasshopper, Chorthip- the 'birth' of adults is a complex process involving at
pus brunneus, are illustrated in Fig. 1.5. These were least six stages. The first stage is the laying of egg-pods
obtained by a combination of field samples and in the soil by adult females. On average, each female
back-up laboratory observationson a population near laid 7.3 pods, each containing 11eggs. F is, therefore,
Ascot in Berkshire (Richards & Waloff, 1954). The 80.3. These eggs remained dormant over winter, and
population was isolated so that imigration and by early s u m e r only 0.079 of them had survived to
emigration could be ignored. hatch into first-instar nymphs. Subsequently, the
transition probabilities between instars were fairly
The first point to note about Fig. 1.5 is that no

CHAPTER 1: DESCRIBING POPULATIONS 7

Fig. 1.6 Diagrammatic life tables for species with discrete one summer, the population contains both young
breeding seasons. (a) Generations do not overlap. adults which will not reproduce until the following
(b)Generations overlap. (Birth processes are simplified.) year, and mature , reproducing adults.

constant, taking a remorseless toll on the surviving Ragwort, Seneciojacobaea, is a biennial plant with a
population; less than a third of the first-instar nymphs life cycle in which seeds germinate principally in the
survived to be 'born' into the adult population. Despite autumn. Then, during the next year, young plants
their apparently high fecundity, therefore, the adults form a rosette of leaves. In the second year a flowering
of 1947 did little more than replace themselves with stem is formed. A diagrammatic life table for S.
newly born adults in the following year. jacobaea is shown in Fig. 1.7, in which the birth
process has been expanded to include some extra
The Ch. brunneus diagrammatic life table is illus- stages which are specific to plants. The data come
trated in a simplified form in Fig. 1.6a. This life table is from measurements made on a population living in
appropriate for all species which breed at a discrete sand dune environments in the Netherlands (van der
period in their life cycle, and whose generationsdo not Meijden, 1971). Of the 5040 seeds that are produced,
overlap. If the time between to and t, is 1year, the life 62% fall on to the ground;the other 38% are dispersed
history is referred to as annual. by the wind to other areas. By the same token there is
quite a high chance that immigrants enter this popu-
1.3.3 Ragwort, a biennial lation. This necessitates a further modification of our
life table, indicated in Fig. 1.7 by the inclusion of
An annual life history is only one of a number of invading seeds, which may contribute either to the
possible patterns. If we consider species that live for 2 seed banks or to the incoming seed 'rain'.
years rather then 1, reproducing only in the final year,
then we have a life history that involves breeding at Having arrived on the ground, various potential
one discrete time in the life cycle, but in which fates await ragwort seeds. They lie on the surface of
generations of adults may well overlap; this is illus- the sand in the 'surface seed bank', where they may
trated in Fig. 1.6b. If the time periods are years, then germinate, be eaten or just die. Alternatively,wind or
this life cycle is referred to as 'biennial'. During any insects, acting as migratory agents, may transport
them to neighbouring areas; or they may become

8 PART 1: SINGLE-SPECIES POPULATIONS

Fig. 1.7 Diagrammatic life table of the
biennial ragwort Senecio jacobaea.
(Population sizes are per 4 m2:data
from van der Meijden, 1971.)

buried. The detailed fates of ragwort seeds in sand seeds that rain on to the soil only 40 actually
geminate successfully. However, seedlings can arise
dune environments are not fully known, but only from an additional source: the buried seed bank. We
11.4O/ostay in the surface seed bank; and of the 3124

CHAPTER 1: DESCRIBING POPULATIONS 9

do not know how many seeds are buried in the sand Fig. 1.8 Diagrammatic life table of the perennial great tit
profile, but for many plant species, especially weeds, Parus major. (Population sizes are per hectare; data from
the numbers of buried seeds can be very high (up to c. Perrins, 1965.)
50 000 m-2), and a proportion of each season's seed
crop does become buried. To indicate that this is a nestlings are themselves subject to many dangers, and
birth route we have added to the 'seedling' and by the late summer only 71% of them survive to
'established plant' components a fraction of the buried fledge-leaving the nest and fending for themselves. Of
seed bank, denoted by S. Finally, the transition from these fledglings, only a small proportion live through
seedlings to young, established, photosynthetically the winter to become breeding adults. However, a
independent adults in sand dune environments is also rather larger proportion of the previous generation's
an exceedingly risky phase for ragwort: only 1.7% of adults have also survived. The population of breeding
the seedlings actually become established. adults, therefore, consists of individuals of various
ages, from 1to 5 or more years old. As Fig. 1.8 shows,
The life table in Fig. 1.7, therefore, illustrates the
importance of additional seed sources to the 4 m2
area, since from to to t, the original ragwort density of
1becomes reduced to 0.69. Thus, to keep the number
of young adults at t, up to exactly 1we might argue
that there are 155 seeds in the buried bank which

germinate (since if 0.69 + 0.002s = 1, then S = 155).

Alternatively,some of these 155 might enter the 'birth
process' as immigrants; and if we recall that 38% of
the 5040 seeds were dispersed, we can see that there
are ample numbers to rely upon. To complete this life
table, however, we should note that the chance of a
young adult surviving to become a mature one produc-
ing seed is only 0.25. To ensure that the population
size at t, is still 1, therefore, we will have to imagine a
further input of seeds into the birth process.

Such data as these emphasize the extreme severity
of the sand dune habitat to plant life, and the
considerable mobility of seeds in the life cycle of
ragwort: individual seeds may travel at least 15 m.
Since sand dunes, by their nature, offer shifting and
temporarily suitable habitats for ragwort, we can infer
that seed movement by dispersal on or above the sand
is a very necessary feature in the life of this plant.

1.3.4 More complex life cycles

Overlappinggenerations are not confined to biennials.
Consider the population of great tits (Parus major) near
Oxford studied by Perrins (1965) and illustrated in
Fig. 1.8. Adult birds build their nests and lay eggs in
the early summer, but of these eggs only a proportion
(0.84 in this case) survive to hatch as nestlings. These

10 PART 1: SINGLE-SPECIES POPULATIONS

this situation is readily described by a variant of our Fig. 1.g, the population at any one time consists of
diagrammaticlife table very similar to Fig. 1.4. We are individuals in a range of age classes: a, individuals are
dealing with a population in which breeding occurs at in the youngest age-class, a, individuals in the next
discrete time periods, but in which the individuals are oldest, and so on. With the passage of one unit of time
potentially long lived so that many generations over- a proportion of the individuals in one age group
lap. survive to become individuals in the next oldest age
group. Thus po, is the proportion of the a, individuals
We have assumed with our great tits, however, that surviving to become a, individuals one time unit later,
adults of different ages are equivalent and may be p,,, is the proportion of the a, individuals surviving to
treated as equal members of a common pool. Yet there become a, individuals, and so on (though in practice
will be many instances in which their demographic these p-values will, of course, vary with the changing
characteristics will be 'age-dependent' or 'age- circumstances of the population). Figure 1.9 also
specific'. In such cases, a diagrammaticlife table of the shows that each age group has the potential to
type shown in Fig. 1.9 may be more appropriate. In contribute to the youngest age-class via the birth
process. For simplicity, birth froxii all age groups has
Fig. 1.9 A diagrammaticlife table for any species that been fused together; in reality, fecundity,like survival,
reproduces continuouslywith overlapping genera~onsa, ,, would vary from age-class to age-class. Nevertheless,
despite this increased sophistication,inspection of the
a, - a, represent age groups of individuals, a, being the life table in Fig. 1.9 reveals that it is built up of units
which are little more than the diagrammatic life table
oldest group. pij is an age-specific probability of survival, with which we are already familiar. One such unit is
where, for example, p,, the probability of individuals in a, illustrated in the inset in Fig. 1.9.
at one time surviving to reach a, by the next time period
(06 piid 1).The inset shows a subset of the general life The implication in Fig. 1.9 is that breeding occurs at
table. discrete pehods, even though generations overlap and
there are many age-classes each with their own birth-
and survival-rate, In many species, however, birth
(and death) occur continuously within a population.
Figure 1.9 is still appropriate in such cases, but time
must be split arbitrarily into intervals, and the various
terms take on slightlydifferent meanings. Suppose, for
instance, that we consider the numbers in a popula-
tion at monthly intervals. At to, a, is the total number
of individuals between 2 and 3 months old. One
month later (at t,), p23 of these will survive to become
the a, individuals that are between 3 and 4 months
old. Thus, even though birth and death are occurring
continuously, they are considered 'one month at a
time'.

1.3.5 Age and stage: the problems of describing
some plant and animal popdations

Figure 1.9 illustrates the age-dependent transitions
that may occur in populations with overlapping gen-
erations. As a means of describing flux in populations,

CHAPTER 1: DESCRIBING POPULATIONS 11

this approach is only justifiable if individuals can be In studying the population dynamics of reef coral
classified meaningfully by age alone. For many plant Agaricia agaricites, off the coast of Jamaica, Hughes
species, however, especially those that are perennial, (1984) classified individual coral colonies on the basis
the fate of an individual is not so much dependent on of age-state-'larva' or 'coral colony'-and on the size
its absolute age as on its size or stage. of growth. In of colony. By repeated photography of the reef he was
grasses, for instance, the chance of being grazed may able to record size changes as well as larval recruit-
be crucially size-dependent, and an individual with a ment. A diagrammatic representation of the popula-
few tillers may escape the notice of a herbivore whilst tion structure is shown in Fig. 1.10. Coral colonies
a conspicuous one bearing many tillers may not. may remain static in size, they can grow, they can
Equally important is the fact that the grazed individ- shrink, and they can reproduce sexually by free-
ual, though reduced in size, may not necessarily die, swimming larvae as well as asexually by fission. The
but may generate from basal growing points (buds) to chances of their doing so for each size-class are shown
achieve its former size. Age of the plant under such in this figure, for a year when storms were absent and
circumstances may have little relevance. Size of the conditions ideal for coral growth. This coral species
plant is the more important determinant of its fate. has a mean annual lateral extension rate of less than
Considerationsof this sort have led a number of plant 2 cm. Thus, a large proportion of the population
ecologists, particularly in the Soviet school (Gatsuk remained in the same size-class from one season to the
et al., 1980)to reject age per se in favour of 'age states' next. Moreover, whilst only a small fraction of the
as a useful criterion for describing individuals(Uranov, colonies increased in size, a more likely occurrence
1975; see Silvertown, 1982 for a worked example). was that they should shrink to smaller size-classes, a
Thus, individuals may be classified on an ontogenetic fate moreover that was size-dependent. This shrink-
or developmental basis and categories might include age may represent a series of remorseless steps to-
seed, seedling, juvenile, immature, virginile, repro- wards mortality of the individual, but equally it may
ductive, subsenile and senile states. Such a classifica- also reflect fission of the colony and hence asexual
tion recognizes that there are broad morphological reproduction. Indeed, in the case of size-class 4, it
changes that occur during the growth and develop- must do so since the sum of the fractional transitions
ment of a plant species but that the duration of time exceeds unity.
spent in each may differ widely. Mertz and Boyce
(1956), for instance, have shown that almost 75% of This sort of description, based primarily on size
the oak tree 'seedlings' developing after a forest felling alone, has limitations in so far as it does not readily
were in fact sprouts attached to roots up to 40 years distinguish between survival and fecundity, especially
old. Presumably this 'seedling' population had re- when asexual reproduction is involved. Moreover, in
mained suppressed at an early stage or 'age state' due
to factors such as grazing, trampling and poor condi- the majority of classifications of this type, at least one
tions for growth. additional category, as we have already mentioned,
must be included to complete the life cycle: larvae.
An alternative classification of individuals is by size Hughes recorded 1.5 larvae mP2 settling as new
alone and indeed this can be superimposed upon an recruits during a year in his study. In Agaricia the
age-state classification. Terrestrial plants that can probability of reproducing sexually by larvae is un-
'reiterate' their growth form (see section 1.6) can not known (Connell, 1973),but even if size-specificfecun-
only regress or advance from one age-state to another, dities were meansurable, they might have little value
but within an age-state they may also change in size. in describing the local populations of this coral since
The choice between a strictly size-based and an larvae tend to be very widely dispersed. Using this
age-state classification, or indeed a hybrid between figure for larval recruitment, Hughes was able to
the two, is very much dependent upon the organism calculate by matrix methods (see Chapter 3) that the
under study. population was almost static in size.

A comparable approach describing a plant species is

12 PART l : SINGLE-SPECIES POPULATIONS

Fig. 1.10 A size-based diagrammatic life table for the reef a more faithful representation of the biological events
coral Agaricia agaricites growing in calm seas. (Data from that occur, we must recognize that the generalized
Hughes, 1984.) life-table diagram is inadequate and accept a more
complex flow diagram (Fig. 1.11). In essence this is an
the one used by Sarukhan and Gadgil (1974) for the age-state classification in which the f l u e s are pre-
'creeping buttercup', Ranunculus repens in Britain. cisely defined chronologically. This approach makes
This species reproduces sexually by seed and by an additional important distinction, in that asexually
asexual propagation, though recruitment by these produced 'vegetative' daughters are classified sepa-
means occurs at different times during the season. rately from sexually produced seedlings, at least
Seeds germinate in late spring and early summer, during the first year of life. For the purposes of
whilst in late summer new 'daughter' plants become generality,Sarukhan and Gadgil lumped these recruits
established as separate adult plants from shoots borne together once they attained 1year of age, but there is
at nodes along creeping stolons. If we require a no reason why this distinction could not be main-
description of these events within a season, and hence tained if continued resolution was required.

CHAPTER l: DESCRIBING POPULATIONS 13

Fig. 1.11 The transitions occurring throughout the year in buttercups, bulbs, tillers, polyps of Obeliu, corals)and
a buttercup population (Ranunculus repens) as envisaged by have the potential for growth independent of the
Sarukhan and Gadgil(1974). parent are called ramets; and a population of ramets
with the same ('maternal') parentage constitutes a
In describing populations by diagrmmatic means, clone. A genet, on the other hand, is an organism,
then, we have considered a range of forms of descrip- however much ramified, which has arisen from a single
tion. Some have been based on generation-to- zygote-all parts having the same genotype.
generation changes classifying by age, while others
have been based on size taking for convenience 1.4 Conventional life tables
season-to-season or month-to-month time-steps. In
this latter instance, it is easy to preclude particular 1.4.1 The cohort life table
life-cycle transitions (if the biology of the species
demands this) by setting them to zero. The most reliable method of determining age-specific
mortality and fecundity for a continuously breeding
Additionally, we can impose a genetic subclassifica- population, or simply one in which generations are
tion on our life table. Individuals in a population may overlapping, is to follow the fate of a group of
be known to be genetically distinct. Conversely, 'indi- individuals, all born during the same time interval.
viduals' may actually be asexually produced ramifica- Such a group is called a cohort. The process is
tions of the same genotype. Kays and Harper (1974) essentially a journey from the top left-hand corner of
recognized this dichotomy and introduced the terms Fig. 1.9 to its bottom right-hand corner, and, in many
genet and ramet to avoid confusion. Thus, individuals respects, it is similar to following the fate of an annual
that are produced asexually (e.g. 'daughter' plants of

14 PART l : SINGLE-SPECIES POPULATIONS

species throughout its yearly cycle. The difference in corded and their reproductive output measured. Law
this case is that each individual has to be recognized (1975),for instance, followed the fate of a cohort of the
annual meadow grass, Poa annua, from initial estab-
and distinguished from those individuals belonging to lishment to the ultimate death of the last individual.
other cohorts which are in population at the same Recording the number alive at successive time-periods
time. The situation is described diagrammatically in and the number of offspring (seeds) produced per
Fig. 1.12 in which individualsare represented by solid plant, he was able to compile a table of data showing
lines, ageing with time, and eventually dying (a 'spot' survivorship and fecundity (Table 1.1). The first (left-
in Fig. 1.12).The cohort of four individuals(born at to) hand) column gives the age at the beginning of each
is observed again at t , (when there are two survivors), time interval. Thereafter, only the second and last
at t , (one survivor),and at t, (no survivors). columns (a, and B,) actually contain field data. All
other columns are derived from the a, column. We
Plants are ideal subjects for such study, since they can see that this (conventional) life table contains
are generally sessile and can be tagged or mapped,
enabling the fates of individuals to be precisely re-

Fig. 1.12 A population portrayed as a series of diagonal beginning of t,; only one of these is alive at the beginning of
lines, each line representing the life 'track' of an individual. t,; and none survives to the start of t,. To construct a
As time progresses, each individual ages and eventually 'static' life table, the 'searchlight' is directed onto the whole
dies. Three individuals are born prior to to, four during to, population during a single segment of time (t,). The ages of
and three during t,. To construct a 'fixed' cohort life table, the seven individuals alive at some time during t, may be
taken as an indication of the age-specific survival-rates if
a 'searchlight' is directed into the cohort of individuals born we assume that the rates of birth and survival are constant.
during to and the subsequent development of the cohort is
(After Skellam, 1972.)
monitored. Two of the four individuals have survived to the

CHAPTER l: DESCRIBING POPULATIONS 15

Table 1.1 A cohort life table for Poa annua. (Adapted from Law, 1975.)
- .- .- -
-- - ..P . . LA.- . . .- - - - ,- .-- Avcrag
L
OX,,,^, ,loglll a, numhcr
Number Stnndrtrdized Standardized
o'bsen~rtal live [flgll,a,, of smls pcr
Age at each n t ~ m b rsun"iuing nurnhr dying
quarfer year at #hestart or age hcirvmn \ I ~ R 1I,, , indivirlual
(in 3-month Mortality- age(! v
mods) 8, intenpalX a4nd v + l rate
1, H,
\ 4*

0 R43 1 0 147 0.143 2.926 3.m 0.067 0

1 722 857 232 0.271 2.859 2.933 0.137 300

2 527 625 250 0 . 4 0 2.712 2.796 0.222 620

3 316 375 204 0.544 1.500 2.574 0.342 430

4 144 171 107 0.626 2.158 2.232 0.426 210

5 54 64 46.2 0.722 1.732 1.8M 0.556 M)

h 15 17.8 14.24 0.800 1.176 1.250 0.699 30

7 3 3.56 3.56 1.000 0.477 0.551 -10
R 0
0-

essentially the same information as the diagrammatic The advantage of the dx-values is that they can be
life tables previously described.
summed over a period of time: the number dying in
The a, column summarizes the raw data collected
in the field by mapping the positions of 843 P. annua the first 9 months is do+ d, + d, ( = 625). The disad-
plants that arose from naturally sown seeds in a
number of metre-square quadrats. From this raw data vantage is that the individual values give no real idea
'I,' values are calculated, by converting the numbers of the intensity or importance of mortality at a
observed at the start of each time interval to the
equivalent number that would have occurred had the particular time. This is because the d,-values are
starting density of the cohort been 1000; e.g. larger, the more individuals there are to die. q,-Values,
l, = 316 X l0001843 = 375. The value of this proce- on the other hand, are a good measure of the intensity
dure is that 1,-values can be compared between of mortality. Thus, in the present example, it is clear
populations, or between species, since they do not from the q, column that the mortality-rate rose
depend on the actual number of individuals consid- consistently with increasing age; this is not clear from
ered in each study. In other words an a, value of 843 the d, column. The q,-values, however, have the
is peculiar to this set of observations, whereas all disadvantage of not being liable to summation:
studies have an I, value of 1000.
q, + q, + q, does not give us the overall mortality-rate
To consider mortality more explicitly, the standard-
ized numbers dying in each time interval (d,) must be for the first 9 months. These advantages are com-
computed, being simply the difference between l, and bined, however, in the penultimate column of
I, + ,; e.g. d, = 857 - 625 = 232. q,-the age-specific
mortality-rate-has also been calculated. This relates Table 1.l in which 'k'-values (Haldane, 1949; Varley
d, to l, in proportional terms, so that, for instance,
q,-the proportion of the 6-month-old individualsthat ,& Gradwell, 1970) are listed. k, is defined, simply, as
die in the subsequent 3-month period-is 2501625 or
0.4 q, can also be thought of as the 'chance of death', log,, a, - log,, a, + (or, equivalently, log,, a,la, + ,),
and is equivalent to (1-p,) where 'p' refers to the and is sometimes referred to as 'killing-power'. Like q,
survival-probabilityconsidered previously. k-values reflect the intensity or rate of mortality, and,
in the present case, they increase consistently with
age. But, unlike q, summing the k-values is a mean-
ingful procedure. Thus the killing-power or k-value of

the first 9 months is 0.067 + 0.137 + 0.222 = 0.426,

which is also the value of log,, a,-log,, a,, Note,

furthermore, that the k,-values can be computed from
the 1,-values as well as the a,-values; and that, like l,,

16 PART l : SINGLE-SPECIES POPULATIONS

Fig. 1.13 Age-specificfecundity (B,.) for the annual meadow indicates quite clearly an initial sharp rise in fecundity
grass Poa annua. (Data from Law, 1975.) reaching a peak at 6 months, followed by a gradual
decline until the death of the last individual after 2
k, is standardized and is, therefore, appropriate for years. Figure 1.14 illustrates a single pattern in three
comparing quite separate studies. k-values will be of different ways. Figure 1.14a is 'survivorship curve'-
considerable use to us in later chapters. log,, l, plotted against age-while Fig. 1.14b contains
two mortality curves, q, and k,, plotted against age.
The age-specific patterns of fecundityand mortality All show a consistent rise in the rate of mortality,
have been plotted in Figs 1.13 and 1.14. Figure 1.13 leading to an increasingly rapid decline in survivor-
ship. Of the three, Fig. l.14a-the survivorship
curve-probably shows this most clearly.

The use of logarithms in the survivorship curve
deserves further comment. consider: for instance, the
halving of a population over l"unit of time, in one case
from 100 to 50 individuals, and in another case from
10 to five individuals. In both cases there has been a
reduction by half, i.e. the rate or probability of death
per individual (usually referred to as the 'per capita
rate') is the same. Nevertheless. the s l o ~ eof an
arithmetic survivorship curve would be - 50 in the
first case but - 5 in the second. With logarithmic
survivorshipcurves, however, the slopes in these two,
equivalent cases are identical. In fact, equivalent
advantages are gained by the use of k,-values: being
based on logarithms, they, too, allow recognition of
cases in which per capita rates of mortality are the
same. Moreover, logarithms also indicate when per

Fig. 1.14 (a)Age-specific
survivorship(log,, I,), and (b)age-
specific mortality-rates (g,) and

killing-powers (k,) for the annual

meadow grass Poa annua. (Data
from Law, 1975.)

CHAPTER 1: DESCRIBING POPULATIONS 17

capita rates of increase are identical. 'Log numbers' column two of Table 1.2. As expected, there were
should therefore be used in preference to 'numbers'
when numerical change is being plotted. many young deer and rather fewer old deer,but we can
treat these raw data as the basis for a life table only if
1.4.2 The static life table we make a certainset of assumptions.We must assume
that the 59 6-year-old deer alive in 1957 were the
Unfortunately,it is not always possible to monitor the survivors of 78 5-year-old deer alive in 1956, which
dynamics of a population by constructing a 'fixed were themselves the survivors of 81 4-year-olds in
cohort' life table. It is, in fact, rarely possible with 1955,and so on. In other words, we must assume that
natural populations of animals, since the individuals the numbers of births and age-specific survival-rates
are often highly mobile, highly cryptic or both. There had remained the same from year to year, or, equiva-
is, however, a rather imperfect alternative, which is lently, that the a, column of Table 1.2 is essentially the
also illustrated diagrammatically in Fig, 1.12. It in- same as would have been obtained if we had followed a
volves examining the age-structureof the whole popu- singlecohort. Having made this assumption,l,, d, and
lation at one particular time, or, since these things q, columns have been constructed. It is clear from
cannot be done instantaneously, during one short Table 1.2, however, that our assumption is false. The
'segment' of time. 'cohort' actually increases in size from years 6 to 7 and
14to 15,leading to 'negative' deaths and meaningless
As an example, we can consider the results, re- mortality-rates.The pitfalls of constructingsuch 'static'
ported by Lowe (1969), of an extensive study of the red life tables are, therefore, amply illustrated.
deer (Cewus elaphus) on the small island of Rhum,
Scotland. Each year from 1957 onwards,Lowe and his Nevertheless, such data are by no means valueless.
co-workers examined every one of the deer that was Lowe's aim was to provide a general idea of the
shot under the rigorously controlled conditions of population's age-specific survival-rate (and birth-rate)
this nature reserve. They also made extensive prior to 1957 (when culling of the population began),
searches for the carcasses of deer that had died from and then to compare this with the situation after
natural causes. Thus, they had access to a large 1957. He was more concerned with general trends
proportion of the deer that died from 1957 onwards, than with the particular changes occurring from one
Deer can be reliably aged by the examination of tooth year to the next. He therefore 'smoothed out' the
replacement, eruption and wear, and Lowe and his variations in population size between the ages of 2-8
co-workers carried out such examinations on all of and 10-16, and created a steady decline in both of
the dead deer. If, for instance, they examined a these periods. The results of this process are shown in
6-year-old deer in 1961, they were able to conclude the final five columns of Table 1.2, and the mortality
that, in 1957, this deer was alive and 2 years old. schedules are plotted in Fig. 1.l5. They do, indeed,
Thus, by examining carcasses, they were able to provide the general picture Lowe required: there is a
reconstruct the age-stmcture of the 1957 population. fairly gentle but increasing decline in survivorship up
(Their results did not represent the total numbers to year 8, followed by 2 years of very heavy mortality,
alive, because some carcasses must have decomposed and then a return to a gentler, though again increas-
before they could be discovered and examined.) Of ing, decline.
course, the age-structure of the 1957 population
could have been ascertained by shooting and examin- Moreover, by examining the internal reproductive
ing large numbers of deer in 1957; but, since the organs of the hinds, Lowe was also able to derive a
ultimate aim of the project was enlightened conserva- sequence of age-specific birth-rates. This is shown in
tion of the deer, this method would have been the sixth column of Table 1.2, and iIlustrated in
somewhat inappropriate. Fig. 1.16. There is, clearly, an initial pre-reproductive
period of 2 years, followed by a sudden increase in
Lowe's raw data for red deer hinds are presented in birth-rate which is maintained for 3 years. There is
then a period of 4 years during which the birth-rate is

18 PART 1: SINGLE-SPECIES POPULATIONS

Table 1.2 A static life table for red deer. (FromLowe, 1969.)
- - --
-. . ..

F vy (4 q, H, Smoothed 4, log,, 4 k,
1, if,
()cam) 0.137 3.000 0.064
13.097 2.936 0.045
1 129 lflOO 116 0.116 0 lOOa 137 0.108 2.891 0.050
2 863 85 0.121 2.841 0.056
3 114 884 8 0.009 0 84 0.137 2.785 0.064
778 84 0.159 0.076
4 1 1 3 676 48 0.05i 0.311 0.190 2.721 0.092
23 694 84 0.502 2,645 0.295
5 R1 625 0.037 0.278 610 0.672 0.487
84 0.141 2.553 O.Oh3
6 78 M15 148 0.245 0.302 526 0.165 2.258 0.085
59 457 - 47 442 85 0.198 1.773 0.092
7 0.m 357 176 0.247 1.708 0.133
6'1 504 78 0.155 0,476 0.329 1,623 0.168
8 181 122 0.492 1.531
55 426 232 0.545 0.358 59 1.m 1.398 0-.276
9 8 1.230
10 25 194 124 0.639 0.447 51 0.954
11 42 9
12 9 7 0 8 0.114 0,289 X
13 8 h2 R 0.129 0.283 34
14 25 9
7 54 38 0.704 0.285
15 2 17 8
16 1 16 - 8 0.5110 0.283 9
23 0.282 8
8 - 9

4 31 1 5 0.484 0.285

I 16 - - 0.284

higher still, followed by a return to the previous level. 1.4.3 Resume
It is interesting to note that the period of high
birth-rates is immediatelyfollowed by a period of high Conventiond (as opposed to diagrmatic) life tables
mortality-rates,an apparent 'cost of reproduction'. are the medium through which age-specific schedules

Fig. 1.15 (a)Age-specific
survivorship(log,, l,), and (b) age-
specific mortality-rates (qx)and
killing-powers(k,) for the red deer,
Cervus elaphus. (Data from Lowe,
1969.)

CHAPTER 1: DESCRIBING POPULATIONS 19

of death (and birth) can be constructed, and it is It should also be stressed that in either case it is
often necessary to collect life-table data over a period
obvious that the compilation of such i~lformationis of time for a number of generations. This allows the
vital if the dynamics of populations are to be under- natural variability in the rates of birth and survival to
stood. These life tables can be of two quite separate be monitored and assessed.
types (see Fig. 1.12).
1.5 Some generalizations
The fixed cohort (or 'dynamic', or 'horizontal') life
table is derived by actually following a cohort of One of the reasons for using life tables to monitor these
individuals from birth to extinction. It provides reliable age-specific rates is that this allows us to discover
information on that cohort; but its construction may patterns of birth and mortality which are repeated in a
variety of species in a variety of circumstances. In
be beset by practical difficulties,which in certain cases turn, this allows us, hopefully, to uncover the com-
will be insuperable. mon properties shared by these various populations,
leading ultimately to a deeper understanding of popu-
The static (or 'time-specific', or 'vertical') life table, lation dynamics in general. Age-specificmortality-rates
conversely, is derived by estimating the age structure were classified by Pear1(1928),and his classificationis
of a population at one point in time. It is equivalent to illustrated in Fig. 1.17 in the form of survivorship
curves. It is very difficultto generalizeabout the shape
a fixed cohort life table only when the survival-ratesin of survivorship curves, not least because they are a
the population are constant. Otherwise the static life reflection of the particular habitat conditionsin which
the population was observed, and the actual densities
table compounds and confuses two quite separate of populations. Figure 1.18 illustrates the range of
things: the age-specific changes in birth- and curves for a sand dune annual plant in natural
mortality-rate,and the year-to-year variations in these populations in similar habitat varying in density and
rates in the past. Nevertheless, it can provide a general
idea of age-specific birth- and mortality-rates in a
population,which is particularly valuablewhen a fixed
cohort life table cannot be derived.

Fig. 1.16 Age-specific fecundity for the red deer Cervus Fig. 1.17 Hypothetical standard survivorship curves, (After
elaphus. (Data from Lowe, 1969.) Pearl, 1928.) For further discussion, see text.

20 PART l : SINGLE-SPECIES POPULATIONS

Fig. 1.18 Survivorshipcurves in
natural populations of Erophila verna
occurring at differing densities
( X 103m-2) (a) 1-2; (b) 5-10; (c) 15-

10; (d) 35-50; and (e) >50. (After
Symonides, 1983.)

we can see that a spectrum of curves may occur. annua, see Fig. 1.13), or to a plateau (the deer in
However, Pearl argued that we can recognize three Fig. 1.19) or tend to increase with age in trees as size
broad types. The first-epitomized perhaps, by hu- increases (Fig. 1.20). As Fig. 1.16 shows, however,
mans in the developed world or cosseted animals in a many species combine elements of the two in a more
zoo-describes the situation in which mortality is complex pattern.
concentrated at the end of the maximum life span. In
the second, the probability of death remains constant Fig, 1.19 Age-specific fecundity for white-tailed deer
with age, leading to a linear decline in survivorship. Odocoileus hemionus in Michigan. (Data from Eberhardt,
This typically occurs in the buried seed populations of 1960.)
plants. In the third type there is extensive early
mortality, but those that remain have a high rate of
survival subsequently. This is true, for instance, of
many marine fish which produce millions of eggs of
which very few survive to become adults.

The difficultywith Pearl's generalizationsis that as a
cohort ages it may well follow, successively,more than
one type of survivorship curve. It is now known, for
instance, that for many grassland plants the survivor-
ship curve of seedlings establishing into adults is type
3 , whereas that of the adults themselves is type 2.

Generalizations regarding age-specific birth-rates
are, in many ways, more straightforward. The most
basic distinction, perhaps, is between species which
are semelparous, reproducing only once, and those
which are iteroparous, reproducing many times. In the
botanical literature, these terns are referred to as
monocarpic and polycarpic, respectively. In either case
there is likefy to be a pre-reproductive period, which can,
of course, vary in length (cf. Figs 1.16 & 1.19). Age-
specific fecundity may then rise, either to a peak (P,

CHAPTER 1: DESCRIBING POPULATIONS 21

Fig. 1.20 Age-dependent seed production in the tree palm 1979; Harper, 1981).Most animals are unitary organ-
Astrocaryurn mexicanurn. (After Sarukhan, 1980.) isms. Development from the zygote (the fertilized egg)
through to the adult involves an irreversibleprocess of
Finally, certain restricted generalizations can be growth and tissue differentiation leading to organ
made regarding population size itself. It is indisputable development according to a highly regulated schedule.
that all populations vary in size: temporal fluctuations Conversely, most plants are modular. Growth and
are the universal rule, But at the same time it is differentiation are normally initiated in 'meristems' at
equally true that these fluctuations are usually limited the apices of shoots and roots (Esau, 1953). Cell
in amplitude. Populations rarely increase in size so divisions occur in these meristems, and they result in
much that they utterly overrun their environment; root and shoot elongation and the laying down of
and even localized extinctions, though by no means further meristems,Growth frommeristems in this way
unknown, are also comparatively rare. Thus, popula- unaccompanied by any further differentiationleads to
tion size, and the processes affecting it, are variable- a repetitive or reiterative modular structure in the
but of limited variability. One of the major aims in the plant body (see Gottleib, 1984 for a succinct discus-
study of population dynamics is to understand these sion). Botanically, a 'module' is an axis (essentially a
limitations,and this is the topic to which we shall turn length of tissue) with an 'apical meristem' at its distal
in the next chapter. Before doing so we must first end. The axis is subdivided by nodes at which leaves,
consider the implications of the ways in which some axillary meristems and vegetative outgrowths (e.g.
plants and animals grow for our means of describing tendrils) may occur. If and when the apical meristem
populations. differentiates into a terminal flower, extension growth
of the axis ceases.
1.6 The modular growth of organisms
Modular organisms increase in size by a programme
Having concentratedon what different types of species of growth and development that is structurally and
population may have in common, we now turn to one functionally repetitive; unitary organisms by contrast
crucial respect in which they may differ. A major do not. The distinction, however, is not simply one
distinction amongst species of both plants and animals between animals and plants. In colonial animals such
lies in the organization and differentiation of tissues. as corals, hydroids, bryozoans and colonial ascidians
This fundamental distinction divides organisms ac- similar modular identities can be seen (Rosen, 1979).
cording to their growth form into those that are We saw in section 1.3.5 that both corals and butter-
unitary and those that are modular (Harper & Bell, cups increased in size through the addition of succes-
sive segments or modular units. Thus, put simply, the
buttercup becomes larger as additional stolons and
ramets are produced while the coral becomes larger as
polyps grow and bud. Each increment in growth can
be measured by the number of modules produced in a
period of time. This feature has proved invaluable to
plant demographers in the construction of static life
tables; since in some species at: least, the age of an
individual plant may be deduced from persisting
morphoIogical or anatomical features. The method
has been used in investigating survivorship in the
Mexican tree palm (Astrocaryum mexicanum) and also
in examining clonal growth in rhizomatous species.
Polygonatum verticilatum is a herb of Scandinavianand
Danish forests which annually produces an above-

22 PART 1: SINGLE-SPECIES POPULATIONS

number of rhizome segments
accumulated
0 number of rhizome segments

I- formed per year
number of above ground
shoots per year

Branch Scar of
Segment above ground

9Renewal segment

+Terminal buds

branch branch segment
buds segment

Fig. 1.21 (a)The morphology of the rhizomatous perennial Three important demographic consequences arise
Polygonaturn verticilatum.(b)Exponential growth of rhizome from recognizing the modular construction of higher
segments in a clone of P. verticilatum.(After Tybjerg & terrestrial plants and colonial animals. The first is that
Vestergaard, 1992.) the addition of modules tends to lead to a branched
structural form. Generally, this is because of the
ground shoot that dies in the autumn leaving a distinct placement of meristems in plants at acute angles to
below-ground scar on the rhizome. The growth form the main axis, which continue growth when extension
enabled Tybjerg and Vestergaard (1992) to be able to of the parental axis ceases. The exact architecture of
age an excavated rhizome system (Fig. 1.21a) retro- the organism will depend on: (i)whether modules vary
spectively over a 20-year period. Careful mapping in form, as in the short and long branches of trees or
indicated that direction of growth was centrifugal the vegetative and generative(i.e. reproductive)polyps
from the initial (seedling) starting point and the of hydroids; (ii) their rate of production; and (iii) their
cumulative number of rhizome segments increased position relative to one another. Nevertheless, the
exponentially (Fig. l.2lb). This arose because the overall form of the organism is a colony of repeating
rhizomes bifurcated in a systematic manner with the modules. The form is important demographically
number of new branches increasing gradually as the since size and shape will influence the nature of
plant aged. interactions amongst static organisms (Horn, 1971).

CHAPTER 1: DESCRIBING POPULATIONS 23
Developing'shoot' group

Direction of growth "Ul Direction of growth

\ Meristem Module 'type 2'

Fig. 1.22 A schematic view of modular growth in a plant generating either 'type l' or 'type 2' modules. Module 'type
that displays two types of module in its constructional 2' is a horizontal stem (rhizome or stolon) bearing a
organization. Natural cloning results from the meristem with the potential to give rise to a 'type 1'
fragmentation of either type of module. Module 'type 1' is a module, axillary meristems and roots. (After Harper & Bell,
'shoot' bearing foliage leaves and one meristem capable of 1979.)

Fig. 1.23 (a) Bulb division and sequential

development of daughter ramets in Alfium

tricoccum. (After Nault & Gagnon, 1993.)
(b) Rhizomatous growth in Carex bigeluwii. (After

Jonsdottir & Callaghan, 1988.)

24 PART 1: SINGLE-SPECIES POPULATIONS

Whether an individual creeping plant, for instance, population biology (equation 1.1 above) applies not
presents a compact as opposed to diffuse arrangement only at the level of the genet (expressed through the
of shoots may have important consequences in com- growth of the clone a whole) but also at the (lower)
petitive interactions with neighbours as will the modular level (Harper, 1977). Harper and Be11 (1979)
branching structure influence interactions amongst argue then that the study of the dynamics of modules
the crowns of trees. themselvesis an essential component in describing the
population ecology of modular organisms and can be
Second, removal of modules (through damage, applied down to the level of individual leaves (Harper,
herbivory or predation for instance) may harm an 1989).Demographic approachesto modular dynamics
organism but not kill it. A modular architectural have employed the same techniques that we have
arrangement of relatively autonomous meristems al- examined earlier for populations of unitary organisms.
lows lost parts to be reiterated, The potential for this Thus, Fig. 1.24 shows a diagrammatic life table for a
very much depends upon the degree of permanent population of meristems on a Fuchsia plant. As the
physiological and morphological differentiation that plant grows, some meristems develop into shoots
has already occurred. Removal of vegetative tillers which may be vegetative (branches bearing new
from a grass plant will often lead to the reiteration of meristems) or generative (branches bearing inflores-
the tiller module; removal of an inflorescence (a
module that has differentiated into a sexually genera- Fig. 1.24 Transitions occurring over a time period amongst
tive structure) may not-often because of the absence meristems in Royal Velvet, a cultivar of Fuchsia.
of further growth points. Conversely,in unitary organ- Measurements were made 75 days after plmting on the
isms although tissue regeneration does occur, removal main shoot when plants were growing exponentially.At
of a whole organ will precipitate death. this stage of growth a constant fraction of vegetative
meristerns become vegetative branches which in turn
A third consequence arises from the fact that produce one vegetative and one flower meristem.(Data
modularity affords the opportunity of natural cloning from Porter, 1983a.)
(Harper, 1985). Natural cloning arises when a genet
fragments and the ramets establish into physiologi-
cally independent parts (Fig. 1.22). This is only poss-
ible when rneristems at nodes retain totipotency: the
ability to produce both shoots and roots. Fragmenta-
tion may arise through physical agencies (e.g. sand
movement in the sand sedge Carex arenaria), the
trampling and grazing of herbivores (in rhizomatous
grasses), or it may be genetically determined (as in
Ranunculus repens; Bell & Tomlinson, 1980). The
important demographic point is that whatever the
agency, it may lead to a colony of physiologically
independent plants of the same genotype which are
potential competitors. The extent to which the ramets
of a clone constitute truly independent individuals
when they retain apparent physical connections re-
quires careful scrutiny. In some cases the true disjunc-
tion of individualsis an agelsize-dependent process (as
in Allium tricoccum; Fig. 1.23a), but is more problem-
atic in perennial grasses (Fig. 1.23b).

These observations on modularity have prompted
the suggestion that the fundamental equation of

CHAPTER 1: DESCRIBING POPULATIONS 25

Fig. 1.25 Flux in tillers in Phleum pratense: (a) the total fate of grass tillers on individual timothy plants
number of living tillers; (b) survivorship curves of successive (Phleum pratense) over a period of 2 years. His data
monthly cohorts of tillers; (c) tiller age structure at (Fig. 1.25)illustrate that tiller births and deaths are an
successive monthly periods (each ordinate division is 1Wo). intrinsic feature of the life of an individual plant.
Data were gathered from 40 plants each grown from seed Whilst the size of cohorts recruited each month was
in soil in separate 20-cm diameter pots. (From Langer, seasonally dependent, the pattern of mortality in
1956; after White, 1980.) cohorts was remarkably similar, following a type 1
survivorship curve. This mortality mainly resulted
cences), some meristems remain dormant, whilst from the 'monocarpic' nature of tillers (the production
othes abort. The transitions given in Fig. 1.24 are of an inflorescence on a tiller is followed inevitably by
those occurring during growth in an unrestricted tiller death) but also occurred amongst non-generative
environment once plants have started flowering. tillers when recruitment of tillers was at its highest in
Death of meristems, whether vegetative or flowering, JuneIJuly.Tillers formed in April and May were either
is absent and only occurs when flowers (the products annual (flowering in the following August and Sep-
of generative meristems) senesce. tember) or biennial, remaining vegetative over winter
and flowering the next year. This resulted in the
Flux in modules, however, can be much more stepped survivorship curves seen in Fig. 1.25.
noticeable in other species. Langer (1956)followed the

26 PART l : SINGLE-SPECIES POPULATIONS

Fig. 1.26 The interrelationships between states of seed large fraction of the total population may be present as
dormancy in a buried seed population. Arrows indicate dormant individuals within the soil profile, such that
direction of transition according to definitions of dormancy the number of live plants above ground gives a very
state (see text for details). (After Sagar & Mortimer, 1976.) poor reflection of the true population size.

In conclusion, it is clear that in describing a Thompson and Grime (1979)distinguished between
population we must carefully define the individual. two classes of species possessing buried seed banks:
This in part will depend on the nature of the scientific those with seeds that have limited longevity, specifi-
enquiry, but more often than not it will be determined cally no longer than a year following dispersal and
by the growth form of the organism. often no longer than the species generation time-
transient banks; and those in which a proportion of
1.7 Buried seed banks seeds survives in a dormant state for more than one
generation time-persistent banks. Seed survival for
Although we have referred in passing to the existence long periods in the soil is controlled by three types of
of buried seed banks (see section 1.5),it is important to dormancy mechanism (Harper, 1977). Enforced dor-
recognize that populations of both terrestrial and mancy arises where there is the absence of at least one
aquatic plants may differ from animal populations in exogenous factor. Thus insufficient water availability
this additional respect. In many plant species, a very or burial at depth away from light prohibits germina-
tion which occurs on removal of the limiting factor(s).
Conversely, innate dormancy is an endogenous physio-
logical or morphological condition possessed by a seed
at the time of dispersal from the mother plant and
which is broken by a subsequent appropriate cue-for
instance passage through the gut of an animal or
experience of a temperature shift. Finally induced
dormancy is a responsive form of dormancy that arises
as a consequence of an environmental stimulus.
Release from this form of dormancy arises on receipt
of a further stimulus which may well be of a seasonal
nature (Roberts, 1972). Thus dormancy induced by
low soil temperatures in autumn that herald winter
may be broken by elevated temperatures in spring.
The dormancy structure of a buried seed population
may be classified in this tripartite manner as illus-

Fig. 1.27 Seasonal changes in
induced seed dormancy in two
annuals; (a)Arabidopsis thaliana, and
(b)Ambrosia artemisifolia. Buried
seeds were retrieved each month

and germinated at their respective

optimum temperature. (After Baskin

& Baskin, 1980, 1983.)

CHAPTER l : DESCRIBING POPULATIONS 27

Year trated in Fig. 1.26 and it is possible with the appropri-

Fig. 1.28 The decrease in the number of viable dormant ate techniques to estimate the proportion in each
seeds (a four species mixture) buried in soil, disturbed at category (Baskin & Baskin, 1980).Repeated sampling
diiering frequencies throughout the year. Note numbers has shown that annual cycles in dormancy status
are presented on a logarithmic scale. 0,undisturbed soil; occur in viable seed populations (Fig. 1.27)and if there
0,soil cultivated twice a year; 0,soil cultivated four times is loss by gemination and no recruitment of newly
a year; H, soil cultivated under a cropping rotation. (After dispersed seed, then the seed bank declines. Meticu-
Roberts & Dawkins, 1967.) lous studies have shown that the rate of this loss tends
to be constant (Fig. 1.28)for a particular habitat when
viewed on an annual basis although losses may be
concentrated at particular seasons of the year. In some
temperate plants the longevity of buried seed may be
considerable-in poppies for instance in excess of 80
years. In contrast, in many tropical species it is often
restricted to 15-20 months (Garwood, 1989).

Chapter 2

2.1 The nature of intraspecific and the fewer eggs she will lay per unit of time.
competition Moreover, along with this increased expenditure of
time will go an increased expenditure of energy. This
In order to examine further the way in which the will lead to a decrease in the energy available for egg
properties of individuals determine population dy- development, and also a decrease in general viability,
namics, we will have to consider a proposition which leading to a possible shortening of total life span.
we have not mentioned explicitly so far, but which is These, in their turn, will lead to a decrease in the
generally taken for granted: that each individual number of eggs laid; and the more competing females
within a population affects, and is affected by, other there are, the greater this decrease will be.
individuals within the population. Consider, for in-
stance, a thriving population of grasshoppers (allof the Of course, in order to live, grasshoppers (male and
same species) in a field of grass. Adult males attract female) must consume food (grass) to provide them-
and court adult females by 'stridulating': they rub the selves with energy, but they must also expend energy
insides of their hind legs against the outsides of their in the process of finding and consumingthe food. Each
hardened forewings to produce a species-specific grasshopper will frequently find itself at some spot
'song'. If a male manages to attract, court and where there had previously been a palatable blade of
inseminate a female, he will have made some contri- grass-before that is, some other grasshopper ate it.
bution to the next generation; and the more females Whenever this happens the first grasshopper must
he manages to inseminate, the greater this contribu- move on; it must expend more energy than it would
tion will be. The most successful or fittest males within otherwise have done before it takes in food. Once
a population are those which make the greatest again, this increased energy expenditure will lead on
contribution. A solitary male amongst many females the one hand through increased mortality and on the
in the population might eventually inseminate every other hand through decreased rates of development,
one of them. But if there are several males in the to a decreased contribution to the next generation. So
population, then they will be competing with one the more competitors there are, the more 'moving on'
another for the females' attentions, and each will each grasshopper will have to do, and the greater the
inseminate fewer females than he would have done decrease in contribution will be.
had he been alone. The more males there are, the
more intense this intraspecific competition will be; Considering the same hypothetical ecosystem, we
and the general effect will be to reduce the males' can turn now to the grass itself. (We will assume, for
contributions to the next generation. simplicity, that it is all of one species, although in
practice this is very unlikely to be so.) The contribu-
Subsequently, the inseminated grasshoppers will tion of an individual grass plant to the next generation
have eggs to lay. For this they require bare soil, which will be dependent on the number of its progeny which
may, in a grassy field, be quite rare. More to the point, eventually develop into reproductive adults them-
they require bare soil not already occupied by another selves. An isolated seedling in fertile soil will have a
female. They can increase their contribution to the very good chance of developing to reproductive matu-
next generation by increasing the number of eggs they rity, and will also be likely to reproduce vegetatively,
lay. But the more competing females there are, the consisting (as a result) of multiple copies of the
longer it will take each one to find an appropriate site, simplest plant form. However, a seedling which is
closely surrounded by neighbours (shading it with

CHAPTER 2: INTRASPECIFIC COMPETITION 29

their leaves and depleting its soil with their roots) will other resources we have discussed so far. They are
be very unlikely to survive at all, and will almost only competed for if they are in limited supply.
certainly be small and simple. The more competing
individuals there are, the more likely it is that seed- The third feature of intraspecific competition is
lings will find themselves in the latter, rather than the reciprocity. In other words the competing individuals
former, situation. Increases in density will, therefore, within a population are all essentially equivalent (in
lead to decreases in the contributionsof individuals to contrast to the situationof a predator eating its prey, in
the next generation. which the predator is inherently the inflictor of the
adverse effect and the prey inherently the receiver). Of
2.2 Three characteristicsof course, in any particular case intraspecificcompetition
intraspecific competition may be relatively one-sided: the strong early seedling
shading the stunted late one; the 'resident' egg-laying
Certain common features of intraspecific competition grasshopper causing the later arrival to move on.
have obviously emerged. The first of these is that the However, despite this, because the earlyllate or
ultimate effect of competition is a decreased contribu- residentlnon-resident roles might easily be reversed,
tion of individuals to the next (or, in fact, to all future) the competing individuals are inherently equivalent.
generations; a decrease, that is, from the potential
contributionthat the individual would have made had 2.3 Density-dependence:
there been no competitors. a fourth characteristic

In some cases-stridulating males competing for The fourth and final feature of intraspecific competi-
females, for instance-the connection between com- tion is that the effect of competition on any individual
petition and contributions to future generations is (i.e. the probability of an individual being adversely
obvious and direct. With grass seedlings competing for affected) is greater, the greater the number of com-
growth resources, however, or with grasshoppers petitors there are. The effects of intraspecific competi-
competing for food, the connection is slightly less tion are, therefore, said to be density-dependent. Not
direct, since competition leads to a decrease in survi- surprisingly, they can be contrasted with density-
vorship and/or fecundity. Nevertheless, in terms of independent effects, yet the point of contrast is very
ultimate effects, male grasshoppers competing for often confused. This can be avoided by reference to
females, seedlings competing for light and grasshop- Fig. 2.1 (after Solomon, 1969).In Fig. 2.la the number
pers competing for food are all essentially equivalent. of deaths is dependent on density (and, indeed,
Intraspecific competition acts more or less directly on increases with density)in each of the four lines, but of
either survivorship or fecundity, or on both, but in all these four, only three show density-dependenteffects.
cases it decreases contributionsto future generations. In the fourth, the proportion of the population dying (or
the probability of an individual dying) remains con-
From a practical point of view, however, this is not stant, even though the number dying increases with
quite enough. Competition must not only be likely; it density: the rate of mortality is density-independent.
must also manifest itself in measurable decreases in Figure 2.lb, which portrays precisely the same situa-
survivorship, fecundity or some other, less direct tion as Fig. 2.la, makes this abundantly clear. Of
characteristic. Only then have we the right to con- course, in reality, the points leading to the density-
clude that it is occurring. independent plots will not all lie exactly on the straight
lines. They may, in fact, be very widely spread on
The second common feature of intraspecificcompe- either side of them. However,this would not alter their
tition is that the resource for which the individualsare essential feature: with density-independentmortality,
competing must be in limited supply. Oxygen, for there is no tendency for the mortality-rate to increase
instance, although absolutely essential, is not some- with increasing density. The analogous situation for
thing for which grasshoppers or grass plants need
compete. Nor necessarily is space, food or any of the

30 PART l : SINGLE-SPECIES POPULATIONS

Fig. 2.1 Density-dependent and density-independentdeath make this quite clear. Nevertheless, all density-
(a)and (b), and birth (c) and (d). The vertical axes in (a)and dependent effects do share a tendency to regulate
(c)are numbers; those in (b) and (d)are rates. (After population size.
Solomon, 1969.)
We have already suggested (in Chapter 1)that such
fecundity is illustrated in Figs 2.lc and 2.ld. regulation is extremely widespread, and the subject
Intraspecific competition and density-dependence will be examined in greater depth in Chapter 6; but
three pertinent comments can be made now. First,
are obviously bound closely together; whenever there 'regulation' refers to the ability to decrease the size of
is intraspecific competition, its effects-whether on populations which are above a particular level, but to
survival, fecundity or a combination of the two-is allow an increase in the size of populations below that
density-dependent. However, not all density- level. This particular population level will, therefore,
dependent effects are the result of intraspecific com- be a point of equilibrium. Populations below it in-
petition. Chapter 4 on interspecific competition, and crease, populations above it decrease,and populations
Chapter 5 on predation, parasitism and herbivory will actually on it neither increase nor decrease: popula-

CHAPTER 2: INTRASPECIFIC COMPETITION 31

Fig. 2.2 Population regulation with (a)density-independent competition), invoked by various density-dependent
birth and density-dependent death, (b) density-dependent factors: food, space and so on. It should be remem-
birth and density-independentdeath, and (c)density- bered, however, that the effects of intraspecific com-
dependent birth and density-dependentdeath. Population petition can easily be discussed without specifying the
size increases when birth-rate exceeds death-rate below the factor involved; and these effects-on either mortality
carrying capacity,K; and decreases when death-rateexceeds or fecundity-can even be measured. Yet if, ulti-
birth-rate above K. K is, therefore, a stable equilibrium. mately, we are to understand the dynamics of a
population, we must identify the density-dependent
tion size is subject to negative feedback (Fig. 2.2). In factor itself.
the case of the effects of intraspecificcompetition, this
equilibrium level is often called the 'carrying-capacity' 2.4 Scramble and contest
of the population. In reality, however, no single
carrying-capacity can ever characterize a natural The density-dependent effects of intraspecific compe-
population: most aspects of its environmentare far too tition are of central importance in the dynamics of
variable, and its own behaviour is never wholly natural populations, but so far they have only been
predictable. For this reason 'regulation' may, more outlined. We have still to describe the precise effects
reasonably, be taken as the ability to act on a very that intraspecific competition can have on the quan-
wide range of starting densities, and bring them to a tity and quality of individuals within a population. Of
much narrower range of final densities. course, competitive interactions do not all conform to
precisely the same pattern. On the contrary, there is a
Second, the word 'tendency' is used advisedly. If a whole spectrum of interactions, varying in their un-
density-dependent effect is not operative at all densi- derlying biological causes, and in their effects on the
ties, or is not operative under all environmental quantity and quality of individuals; but in order to
conditions, is weak, or happens after a time delay, appreciatethis variety, it will be useful to have certain
then the effect-although density-dependent-may standards against which actual examples can be
not actually regulate population size. Similarly,if there matched. The most appropriate standards are the
are several density-dependent factors acting on a extreme forms of competition described by Nicholson
population, then each factor alone may be incapable (1954b): 'scramble' and 'contest'.
of regulating the population, even though each tends
to do so. The essential features of scramble and contest are
illustrated in Figs 2.3 and 2.4 respectively (adapted
Third, all density-dependent effectsare the result of from Varley et al., 1975).It is particularly important to
a density-dependent factor acting through a density- note that Figs 2.3b and 2.4b make use of the 'k-values'
dependent process. Until now only one density-
dependent process has been considered (intraspecific

32 PART l : SINGLE-SPECIES POPULATIONS

Fig. 2.3 Scramble competition. Mortality relationships (a) in the exact compensation of contest competition.
terms of numbers surviving and percentage mortality, and Scramble and contest can also be seen in terms of
(b) in terms of k plotted against the logarithm of density.
fecundity. Below the threshold there is no competi-
described in Chapter l. In both cases there is no tion, and all individuals produce the maximum num-
competition at all at low densities: all individuals have ber of offspring. Above the threshold, scramble leads
as much resources as they need, and all individuals to the production of no offspring whatsoever; while
need and get the same amount (010mortality = 0; A = B; contest leads to T individuals producing the maximum
k =log,, BIA = 0). Above a threshold density of T number of offspring and the rest producing none at
individuals, however, the situation changes. In scram- all.
ble competition(Fig. 2.3), all the individualsstill get an
equal share, but this is now less than they need, and Our 'standards' of competition have now been
as a consequence they all die. The slope, b, of Fig. 2.3b defined. In terms of the quantity of individuals,
therefore changes suddenly from zero to infinity as the neither scramble nor contest are effective below some
threshold, T, is passed. Conversely, in contest compe- threshold; but above this threshold scramble reduces
tition (Fig. 2.4) the individuals fall into two classes numbers to zero, while contest maintains a numerical
when the threshold is exceeded. T individuals still get constancy. In terms of quality, both scramble and
an equal and adequate share of the resource, and contest allow only two classes of individual: those
survive; all other individuals get no resource at all, getting all they require and therefore surviving (or
and therefore die. There are always just T survivors in producing the maximum numbers of offspring), and
contest, irrespective of the initial density, because those getting less than they need and therefore dying
mortality compensates exactly for the excess number (or producing no offspring at all). The difference is that
of individuals. In Fig. 2.4b the slope changes at the in scramble all individuals move suddenly from the
threshold from zero to 1; this b-value of 1is indicative of first class to the second at threshold; while in contest
there are still T individuals in the first class, even when
threshold is exceeded.

CHAPTER 2: INTRASPECIFIC COMPETITION 33

Fig. 2.4 Contest competition. Mortality relationships (a) in actually germinated and produced seedlings ('germi-
terms of numbers surviving and percentage mortality, and nation' in Table 2.1), the percentage that subsequently
(b)in terms of k plotted against the logarithm of density. died before setting their own seed at the end of the
summer, and the percentage that remained alive but
2.5 Actual effects of intraspecific failed to reproduce ('vegetative' in Table 2.1). The
competition number of seeds produced by each individual was
then counted, and the 'mean number of seeds per
2.51 Palmblad's data reproducing individual' and the 'total number of seeds
per pot' computed. Finally, the total dry weight of
Having described these hypothetical extremes, it is plants, both reproductive and vegetative, was mea-
appropriate to examine some actual examples. Studies sured for each pot.
of plants indicate the inadequacies of 'scramble' and
'contest' particularly clearly. The results are also summarized in Fig. 2.5, where
the k-values of the various processes are plotted
Palmblad (1968) undertook an experimental study againstthe log,, of the sowing density (as they were in
on the effects of intraspecific competition on several
species of weed. Some of his results are summarizedin Figs 2*3band 2.4b)*kgermination? kmortatity and kvegetative
Table 2.1 and Fig. 2.5. They refer to two annual are all self-explanatory;kJ,,,,,,, refers to the reduction
species, CapseIla bursa-pastoris (Shepherd's purse) and in the number of seeds produced per individual, log,,
Conyza canadensis (Canadian fleabane), and the peren- (maximum seedslactualseeds);while k,,, refers to the
nial, Plantago major (plantain). Palmblad's procedure reduction in the total number of seeds produced, but
was simply to sow seeds of each species under is also the sum of all the other k-values.
controlled conditions at a range of densities (1, 5, 100
and 200 seeds per pot), and then keep a careful record The first point to note is that, almost without
of their subsequent progress. As Table 2.1 shows, he exception, the 15 plots in Fig. 2.5 show k increasing
was able to compute the percentage of seeds that with density. The density-dependent nature of the
various responses of these plants to intraspecific
competition is, therefore, immediately confirmed. It is



34 PART 1: SINGLE-SPECIES POPULATIONS

CHAPTER 2: INTRASPECIFIC COMPETITION 35

Fig. 2.5 The varied effects of intraspecific competition: because the plants were not spaced with total regular-
experiments on populations of three species of weed. (Data ity, different plants experienced different degrees of
from Palmblad, 1968.)For further discussion see text. crowding. Another is that the plants themselves were
inherently (i.e. genetically) different. Other reasons
also apparent, however, that the sudden threshold, will soon become apparent.
characteristic of scramble and contest, is generally
lacking in these real examples. Instead, as density In all three species, intraspecific competition ex-
increases, the slopes tend to increase gradually. This, erted its density-dependent effects on the proportions
not surprisingly, is characteristic of many real germinating, surviving and remaining vegetative, and
examples: as density increases, so the intensity of in each case the plants fell, as a result, into one of two
competition increases. One reason for this is that, categories: those that 'did', and those that 'did not'.
With reproduction, however, the situation was far

36 PART 1: SINGLE-SPECIES POPULATTONS

more complex, the density-dependent effects of in- was achieved by a variable number of survivors
traspecific competition were no less obvious, but the producing a variable number of offspring.
response was very far from being all-or-none. Instead,
the mean number of seeds produced per individual Looking at these graphs more closely,we see that at
varied continuously throughout an almost 200-fold lower sowing densities-below 50 in Capsella, and
range in Plantago major, and an approximately 100- below 5 in Conyza and Plantago-the slopes of the k,,,
fold range in Capsellabursa-pastorisand Conyzacanaden- graphs are, in fact, less than 1. This indicates under-
sis. This plasticity of response-admittedly exemplified compensation (i.e. less than the exact compensation of
by seed production in plants-is common throughout b = l);although there is a reduction in individual
both the plant and animal kingdoms. Intraspecific output, this is not enough to compensate for the
competition leads not only to quantitative changes in increasing density, and the total output increases
the numbers surviving in populations, but also to (Table 2.1). Conversely, at higher densities (with the
qualitative changes in those survivors; and these pro- exception of Conyza between 100 and 200), there is
gressive decreases in quality as density increases con- overcompensation; the reduction in individual output
tribute significantly to the increasing intensity of more than compensates for the increased density, and
competition. total output decreases. This is indicated by a slope
greater than 1.In each species, therefore, the yield of
In Palmblad's experiments these qualitative changes seed reaches a peak towards the middle of the density
were not confined to average seed production. Despite range. Its precise position is indicated by the point on
the considerable variation in the density of surviving the graph where the slope equals 1exactly. Thus, not
plants, the total dry weight for each species, after an only do the graphs in Fig. 2.5 show the degree of
initial rise, remained remarkably constant with in- compensation resulting from competition, they also
creasing density. In other words, at higher densities indicate the sowing density that would maximize the
individualplants were smaller. There was 'compensa- final yield of seed. For commercially valuable crops,
tion' so that the final 'yield' remained largely un- such graphs may be of considerable impoftance.
changed.
Finally, it is apparent from Fig. 2.5 that the relative
Of course, the qualitative changes in dry weight and importance of gemination, mortality and so on in
seed production are closely connected: smaller plants regulating output is different in the three species. This
produce fewer seed. This, as TabIe 2.1 shows, leads to is made particularly clear by the fact that k,,, (the
a comparative constancy in the total number of seeds total effect) is the sum of all the other k-values. In
produced. Thus, the regulatory tendencies of intra- Capsella bursa-pastoris the effects of competition are
specific competition are amply illustrated; despite a almost entirely on the growth, and therefore the seed
200-fold range of sowing densities, the range of seed production, of surviving individuals. In Conyza cana-
output is only 1.4 in Capsella bursa-pastoris, 2.9 in densis seed production is also of primary importance,
Plantago major and 1.7 in Conyza canadensis. That such but a substantial proportion of the totaI effect is the
regulation does indeed occur is illustrated in another result of reduced rates of germination. Conversely, in
way in Fig. 2.5. Remember that in contest competition Plantago major the tendency to remain vegetative and
there was an absolute constancy of output illustrated (to a lesser extent) mortality play an important role;
by a slope (b)of 1. In Fig. 2.5 the slopes of the three this is no doubt associated with the perennial habit.
graphs for k,,,,,, taken over the whole range, are also Thus, although the end-resultsare similar in the three
close to 1, indicating the near-constancy of output species, the ways in which they are achieved are
already noted. The resemblance to contest, however, rather different.
is only superficial.In contest, constancy is achieved by
a constant number of survivorsall producing the same In summary, then, we have learnt a great deal that
number of offspring. In Palmblad's experiments,as in is of general relevance from this limited example.
real examples generally, the near-constancyof output Typically, intraspecificcompetition affects not only the
quantity of survivors, but their quality as well, which

CHAPTER 2: INTRASPECIFIC COMPETITION 37

becomes more and more affected as density increases. after the action of competition, always on a constant
This, combined with the variability of both environ- area basis. This yield may be measured in a variety of
ment and individuals, means that there is usually no ways either as a direct fitness component (e.g. seed
sudden threshold for competition in nature. Rather, it produced)or less directly as biomass, either of the total
increases gradually over an extended range. Palm- plant or some of its constituent parts. The form of
blad's experiment also reiterates that the ultimate response is either :(i)asymptotic (Fig. 2.6a)where yield
effect of intraspecific competition, acting through per unit area levels off with increasing density (i.e.
survival and fecundity, is on the contributions to perfect compensation; constant final yield); or (ii)
future generations;that individuals are affected recip- parabolic (Fig. 2.6b), where a maximum yield is
rocally; that intraspecificcompetitiontends to regulate reached at an intermediate density before falling at
populations; and that the effects can be measured high densities (i.e. overcompensation). From these
without the unequivocal identificationof the resource examples, we can see (as we might expect) that the
in limited supply. influence of adding more resources for growth (by
fertilizer) increases the,size of the population, mea-
2.5.2 Competition in plants: sured as the height of the asymptote or peak of the
a deeper look parabola.

Palmblad's experiments also illustrate two important The asymptotic constant yield response, which
interlinked events that can occur when plant popula- develops progressively, can best be explained by
tions are grown in resource-limited environments. looking at the changes in the population with time and
The first is that the size of individuals (as measured for the performance of individuals. Soybeans grown over
instance by individual biomass or seed production) is a 1000-fold density range show particularly well
reduced; the other is that ultimately mortality may (Fig. 2.7a). At sowing (day 0), yield per unit area and
ensue. These events occur along a spectrum of com- density are directly proportional to one another: the
petitive effects on the growth of individual plants. The yield is the weight of the seed sown! With time this
extremitiesare the death of the individual(growth and linear proportionality disappears, as plants grow to
maintenance ceased) and unconstrained growth sizes at which they interfere with one another, the
(growth rate = maximum for that environment). The interference occurring first at the highest density. The
'in between' is a reduced growth rate (less than yield curves therefore display a successively pro-
maximum) which is reflected at some point in time nounced shoulder as the linear proportionality disap-
(harvest of the plant) in a reduced plant size. pears, but this in its turn is replaced (after 119 days)
by a horizontal yield curve when final yield is inde-
Evidence for the density-dependent effects of com- pendent of original population size. Compensation by
petition can be examined at various levels: at the level individuals on this sort of scale &ere 10 and 1000
of the population itself, amongst individualswithin the plants m-2 yielding the same biomass after 119 days)
population and within individual plants. We will is a direct reflection of the enormous plasticity that
follow this progression, which is, perhaps not surpris- species with modular growth possess. Such plasticity
ingly, the way our scientific understanding has histor- has been shown to occur in a wide range of species
ically developed. Finally, we attempt to integrate our including pine trees, grasses and herbs. Re-examining
understanding of the whole process. the same data, but from the viewpoint of an average
individual soybean plant, shows us that compensation
Figure 2.6 shows the two general forms of 'yield- through adjustment of the performance of individuals
density' relationship that have emerged from the is indeed occurring. From being initially independent
wealth of studies conducted by agronomists and of density (at day O), the average weight of a plant
ecologists. The figures relate population density before becomes increasingly related to it (Fig. 2.7b). Plants at
the action of competition-often the number of plants low density (10 mP2)achieved a final mean weight of
sown as seed or planted-to population density held)

38 PART l : SINGLE-SPECIES POPULATIONS

Fig. 2.6 Illustrative yield-density
relationshipsin plants. (a)Bromus
uniloides at three nitrogen fertilizer
levels. (From Donald, 1951.) @) Zea
mugs at three fertilizer levels. (Data
of Langer et al., 1956; from Willey &
Heath, 1969.)See text for

explanation.

nearly 70 g whereas those in popuIations of 50 other members of the population; and (ii) species
were onIy 14g. Moreover, it is important to realize respond difleuentiallg according to their developmental
that these adjustments occurred in the absence of stage. To appreciate these expIanations we must first
mortality. Yield density esperirnents in both agricul- give further consideration to two features of plant
ture and forestry have frequently reaffinned that in growth.
many situations (species and environments) mean
yield per plant is inversely proportional to density or The first is that the production of flowersand hence
that total yield per unit area is independentof density. seeds requires the differentiation of floral meristems.
This observation has been described as the 'law of These may arise from the permanent conversion of
constant final yield' (Kira et al., 1953). vegetative meristems, or they may be borne laterally
on an axis that retains a vegetative meristem at its tip.
How then can we explain situations in which the This difference leads to a dichotomy in growth form.
law of constant final yield is not obeyed (e.g. Fig. 2.6b), Species may show indeterminate growth, bearing flow-
and yield at high densities declines from an inter- ers at nodes laterally to growing axes and thus
mediate optimum? This question cannot be fully retaining the potential for indefinite vegetative exten-
answered for all cases, but two cogent possible expla- sion. In contrast, species may show determinate
nations are: (i) plant mortality does occur during the growth, where the conversion of vegetative meristems
course of competition, but the surviving plants are into floral structures prohibits further vegetative de-
unable to exploit fully resources freed by the death of velopment. Conversion may be triggered by changes

CHAPTER 2: INTRASPECIFIC COMPETITION 39

Fig. 2.7 Yield-density relationships in soybean Glycine max: is young, before the influence of competition has
the progressive changes with time (a)on a unit area basis, become marked. Thus, the response to density-
and (b)per plant. (From Shinozaki & Kira, 1956; after induced resource limitation cannot be a reduction in
Harper, 1977.) capitulum number. Instead it is etiolation of the plant,
and reduction both in the proportion of flowers within
in day length and/or temperature (vernalization), or the capitulum that set mature achenes (seeds)and the
may be genetically fixed. size of those achenes. In the field bean (Viciafaba) on
the other hand (Fig. 2.8b) responses to density are
The second feature that we must consider is how seen at all developmental stages in the production of
yield is formed. In the case of seed, it requires the seeds. Part of the response is a reduction in the
production of a range of plant parts, i.e. the components number of stems per plant and flowers per stem, and
of yield (e.g. stems, flower-bearing branches, flowers, part is the abscission of flowers and pods. The overall
pods and seeds). All components may respond to outcome of this plasticity is near constancy in seed
density but as successive components are produced population size per unit area. One further contrast
we might expect the type of density response to may be drawn from this example. In Helianthus,
change. individual seed weight declined markedly with plant
density, whereas in Vicia it remained constant. The
Populations of cultivated sunflowers (Helianthus an- former response, however, is the exception to the
nus) provide us with an illustration of one type of generally observed phenomenon of homeostasis in
yield-density response (Fig. 2.8a) in which there is seed size in response to density. (Wild progenitors of
overcompensation. In this sunflower, plants usually Helianthus absorb density stress by reducing the
bear a single large capitulum (flower head). This
develops from the terminal meristem when the plant

40 PART l : SINGLE-SPECIES POPULATIONS

Fig. 2.8 Yield-density responses in (a) cultivated sunflowers increasing density, whereas in the indeterminate form
(data replotted from Clements et al., 1929). and (b)field yield component responses were noticeably more
bean (data from Hodgson & Blackman, 1956). varied.

numbers of branches and capitula, preserving con- Many annual grasses, as exemplified by wheat
stancy of seed weight; Bradshaw, 1965.) (Triticum aestivum), exhibit a density response that is of
a combined form. Seed production in wheat is the
Sunflowers and field beans provide us with clear product of the number of fertile tillers per plant and
illustrations of some of the responses of determinate the number of grains (seeds) per ear: a fertile tiller
and indeterminate growth forms to intraspecific com- bears only one ear which may vary in size and thus in
petition but we should not assume that yield responses floret and seed number. Prior to flowering and ear
can be inferred from knowledge of the growth form of formation, density stress is reflected in reduced vege-
the plant. Final seed yield is the product of a number tative biomass and plant parts, but afterwards it is
of yield components each of which may respond to reflected in the size of the ears. This is shown
density in a specific way. Figure 2.9 illustrates these (Fig. 2.10) by a field experiment of Puckridge and
yields within a species (field bean) in which determi- Donald (1967) who grew wheat over a 1000-fold
nate and indeterminate growth forms have been density range and followed the course of grain yield
selected(Pilbeamet al., 1991).In the determinate form development. After 14 weeks growth, plants had
all yield components (stemslplant, nodeslstem, pods1 received stimuli for flowering. At this time the number
node, seedslpod)tended to decline systematicallywith of tillers per plant was strongly density-dependent