10
Population Growth
and Regulation
Chapter 10 Population Growth and Regulation
CONCEPT 10.1 Life tables show how
survival and reproductive rates vary with
age, size, or life cycle stage.
CONCEPT 10.2 Life table data can be used
to project the future age structure, size, and
growth rate of a population.
CONCEPT 10.3 Populations can grow
exponentially when conditions are
favorable, but exponential growth cannot
continue indefinitely.
Chapter 10 Population Growth and Regulation
CONCEPT 10.4 Population size can be
determined by density-dependent and
density-independent factors.
CONCEPT 10.5 The logistic equation
incorporates limits to growth and shows
how a population may stabilize at a
maximum size, the carrying capacity.
Introduction
One of the ecological maxims is: “No
population can increase in size forever.”
The limits imposed by a finite planet
restrict a feature of all species: A
capacity for rapid population growth.
Ecologists try to understand the factors
that limit or promote population growth.
Introduction
Understanding the factors that influence
population growth will help us
understand populations of endangered
species and what methods of protection
will be most effective.
CONCEPT 10.1
Life tables show how survival and
reproductive rates vary with age, size, or
life cycle stage.
Concept 10.1
Life Tables
A life table is a summary of how survival
and reproductive rates vary with age.
Life table data for the grass Poa annua
were collected by marking 843 naturally
germinating seedlings and then
following their fates over time.
Table 10.1
Concept 10.1
Life Tables
Sx = survival rate: Chance that an
individual of age x will survive to age
x + 1.
lx = survivorship: Proportion of
individuals that survive from birth to
age x.
Fx = fecundity: Average number of
offspring a female will have at age x.
Concept 10.1
Life Tables
A cohort life table follows the fate of a
group of individuals all born at the same
time (a cohort).
Mostly used for sessile organisms.
Organisms that are highly mobile or
have long life spans are difficult to track.
Concept 10.1
Life Tables
Static life table: Survival and
reproduction of individuals of different
ages during a single time period.
It requires estimating the age of
individuals.
Concept 10.1
Life Tables
Survivorship curve: Plot of the number
of individuals from a hypothetical cohort
that will survive to reach different ages.
Survivorship curves can be classified into
three general types.
Concept 10.1
Life Tables
Type I: Most individuals survive to old
age (Dall sheep, humans).
Type II: The chance of surviving remains
constant throughout the lifetime (some
birds).
Type III: High death rates for young;
those that reach adulthood survive well
(species that produce a lot of offspring).
Figure 10.5 Three Types of Survivorship Curves
Figure 10.6 Species with Type I, II, and III Survivorship Curves (Part 1)
Figure 10.6 Species with Type I, II, and III Survivorship Curves (Part 2)
Figure 10.6 Species with Type I, II, and III Survivorship Curves (Part 3)
Concept 10.1
Life Tables
Survivorship curves can vary:
• Among populations of a species
• Between males and females
• Among cohorts that experience
different environmental conditions
CONCEPT 10.2
Life table data can be used to project the
future age structure, size, and growth rate
of a population.
Concept 10.2
Age Structure
Age structure: Proportion of the
population in different age classes.
Age structure influences how fast a
population will grow.
If there are many people of reproductive
age (15 to 30), it will grow rapidly.
A population with many people older than
55 will grow more slowly.
Figure 10.7 Age Structure Influences Growth Rate in Human Populations (Part 1)
Concept 10.2
Age Structure
Population growth rate (λ): Ratio of
population size in year t + 1 (Nt+1) to
population size in year t (Nt).
N t 1

Nt
Concept 10.2
Age Structure
When age-specific survival and fecundity
rates are constant over time, the
population ultimately grows at a fixed rate.
The age structure does not change—the
population has a stable age distribution.
Concept 10.2
Age Structure
Environmental factors can alter survival or
fecundity and thus change population
growth rates.
Knowledge of these factors helps develop
management practices to decrease pest
populations or increase an endangered
population.
CONCEPT 10.3
Populations can grow exponentially when
conditions are favorable, but exponential
growth cannot continue indefinitely.
Concept 10.3
Exponential Growth
Geometric growth: When a population
reproduces in synchrony at discrete
time periods and growth rate does not
change.
The population increases by a constant
proportion: The number of individuals
added is larger with each time period.
Figure 10.10 Geometric and Exponential Growth
Concept 10.3
Exponential Growth
Geometric growth:
Nt 1  Nt
λ = geometric growth rate or per capita
finite rate of increase.
Concept 10.3
Exponential Growth
Geometric growth can also be
represented by:
Nt  N0
t
This predicts the size of the population
after any number of discrete time
periods.
Concept 10.3
Exponential Growth
Exponential growth: When individuals
reproduce continuously and generations
can overlap and the population changes
in size by a constant proportion at each
instant in time.
Figure 10.10 Geometric and Exponential Growth (Part 1)
Concept 10.3
Exponential Growth
Exponential growth is described by:
dN
 rN
dt
dN
= rate of change in population size at
dt
each instant in time
r = exponential population growth rate
or per capita intrinsic rate of increase
Concept 10.3
Exponential Growth
Exponential growth can also be
described by:
N (t )  N (0)e
rt
This predicts the size of an exponentially
growing population at any time t.
Concept 10.3
Exponential Growth
If a population is growing geometrically
or exponentially, a plot of the natural
logarithm of population size versus time
will result in a straight line.
Figure 10.10 Geometric and Exponential Growth (Part 2)
Concept 10.3
Exponential Growth
When λ = 1 or r = 0, the population stays
the same size.
When λ < 1 or r < 0, the population size
will decrease.
When λ > 1 or r > 0, the population grows
geometrically or exponentially.
Figure 10.11 How Population Growth Rates Affect Population Size
CONCEPT 10.4
Population size can be determined by
density-dependent and densityindependent factors.
Concept 10.4
Effects of Density
Under ideal conditions, λ > 1 for all
populations.
But conditions rarely remain ideal, and λ
fluctuates over time.
Growth rate may change independently
of density or as a function of density.
Concept 10.4
Effects of Density
Density-independent factors: Effects on
birth and death rates are independent of
the number of individuals in the
population.
• Weather conditions, such as
temperature and precipitation
• Catastrophes, such as floods or
hurricanes
Concept 10.4
Effects of Density
In the insect Thrips imaginis, population
size fluctuation is correlated with
temperature and rainfall (Davidson and
Andrewartha 1948).
Density-independent factors can have
major effects on population size from
year to year.
Figure 10.13 Weather Can Influence Population Size
Concept 10.4
Effects of Density
Density-dependent factors: Birth,
death, and dispersal rates change as
the density of the population changes.
As density increases, birth rates often
decrease, death rates increase, and
dispersal (emigration) increases, all of
which tend to decrease population size.
Figure 10.14 Comparing Density Dependence and Density Independence
Concept 10.4
Effects of Density
Population regulation: Densitydependent factors cause population to
increase when density is low and
decrease when density is high.
Ultimately, food, space, or other
resources are in short supply and
population size decreases.
Concept 10.4
Effects of Density
Density-independent factors can have
large effects on population size, but do
not regulate population size.
Figure 10.15 Examples of Density Dependence in Natural Populations (Part 2)
CONCEPT 10.5
The logistic equation incorporates limits to
growth and shows how a population may
stabilize at a maximum size, the carrying
capacity.
Concept 10.5
Logistic Growth
Logistic growth: Population increases
rapidly, then stabilizes at the carrying
capacity (maximum population size
that can be supported indefinitely by the
environment).
Figure 10.17 An S-Shaped Growth Curve in a Natural Population
Concept 10.5
Logistic Growth
The growth rate decreases as population
nears carrying capacity because
resources begin to run short.
At carrying capacity, the growth rate is
zero, so population size does not
change.
Concept 10.5
Logistic Growth
The logistic equation assumes that r
declines as N increases:
dN
 N
 rN 1  
dt
 K
N = population density
r = per capita growth rate
K = carrying capacity
Figure 10.18 Logistic and Exponential Growth Compared
Concept 10.5
Logistic Growth
When densities are low, logistic growth is
similar to exponential growth.
When N is small, (1 – N/K) is close to 1,
and the population increases at a rate
close to r.
As density increases, growth rate
approaches zero as population nears K.
Concept 10.5
Logistic Growth
Pearl and Reed (1920) derived the
logistic equation and used it to predict a
carrying capacity for the U.S.
population.
The logistic curve fit the U.S. data well up
to 1950. After that, actual population
size differed from the predicted curve.
Figure 10.19 Fitting a Logistic Curve to the U.S. Population Size
Concept 10.5
Logistic Growth
Agricultural productivity and import of
resources increased, allowing the
population to grow beyond the predicted
carrying capacity.
Some ecologists have shifted to the
concept of the ecological footprint—the
total area required to support a human
population.
Figure 10.22 United Nations Projections of Human Population Size
Connection in Nature: Your Ecological Footprint
Ecological footprint: Total area of
productive ecosystem required to
support a population.
This method uses data on agricultural
productivity, production of goods,
resource use, population size, and
pollution.
The area required to support these
activities is then estimated.
Connection in Nature: Your Ecological Footprint
The ecological footprint approach
highlights the fact that all of our actions
depend on the natural world, and they
also affect the natural world.