10Population 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).

t

t

N

N 1

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:

λ = geometric growth rate or per capita finite rate of increase.

tt NN 1

Concept 10.3

Exponential Growth

Geometric growth can also be represented by:

This predicts the size of the population after any number of discrete time periods.

0NN tt

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:

= rate of change in population size at each instant in time

r = exponential population growth rate or per capita intrinsic rate of increase

rNdt

dN

dt

dN

Concept 10.3

Exponential Growth

Exponential growth can also be described by:

This predicts the size of an exponentially growing population at any time t.

rtNtN e)0()(

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 density-independent 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: Density-dependent 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:

N = population densityr = per capita growth rateK = carrying capacity

K

NrN

dt

dN1

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.