(c) 2001 w.h. freeman and company chapter 14: population growth and regulation robert e. ricklefs...

(c) 2001 W.H. Freeman and Company

Chapter 14: Population Growth and Regulation

Robert E. RicklefsThe Economy of Nature, Fifth Edition


1. Populations grow by multiplication rather than addition

2. Age structure influences population growth rate

3. A life table summarizes age-specific schedules of survival

and fecundity

4. The intrinsic rate of increase can be estimated from the life

table

5. Population size is regulated by density-dependent factors

Chapter Concepts


Chapter Opener


Human Population Growth 1

Growth of the human population is one of the most significant ecological developments in the earth’s history.

Early population growth was very slow: 1 million individuals lived a million years

ago 3-5 million individuals lived at the start of

the agricultural revolution (10,000 years ago)


Human Population Growth 2

More recent population changes have been quite rapid: population increased 100-fold from 10,000

years ago to start of eighteenth century in the past 300 years, population has

increased from 300 million to 6 billion, a 20-fold increase

the most recent doubling (3 billion to 6 billion) has taken place in the last 40 years


Figure 14.1


Figure 14.2


How many humans?

Has the human population exceeded the ability of the earth to support it? there is no consensus 共识 on this point clearly, continued growth will further stress the

biosphere

When, and at what level, will the human population cease to grow? there are many unknowns the United Nations estimates a plateau at 9

billion


Demography

Demography is the study of populations: involves the use of mathematical

techniques to predict growth of populations

involves intensive study of both laboratory and natural populations, with emphasis on:causes of population fluctuationseffects of crowding on birth and death rates


Populations grow by multiplication.

A population increases in proportion to its size, in a manner analogous 类似于 to a savings account earning interest on principal: at a 10% annual rate of increase:

a population of 100 adds 10 individuals in 1 yeara population of 1000 adds 100 individuals in 1

year

allowed to grow unchecked 无限制地 , a population growing at a constant rate would rapidly climb toward infinity 无穷大


Two Models of Population Growth

Because of differences in life histories among different kinds of organisms, there is a need for two different models (mathematical expressions) for population growth: exponential growth: appropriate when young

individuals are added to the population continuously

geometric growth: appropriate when young individuals are added to the population at one particular time of the year or some other discrete interval离散间隔


Exponential Population Growth 1

A population exhibiting exponential growth has a smooth curve of population increase as a function of time.

The equation describing such growth is:N(t) = N(0)ert

where:N(t) = number of individuals after t time unitsN(0) = initial population sizer = exponential growth ratee = base of the natural logarithms (about 2.72)


Figure 14.3


Exponential Population Growth 2Exponential growth results in a continuously

accelerating curve of increase (or continuously decelerating curve of decrease).

The rate at which individuals are added to the population is:

dN/dt = rNThis equation encompasses 包含 two principles:

the exponential growth rate (r) expresses population increase on a “per individual basis”

the rate of increase (dN/dt) varies in direct proportion to N


Geometric Population Growth 1

Geometric growth results in seasonal patterns of population increase and decrease.

The equation describing such growth is:N(t + 1) = N(t)

where:N(t + 1) = number of individuals after 1 time unitN(t) = initial population size

= ratio of population at any time to that 1 time

unit earlier, such that λ = N(t + 1)/N(t)


Figure 14.4

鹌鹑


Geometric Population Growth 2

To calculate the growth of a population over many time intervals, we multiply the original population size by the geometric growth rate for the appropriate number of intervals t:

N(t) = N(0) t

For a population growing at a geometric rate of 50% per year ( = 1.50), an initial population of N(0) = 100 would grow to N(10) = N(0) 10 = 5,767 in 10 years.


Exponential and geometric growth are related.

Exponential and geometric growth equations describe the same data equally well.

These models are related by: = er

andloge = r


Figure 14.5


Varied Patterns of Population Change

A population is: growing when > 1 or r > 0 constant when = 1 or r = 0 declining when < 1 (but > 0) or r

< 0


Figure 14.6


Per Individual Population Growth Rates

The per individual or per capita growth rates of a population are functions of component birth (b or B) and death (d or D) rates:

r = b - dand

（每头年增长率） = B - DWhile these per individual or per capita rates

are not meaningful on an individual basis, they take on meaning at the population level.


Age structure determines population growth rate.

When birth and death rates vary with the age of individuals in the population, contributions of younger and older individuals must be calculated separately.

Age specific schedules of survival and fecundity enable us to project the population’s size and age structure into the future.


Table 14.1


Table 14.2


Stable Age Distribution

When a population grows with constant schedules of survival and fecundity, the population eventually reaches a stable age distribution (each age class represents a constant percentage of the total population):

Under a stable age distribution: all age classes grow or decline at the same rate, the population also grows or declines at this

constant rate,


Table 14.3


Figure 14.7


Life Tables

Life tables summarize demographic information (typically for females) in a convenient format, including: age (x) number alive survivorship (lx): lx = s0s1s2s3 ... sx-1

mortality rate (mx)

probability of survival between x and x+1 (sx)

fecundity (bx)


Cohort 同龄群 and Static Life Tables 动态和静态生命表http://apps.who.int/gho/data/?theme=main&vid=60340 世卫组织分国家人口生命表 - 中国

Cohort life tables are based on data collected from a group of individuals born at the same time and followed throughout their lives: difficult to apply to mobile and/or long-lived animals used by Grants to construct life tables for Darwin’s

finches on Galápagos Islands

Static life tables consider survival of individuals of known age during a single time interval: require some means of determining ages of individuals used by Olaus Murie to construct life tables for Dall

mountain sheep 野山羊 in Denali National Park

http://apps.who.int/gho/data/?theme=main&vid=60340

http://apps.who.int/gho/data/?theme=main&vid=60340


Table 14.4


Figure 14.9


Figure 14.11


Table 14.5


The Intrinsic Rate of Increase 1

The Malthusian parameter (rm) or intrinsic rate of increase is the exponential rate of increase (r) assumed by a population with a stable age distribution.

rm is approximated (ra) by performing several computations on a life table, starting with computation of R0, the net reproductive rate, (Σlxbx) across all age classes.



The net reproductive rate, R0, is the expected total number of offspring of an individual over the course of her life span. R0 = 1 represents the replacement rate

R0 < 1 represents a declining population

R0 > 1 represents an increasing population

The generation time for the population is calculated as T = Σxlxbx/Σlxbx


Table 14.6



Computation of ra is based on R0 and T as follows:

ra = logeR0/TClearly, the intrinsic rate of natural

increase depends on both the net reproductive rate and the generation time: large values of R0 and small values of T lead to

the most rapid population growth


Most populations have a great biological growth potential.

Consider the population growth of the ring-necked pheasant 环颈雉 : 8 individuals introduced to Protection Island,

Washington, in 1937, increased to 1,325 adults in 5 years:

166-fold increaser = 1.02, = 2.78

another way to quantify population growth is through doubling time:

t2 = loge2/loge = 0.69/loge = 0.675 yr or 246 days for the ring-necked pheasant


Figure 14.12


Environmental conditions and intrinsic rates of increase.

The intrinsic rate of increase depends on how individuals perform in that population’s environment.

Individuals from the same population subjected to different conditions can establish the reaction norm for intrinsic rate of increase across a range of conditions: these vary within and between species


Figure 14.13


Intrinsic rate of increase is balanced by extrinsic factors.

Despite potential for exponential increase, most populations remain at relatively stable levels - why? this paradox was noted by both Malthus

and Darwin for population growth to be checked

requires a decrease in the birth rate, an increase in the death rate, or both


Consequences of Crowding for Population Growth

Crowding: results in less food for individuals and

their offspring Aggravates 加剧 social strife promotes the spread of disease attracts the attention of predators

These factors act to slow and eventually halt population growth.


The Logistic Equation

In 1910, Raymond Pearl and L.J. Reed analyzed data on the population of the United States since 1790, and attempted to project the population’s future growth.

Census data showing a decline in the exponential rate of population growth suggested that r should decrease as a function of increasing N.


Figure 14.14


Figure 14.15


Behavior of the Logistic Equation

The logistic equation describes a population that stabilizes at its carrying capacity, K: populations below K grow populations above K decrease a population at K remains constant

A small population growing according to the logistic equation exhibits sigmoid growth S型增长 .

An inflection point转折点 at K/2 separates the accelerating and decelerating phases of population growth.


The Proposal of Pearl and Reed

Pearl and Reed proposed that the relationship of r to N should take the form:

r = r0(1 - N/K)

in which K is the carrying capacity of the environment for the population.

The modified differential equation for population growth is then the logistic equation:

dN/dt = r0N(1 - N/K)


Figure 14.16


Figure 14.17


Figure 14.18


Pearl and Reed’s Projections

Pearl and Reed projected a U.S. population stabilized at 197,273,000.

The U.S. population reached this level between 1960 and 1970 and has continued to grow vigorously 有力地 .

Pearl and Reed could not have foreseen预见 improvements in public health and medical treatment that raised survival rates.


Population size is regulated by density-dependent factors.

Only density-dependent factors, whose effects vary with crowding, can bring a population under control; such factors include: food supply and places to live effects of predators, parasites, and diseases

Density-independent factors may influence population size but cannot limit it; such factors include: temperature, precipitation, catastrophic events


Density Dependence in Animals

Evidence for density-dependent regulation of populations comes from laboratory experiments on animals such as fruit flies: fecundity and life span decline with increasing density in

laboratory populations

Populations in nature show variation caused by density-independent factors, but also show the potential for regulation by density-dependent factors: song sparrows exhibit density dependence of territory

acquisition 获得 , fledging of young, and juvenile survival on density


Figure 14.19


Figure 14.20a


Figure 14.20b, c


Figure 14.21a


Figure 14.22


Density Dependence in Plants 1

Plants experience increased mortality and reduced fecundity at high densities, like animals.

Plants can also respond to crowding with slowed growth: as planting density of flax seeds is increased,

the average size achieved by individual plants declines and the distribution of sizes is altered


Density Dependence in Plants 2

When plants are grown at very high densities, mortality results in declining density: growth rates of survivors exceed the rate of

decline of the population, so total weight of the planting increases:

in horseweed 小白酒草 , a thousand-fold increase in average plant weight offsets 抵消 a hundred-fold decrease in density


Figure 14.23


Figure 14.24


Self-Thinning Curve 自疏

A graph of log (average weight) versus log (density) for plants undergoing density-induced mortality has points falling on a line with slope of approximately -3/2: this kind of graphical representation is known

as a self-thinning curve similar patterns are seen for a wide variety of

plants:this relationship is known as the -3/2 power law


Figure 14.25


Summary 1

Population growth can be described by both exponential and geometric growth equations.

When birth and death rates vary by age, predicting future population growth requires knowledge of age-specific survival and fecundity.

Life tables summarize demographic data.Analyses of life table data permit

determination of population growth rates and stable age distributions.


Summary 2

Populations have potential for explosive growth, but all are eventually regulated by scarcity of resources and other density-dependent factors. Such factors restrict growth by decreasing birth and survival rates.

Density-dependent population growth is described by the logistic equation.

Both laboratory and field studies have shown how population regulation may be brought about by density-dependent processes.

(c) 2001 w.h. freeman and company chapter 14: population growth and regulation robert e. ricklefs...

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