BIOL 4120: Principles of Ecology Lecture 9: Population Growth and Regulation

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BIOL 4120 Principles of Ecology Lecture 9
Population Growth and Regulation

• Dafeng Hui
• Office Harned Hall 320
• Phone [phone]
• Email dhui_at_tnstate.edu

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World population
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Outline

• 9.1 Population grow by multiplication rather than
  addition
• 9.2 Age structure influences population rate
• 9.3 A life table summaries age-specific schedules
  of survival and fecundity
• 9.4 The intrinsic rate of increase can be
  estimated from the life table
• 9.5 Population size is regulated by
  density-dependent factors

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9.1 Populations grow by multiplication rather
than addition

• Definition Population growth, how the number of
  individuals in a population increases or
  decreases with time
• Growth is controlled by rates of birth,
  immigration and death and emigration.
• Open or closed population no immigration and
  emigration, or immigration rateemigration rate.
• In closed population, growth is determined by
  birth rate and death rate. Rate of growth is on a
  per capita basis.
• Demography study of population.

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Calculating population growth rates

• Geometric growth
• Assume a population, at t0, population size is
  N(0), ratio of population size change in one year
  to the size of the proceeding year is ?.
• If at time t, population size is N(t), then at
  time t1,
• N(t1)N(t) ?
• So N(1)N(0) ?, N(2)N(1) ?N(0) ?2
• thus
• N(t) N(0) ? t
• geometric growth model.

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Geometric growth curve N(0)100, ?1.5 (a) y
on a arithmetic scale (b) y on a logarithmic
scale.
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Exponential growth

• NtN0exp(rt)
• Where r is the exponential growth rate
• Compare to N(t)N(0) ?t
• ?exp(r) or rln(?)
• These models are used to describe dynamics of
  populations. Geometric growth is used for
  population generations not overlap (discrete time
  interval), exponential growth model is for
  continuous population.

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• Population size change and model parameter
• Increasing population, ?gt1, rgt0
• Constant pop. Size, ?1, r0
• Decreasing population, 0lt?lt1, rlt0

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Calculating population growth rates from birth
and death rates

• In a closed population, population size change is
  related to birth rate (b) and death rate (d)
• The difference between birth rate and death rate
  is the intrinsic growth rate (r) (instantaneous
  per capita rate of growth).
• rb-d
• Population growth is related to this intrinsic
  growth rate (r).
• dN/dt(b-d)NrN

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Exponential population growth

• Equations
• 1) dN/dtrN (differential equation form)
• 2) NtN0 exp(rt) (exponential growth model)
• Conditions
• Initial population is small
• No food or resource limitation

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An example
Started in 1910 with only 4 males and 22
females In 1940, there were nearly 2000
Reindeer, St. Paul, Alaska.
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Whooping crane, an endangered speciesrecovered
from near extinction in 1941
How to calculate r? Software, Excel (trendline)
Arkansas National Wildlife Refuge
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Prediction of population growth
NtN0Exp(rt) Give a time t, we can predict the
population size. An Example Deer population
N0300, r0.5, after 5 years, whats the
population size? N5N0 Exp(rt)300exp(0.55)365
5 (495, 815, 1344, 2216, 3655) t10, ?
44,524
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9.2 Age structure influences population growth
rate

• Age structure the proportions of each individual
  in each age class.
• Age structure influences population growth rate,
  as only mature adults can reproduce and increase
  population size.
• A life table is an age-specific account of
  mortality

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Age structure influences population growth rate
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?(t)N(t1)/N(t)
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Age distribution
Stable age distribution by year 7, the
proportion of each age group remain the same year
after year. Population is still growing at a
constant rate.
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In a stable age distribution, each age class
grows at the same rate
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Age structure of human population (2008 data)
Different countries (a) Stable for many years
(b) high birth (growth) rate
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Population structure change over time in
German Birth rates are declining in many human
populations
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9.3 Life table summaries age-specific schedules
of survival and fecundity

• Life table is an age-specific account of
  mortality.
• Purpose of life table to provide a clear and
  systematic picture of mortality and survival
  within a population. Can also be used to simulate
  population size change.

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• Recap
• Population growth
• Growth models Geometric growth model vs
  Exponential growth model
• Life table and use life table to predict
  population growth
• Age structure

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l(x)
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Two types of life tables

• Two types
• Cohort or dynamic life table
• as the above flycatcher, (plants, sessile
  animals)
• Time-specific or static life table

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9.4 Life tables provide data for mortality and
survivorship curves

• Table is better than words, but a graph is worth
  one thousand words.
• Mortality curve and survivorship curve.

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Survivorship curves
I. deer, sheep, human, convex II squire
and adult birds, linear, not change with age III.
Plants, fish, young bird, concave
Log scale for Y axis
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9.5 Intrinsic rate of increase can be estimated
from the life table
Crude birthrate (demographers) of birth over a
period of time divided by population size at the
beginning of the period1000 Age-specific
birthrates, bx Mean of females birth to a
female in each age group. (Only females give
birth birth rates vary with ages) Gross
reproduction rate sum of the bx values across
all age classes, provides an estimate of average
offspring born to a female over her lifetime.
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Birth rate and survivorship determine net
reproductive rate

• Fecundity table take survivorship column, lx,
  from life table and add age-specific birthrate,
  bx.

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Birth rate and survivorship determine net
reproductive rate

• Net reproduction rate, R0 number of female
  offspring a female at birth can produce (or
  average of females that will be produced (left)
  during a lifetime by a newborn females.)

• R0 depends on survivorship and fecundity
• R0 1,
• gt1
• or lt1

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Generation time and growth rate

• Generation time average age at which an
  individual gives birth to its offspring
• TSum(xlxbx)/sum(lxbx)
• T4.2/2.11.95
• N(t)/N(0) ?t (T1.95)
• If tT, then R0 N(T)/N(0), then R0?T
• ?R01/T2.11/1.95 1.46 r ln(?)0.38

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The growth potential of populations

• Capacity of population growth
• Pheasants 2 males 6 females in 1937
• in 5 years, ? 1325 (r1.02, ?2.78)
• Elephant seal in 1900, N0100
• 2000 150,000 (r0.073, ?1.076)
• 2100 225 millions
• Field vole ?24
• Water flee ?1030

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The growth potential of populations

• Doubling time
• t2 ln(2)/ln(?)
• or t2 ln(2)/r
• Field vole t20.22 yr, 79 days (?24)
• Pheasants t2246 days (r1.020)
• Water flea, t23.6 days (r69.07)
• Ln(2)0.693, if r0.01, t269.3

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9.6 Limitation on Population Growth
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Exponential growth model can not explain the
population growth here Need other equation or
model
Barnacle
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Birth rate and death rate change with population
size N
dN/dtrN rb-d bb0-aN dd0cN dN/dt(b0-d0)-(a
c)NN dN/dt(b0-d0)1-(ac)/(b0-d0)NN dN/dtr
N(1-N/K) K(b0-d0)/(ac)
K carrying capacity maximum sustainable
population size under prevailing environment.
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From exponential growth to logistic growth
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Logistic population growth
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Logistic Population Growth

• As resources are depleted, population growth rate
  slows and eventually stops logistic population
  growth.
• Sigmoid (S-shaped) population growth curve.
• Carrying capacity (K) is the number of
  individuals of a population the environment can
  support.
• (r) is per capita increase rate.

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A few examples
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US population (1790-1910) k197 million,
r0.03134.
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9.7 Population size is regulated by density
dependent factors

• Environment limits population growth by altering
  birth and death rates.
• Density-dependent factors
• E.g., Disease, Resource competition
• They influence a population in proportion to its
  size
• Resulted in slowing the rate of increase
• Density-independent factors
• E.g., Natural disasters
• Influence population without regard to the of
  individuals or if the proportion of individuals
  affected is the same at any density

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Density dependence in animals
Fecundity and life span of fruit fly decrease as
population density increase Lab study
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A long-term field study of common terns.
Population started with 200, and leveled off
after suitable nest sites are occupied on the
Bird Island. Birds started to colonize Ram
Island.
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Why level off? Density-dependent factors can
control the size of natural population. Song
sparrow (a) As density increases, more males
cant find territories (b) number of fledglings
produced per female and survival of those
offspring (c) decrease.
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Range quality influence percentage of
white-tailed deer female pregnant and average
number of embryos Selective hunting may improve
population caused by overgrazing.
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Positive density dependence Negative density
dependence common (right panel) Positive (or
inverse) density dependence left panel
A herring near iceland B herring near North Sea
Allee effect with increase in density, easy to
find mates, defend predators, increase diversity
etc.
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Allee effects also occur in plant population.
Reproduction of Primula veris (a small herbaceous
plant grow in nutrient poor grasslands) show
positive density dependence. Seed mass is the
average mass of individual seed. (pollination?)
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Regulation of population size by
density-dependent factors
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Regulation of population size by
density-dependent factors
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Density dependence in plants
Size of flax (Linum) plants grown at different
densities
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Horseweed experiment
Kyoji Yoda, plant ecologist Horseweed was planted
at a very high density (100,000 seeds
m-2) Density declined in several months Weight
per seedling increased.
Self-thinning progressive decline in density and
increase in biomass of remaining individuals in a
population.
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The curve of the average weight and density is
called self-thinning curve. -3/2 power law the
Regularity of this relationship is called -3/2
power law, as the slope is about -3/2.
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• END

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Geometric Growth

• When generations do not overlap, growth can be
  modeled geometrically.
• Nt No?t
• Nt Number of individuals at time t.
• No Initial number of individuals.
• ? Geometric rate of increase.
• t Number of time intervals or generations.

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Another example of squirrel
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Predicted population size change
Population size (N) increases every year.
Lambda (finite multiplication rate)
?N(t1)/N(t).
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Properties of exponential growth
Widely used in biology
r determines the shape of the growth. r0, no
change in population size rlt0, decrease in
population size rgt0, increase in population
size.
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Logistic equation incorporates the influences of
population size and per capita growth rate.
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Mortality curves
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Logistic Population Growth
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• Recap
• Population growth
• Growth models Geometric growth model vs
  Exponential growth model
• Life table and use life table to predict
  population growth

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• Recap
• A life table summaries age-specific schedules of
  survival and fecundity
• The intrinsic rate of increase can be estimated
  from the life table
• Growth models exponential growth and logistic
  growth model