Lecture 10: Population Growth
Population growth
Definition: 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.
Model development A population of freshwater hydra growing in an aquarium in
the laboratory.
Population size N(t) when time is t.
This is a closed population.
Reindeer, St. Paul, Alaska.
Whooping crane, an endangered species recovered from near
extinction in 1941
How to calculate r? Software, Excel (trendline) Aransas National Wildlife Refuge
How to construate dx, a measure of agespecific mortality
Population size change is related to birth rate (b) and death rate (d)
dN/dt=(b-d)N=rN
The difference between birth rate and death rate is the intrinsic growth rate (r) (instantaneous per capita rate of growth). r=b-d
Open or closed population: no immigration and emigration, or immig.=emig.
In closed population, growth is determined by birth rate and death rate.
10.1 Population growth reflects the difference between rates of birth and death
2) N(t)=N(0) exp(rt) (exponential growth model)
Conditions:
Initial population is small No food or resource limitation
An example
Started in 1910 with only 4 males and 22 females In 1940, there were nearly 2000
Prediction of population growth
N(t)=N(0)Exp(rt) Give a time t, we can predict the population size.
An Example: Deer population: N(0)=300, r=0.5, after 5 years, what’s the population size?
N(5)=N(0)Exp(rt)=300*exp(0.5*5)=3655 (495, 815, 1344, 2216, 3655) t=10, ? 44524
10.2 Life table
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
r=b-d
Population growth is related to this intrinsic growth rate (r).
Exponential population growth
Equations:
1) dN/dt=rN (differential equation form)
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).
How to construct a life table?
1. start with a cohort: a group of individuals born in the same period of time;
2. Add a column of lx as the probability at birth of surviving to any given age;
Properties of exponential growth
Properties of exponential growth
Widely used in biology r determines the shape of the growth. r=0, no change in population size r<0, decrease in population size; r>0, increase in population size.