世界人口分布分析

Lecture 10: Population Growth

World population

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.

?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 ?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.

?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

?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). r=b-d

?Population growth is related to this intrinsic growth rate (r).

Exponential population growth

?Equations:

?1) dN/dt=rN (differential equation form)

?2) N(t)=N(0) exp(rt) (exponential growth model)

?Conditions:

?Initial population is small

?No food or resource limitation

An example

Reindeer, St. Paul, Alaska. Started in 1910 with only 4 males and 22 females

In 1940, there were nearly 2000

Whooping crane, an

endangered species

recovered from near

extinction in 1941

How to calculate r?

Software, Excel (trendline) Aransas National Wildlife Refuge

Properties of exponential growth

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.

Properties of exponential growth

Widely used in biology

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, ?Prediction of population growth 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

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

l x as the probability

at birth of

surviving to any

given age;

How to construct a life table (cont.)?

?3. calculate d x, a

measure of age-

specific mortality

?4. Calculate age-

specific mortality

rate, q x

10.3 Different types of life table

?Two types

?Cohort or dynamic life table

?as the above gray squirrel

?Time-specific life table

Elf opine

10.4 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.

Mortality curves