世界人口分布

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;
Population size (N) increases every year. Lambda (finite multiplication rate): =N(t+1)/N(t).
Age distribution
Stable age distribution: by year 7, the proportion of each age group remain the same year after year. Population is still growing.
survivorship and fecundity
newborn females.)
R0=1, >1 or <1
10.7 Project population growth
Given a population with age structure and some other information (age-specific mortality rates and birthrates), we can project future changes of the population size.
Net reproduction
rate, R0: number of female
offspring a female at birth can
R0: depends on
produce (or average # of females that will be produced (left) during a lifetime by a
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
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).
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.
For example, a population of squirrel with 10 adults (1-yr) and 20 juveniles females, what would happen in the next 10 years?
What do we need to project future population size change?
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
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
r=b-d
Population growth is related to this intrinsic growth rate (r).
Exponential population growth
Equations:
1) dN/dt=rN (differential equation form)
Table is better than words, but a graph is worth one thousand words.
Mortality curve and survivorship curve.
Mortality curves
Survivorship curves
Log scale for Y axis
Population size chang 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
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?
Three basic types of survivorship
Type I (convex) Humans and other
mammals and some plants (k-selection)
Type II (survival rates do not vary with age)
Adult birds, rodent, and reptiles, perennial plants
世界人口分布
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
Calculate age-specific survivor rate: sx=1-qx bx is age-specific birthrate
How to construct a population projection table?
How to construct a population projection table?
How to construct a life table (cont.)?
3. calculate dx, a measure of agespecific mortality
4. Calculate agespecific mortality rate, qx
10.3 Different types of life table
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
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.
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.
Type III. Concave Mortality rate high in the beginning (r-selection)
Oysters, Fish, many plant species (most trees)
10.5 Birthrate is age-specific
Crude birthrate (demographers): # of birth over a period of time divided by population size at the beginning of the period*1000
10.6 Birth rate and survivorship determine net reproductive rate
Fecundity table: take survivorship column, lx, from life table and add agespecific birthrate, bx.
Geometric growth vs exponential growth
N(t)=N(0) t N(t)=N(0)exp(rt)
=exp(r) or r=ln()
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.