Week 2: Thu: demography

Demography

The study of how and why population size and structure change over time

Main drivers of population change

Survival reproduction and migration determine population dynamics

Life table

A structured way to describe survival and reproduction at each age in a population

nx

The number of individuals alive at the start of age class x

dx

The number of individuals that die during age class x

qx (mortality rate)

The probability of dying in age class x calculated as dx divided by nx

px (survival rate)

The probability of surviving to the next age class calculated as 1 minus qx

lx (cumulative survival)

The probability that a newborn survives to age x calculated as nx divided by n0

mx (fecundity)

The average number of same sex offspring produced by an individual at age x

lx mx

The expected number of offspring produced at age x accounting for both survival and reproduction

Key idea of lxmx

It combines survival and reproduction to show real contribution to the next generation

Net reproductive rate R0

The average number of same sex offspring an individual produces over its lifetime

R0 formula

R0 = sum of lxmx across all ages meaning total lifetime reproduction

Interpretation of R0 greater than 1

Each individual replaces itself with more than one offspring so population grows

Interpretation of R0 equal to 1

Each individual replaces itself exactly so population stays stable

Interpretation of R0 less than 1

Each individual produces less than one offspring so population declines

Generation time T

The average age at which individuals reproduce in a population

Generation time formula

T = sum of x times lxmx divided by sum of lxmx meaning weighted average age of reproduction

Why generation time matters

It links reproduction per generation to growth per year

Lambda λ (population growth rate)

The factor by which a population multiplies per time step usually per year

Lambda formula

λ = Nt+1 divided by Nt meaning how much the population changes between time steps

Interpretation of λ greater than 1

Population increases in size

Interpretation of λ equal to 1

Population remains constant

Interpretation of λ less than 1

Population decreases

Relationship between R0 T and λ

λ = R0 to the power of 1 divided by T converting growth per generation to growth per year

Continuous growth rate r

The instantaneous growth rate describing continuous population change

Relationship between r and λ

r = ln of λ and λ = e to the power of r

Intuition of r

It represents the underlying growth tendency of the population in continuous time

Population projection

A method to predict future population size and structure using survival and reproduction rates

Key idea of projection

Individuals either survive to the next age or produce offspring

Projection survival step

Number in next age class equals current number times survival rate px

Projection reproduction step

Number of newborns equals sum of all individuals times px times mx

Why survival is applied before reproduction

Only individuals that survive can reproduce in the next time step

Total population size N

The sum of individuals across all age classes

Lambda from projection

λ can be calculated as Nt+1 divided by Nt after each projection step

Why λ changes initially

The age structure is not yet stable so growth fluctuates

Stable age distribution

A situation where the proportion of individuals in each age class becomes constant

Why λ stabilizes

Once age structure stabilizes population grows at a constant rate

Deterministic projection

A projection assuming fixed survival and reproduction without randomness

Stochastic effects

Real populations vary due to randomness in survival reproduction and sex ratio

Carrying capacity K

The maximum population size the environment can sustain

Why populations do not grow infinitely

Limited resources predation disease and space restrict growth

Exponential growth

Population growth where numbers increase multiplicatively without limits

Logistic growth

Population growth that slows down as it approaches carrying capacity

Difference between exponential and logistic growth

Exponential ignores limits while logistic includes environmental constraints

r selected species

Species that reproduce quickly produce many offspring and invest little per offspring

K selected species

Species that reproduce slowly produce few offspring and invest heavily in each

Demography and genetics link

Population size and structure affect genetic diversity and inbreeding

Effect of small population size

Leads to stronger drift more inbreeding and loss of genetic diversity

Effect of unequal sex ratio

Reduces effective population size and genetic diversity

Inbreeding depression link

Increased inbreeding can reduce survival and reproduction

Why generation time matters in genetics

Evolutionary processes like drift and selection act per generation not per year

Population management goal

Maintain growth and genetic diversity while avoiding excessive inbreeding

Key exam insight

Population growth depends on both survival and reproduction and is always multiplicative not linear