Population ecology

Question 1

Population

Answer 1

A group of individuals of the same species occupying a specified geographic area over a specified period of time.
The area may be ecologically relevant (an island) or irrelevant (a political district), and the boundaries may be porous, with individuals immigrating to and emigrating from the population.

Question 2

Population ecology

Answer 2

The study of the dynamics of species’ populations, and their interactions with the environment and one another

Question 3

What are some central population ecology questions?

Answer 3

Basic science:
How do populations change over time?
What mechanisms drive population change?

Applied problems:
What is the risk of a species going extinct within 100 yr?
What is the most cost-effective way to eliminate an invasive species?

To answer these questions, we need a combination of field/lab data and mathematical models.

Question 4

Simple population growth model

Answer 4

See also page 6

Suppose that at time t=0, we have two individuals. And suppose that the population doubles in one timestep. We can express this as a difference equation (or recurrence relation):

Nt+1 = 2Nt

where Nt is the population size at time t. And we have the initial condition N0=1.

We can also generalise the model to arbitrary growth rates and initial population sizes:

Nt+1 = (1+r)Nt

which has the following solution:

Nt = (1+r)^tN0

Here r is the population growth rate (r=0 means constant population size; r<0 means declining population size; r>0 means increasing population size) and N0 is the initial population size.

If exponential growth is calculated in continuous time, the solution becomes:

N = N0e^(rt)

Question 5

Limiting factors to population growth

Answer 5

Lack of food (food is finite)

Lack of space (space is finite)

Disease (spreads more easily in dense populations)

Predation (predators can feed more efficiently on dense populations)

-> Populations cannot grow forewer (carrying capacity and logistic growth)

Question 6

Population structure

Answer 6

Distribution of ages or sizes within a population, and how each group contributes to population growth

Question 7

Spatial structure

Answer 7

How individuals are distributed across space, which may affect interactions and carrying capacity of the environment

Question 8

Stochasticity

Answer 8

Random events that may kill individuals or members of the population, leading to unexpected declines

Question 9

Concept of age and stage-based population models

Answer 9

Page 10

Question 10

Basic steps in population modeling

Answer 10

Write one population dynamics equation for each age/stage class, specifying fecundity and transition rates

Analyse using tools of matrix algebra, combining equations for all classes

Determine long-run growth rate (λ): λ>1 means the population is growing;
λ<1 means the population is declining

Calculate stable age/stage structure: the long-term distribution of age or stage classes at which the population will settle if current demographic trends continue

Calculate elasticities: an elasticity is the proportional change in the growth rate (λ) given a proportional change in a demographic parameter (e.g., mortality, fecundity)

Question 11

Stage structure: Killer whales

Answer 11

See page 19

Question 12

in general see slides for case studies

Answer 12

see slides or lecture recording