Lecture 14 - Population Growth

Question 1

Draw the small population paradigm

Answer 1

See notes.

Question 2

Name 3 stochastic elements of the extinction vortex.

Answer 2

1. Demographic stochasticity. Ex: females only produce male offspring
2. Genetic stochasticity. Ex: Loss of genetic variability making the population less likely to adapt to environmental changes
3. Environmental stochasticity and natural catastrophes.

Ex: Heath hen extinction

Question 3

Define Minimum Viable Populations.

Answer 3

The minimum population size that can prevent the extinction of a species for a specified time (100 years)

Question 4

Name 2 cases of population growths. Which one do we usually see in populations?

Answer 4

1. Populations with discrete generations
   Nt = N0R0
2. Growth of populations with overlapping generations & continuous breeding

2 is usually more common.

Question 5

What is modified to explain dynamic behavior of population size in population with discrete generations?

Answer 5

Assume R0 varies with population density.

R0 = 1.0 - B ( N - Neq)

Question 6

Formula for population growth rate

What does r define?

Answer 6

dN/dt = rN
r = potential per capita growth rate (or intrinsic rate of increase) (ONLY FOR GEOMETRIC GROWTH)
dN/dtN = realized per capita growth rate

Question 7

Name 3 cases where populations grow exponentially.

Answer 7

1. At initial stages of colonization
2. When conditions are favorable or,
3. Sometimes, when recovering from negative environmental perturbation

Question 8

Why do we need Logistic Growth?

Answer 8

Natural populations cannot sustain exponential growth indefinitely. They show a different kind of growth based on carrying capacity.

Question 9

Define Logistic Growth and give formula. Interpret different values of carrying capacity K. What does r mean and what kind of growth does it apply to?

Answer 9

Population grows rapidly then eventually slows and ceases

dN/dt = rN* (1- N/K) where K is the carrying capacity of population

• When N=K, limit = 0, the population stops growing
• When N«

Question 10

Define the Theta logistic growth equation. What do small and large values of theta represent?

Answer 10

Similar to logistic growth but limit term is raised to the power of theta

Small theta value means population is sensitive to population density.
Populations with high theta value can recover well from disturbance.

Question 11

Name 3 alternative growth models.

Answer 11

1. Theta logistic growth equation:
2. Time lag effects (Deterministic VS Probabilistic )
3. Stochastic models

Question 12

What density should we keep a managed population in order to maximize the yield without causing it to decline

Answer 12

N=K/2

Ex: anchovy catch in peru