1. Population ecology
Graphs & Math

2. Survivorship Curves
3 Types
Type I  low death rates during early/middle life; high death rates in old age
Common in animals that have few offspring
Type II  constant death rates throughout life
Type III  high death rates in the young; death rates flatten out as age increases

3. Population Growth:

4. Population growth : Exponential
This type of graph is called a J-shaped graph

5. Population Growth: Logistic
This is called an S-shaped curve.

6. Logistic Population Growth
Selective pressures are hypothesized to drive growth rates in 1 of 2 generalized directions:
K-selection
Density-dependent
Tends to maximize population size and operates in population living at a density near the limit imposed by their resources (like the carrying capacity)
r-selection
Density-independent
Tends to maximize the rate of increase (r); population is lower than the carrying capacity and there is little competition; usually these populations have many small offspring, have little parental care of offspring, and are in disturbed habitats
All populations are either K- or r-selected!

7. Logistic Population Growth: Practice Problem
1. A fisheries biologist is maximizing her fishing yield by maintaining a population of lake trout at exactly 500 individuals. Predict the population growth rate if the population is stocked with an additional 600 fish. Assume that r for the trout is individuals/(individual*day). The carrying capacity is 1000 fish. dN/dt = rmaxN[(K-N)/K] dN/dt = growth rate rmax = rate K = carrying capacity N = total population 2. Suppose a population of butterflies is growing according to the logistic equation. If the carrying capacity is 500 butterflies, the population size is 250 butterflies, and the rmax is 0.1individuals/(individual x month). What is the maximum possible growth rate for the population?

8. Logistic Population Growth: Practice Problems ANSWERS
1. A fisheries biologist is maximizing her fishing yield by maintaining a population of lake trout at exactly 500 individuals. Predict the population growth rate if the population is stocked with an additional 600 fish. Assume that r for the trout is individuals/(individual*day). The carrying capacity is 1000 fish. dN/dt = rmaxN[(K-N)/K] dN/dt = (.005)(1100)[( )/1000] dN/dt = (.005)(1100)[-.1] dN/dt = -.55 fish/day 2. Suppose a population of butterflies is growing according to the logistic equation. If the carrying capacity is 500 butterflies, the population size is 250 butterflies, and the rmax is 0.1individuals/(individual x month). What is the maximum possible growth rate for the population? dN/dt = (.1)(250)[( )/500] dN/dt = (.1)(250)[.5] dN/dt = 12.5 individuals/month

9. Populations have regular Fluctuations
This is due to the interaction between biotic and abiotic factors

10. Human Population Growth: Demographic transition
A regional human population growth can exist in 1 of 2 configurations to maintain population stability
Have high birth rates and high deaths rates OR
Have low birth rates and low death rates

11. Human Population Growth: Age-Structure Pyramids