Population ecology Graphs & Math

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

Population Growth:  

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

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

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!

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 0.005 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?

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 0.005 individuals/(individual*day). The carrying capacity is 1000 fish. dN/dt = rmaxN[(K-N)/K] dN/dt = (.005)(1100)[(1000-1100)/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)[(500-250)/500] dN/dt = (.1)(250)[.5] dN/dt = 12.5 individuals/month

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

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

Human Population Growth: Age-Structure Pyramids