(4/3) Population Ecology Notes

Intro to Population Ecology

• Definition: Population ecology studies how and why population size changes over time and the effects of these changes on the population.
• Distinction from Population Genetics:
  • Population genetics focuses on genetic changes over time and the formation of new populations.
  • Population size can change without genetic change, and vice versa.
• Importance of Studying Population Ecology:
  • Understanding population changes helps in:
    • Planning farms by understanding how food plant populations grow and are limited.
    • Maintaining ecosystems by understanding insect population dynamics.
• Methods in Population Ecology:
  • Conservation biologists determine population size and the reasons for growth or decline.
  • This is achieved by:
    • Monitoring changes in population elements (numbers, ages, sex ratio) over time.
    • Tracking factors affecting these elements.
    • Making predictions about population changes.
  • Example: Caribou on Pribilof Islands.

Exponential Growth

• Scenario: Organisms in an unlimited environment with unlimited resources and space, dividing into 2 every 24 hours.
• Population Growth Chart:
  • Day 1: Population Size 1
  • Day 2: Population Size 2
  • Day 3: Population Size 4
  • Day 4: Population Size 8
  • Day 5: Population Size 16
  • Day 6: Population Size 32
• Characteristics of Exponential Growth:
  • The data, when graphed, yields a curve that starts with a slow increase and quickly turns to a rapid increase in numbers with very little change in time.
• Mathematical Description:
  • b = probability of dividing/giving birth
  • d = probability of dying
  • r = instantaneous rate of growth per individual (per capita), where r = b - d (typically considered as r_{max}).
  • N = population size
  • Rate of population growth = rN
• Exponential Growth Equation:
  • (\Delta N / \Delta t) = rN
  • Translation: The change in population size per change in time (rate of growth) equals the rate of population growth for the individual multiplied by the number of individuals in the population.

Logistic Growth

• Example: Sheep of South Australia.
• Stages of Logistic (Sigmoid) Growth:
  1. Initial exponential growth.
  2. Decelerating growth rates.
  3. Fluctuations around an average population size, K (carrying capacity).
• Logistic Equation:
  • (\Delta N / \Delta t) = rN((K-N)/K)
• Components:
  • N = current population size
  • K = carrying capacity (highest value that N can take)
  • r = relative growth rate (r_{rel}), reflecting how an individual reproduces relative to the influence population size has on the individual.
• Translation of the equation: Describes how the rate of population growth decreases as the population size approaches the carrying capacity.
• Model Comparison:
  • The logistic model more accurately predicts real populations compared to the exponential model.
  • The exponential model does not account for resource limitations.
• Carrying Capacity (K):
  • The point at which the population size is in equilibrium with resources.
  • The number of individuals of a species that the environment can support.
  • The number of individuals that can survive in the environment.
  • Note: K is not constant; it changes with environmental conditions (e.g., food base, resources).
  • The definition of K depends on the point of view: population and environment, the environment, or the population.
• Using the Logistic Model:
  • If N > K: the population is above carrying capacity
  • If N < K: the population is below carrying capacity
  • If N = K: the population is at carrying capacity
• Example Case Study: Gray Wolf populations in Wisconsin

Problems with the Models

• Discussion of the problems with the exponential and logistic models.