Population Ecology

Population Ecology Overview

Chapter 53B Overview

  • Course: Meyer Biology 203

  • Topic: Population Ecology

Logistic Growth Model

Description of Logistic Growth

  • The logistic model describes how populations grow more slowly as they near their carrying capacity.

  • Important Concepts:

    • Exponential Growth:

    • Cannot be sustained indefinitely in any population.

    • Carrying Capacity (K):

    • Definition: The maximum population size that the environment can support.

    • Varies with the availability of limiting resources.

Mathematical Representation

  • The logistic growth model combines the exponential growth model with a term that limits growth as the population size (N) approaches carrying capacity (K).

  • Rate of population growth is mathematically represented as:

    • \frac{dN}{dt} = \frac{(K - N)}{K} rN

    • Where:

    • dN/dt = change in population size over time

    • K = carrying capacity

    • r = intrinsic rate of growth

Effects of Population Size on Growth Rate

  • Dynamics based on the relationship between N and K:

    • When N is small compared to K:

    • The term \frac{(K - N)}{K} approaches 1;

    • The per capita rate of growth is close to r.

    • When N approaches K:

    • The term \frac{(K - N)}{K} approaches 0;

    • The per capita growth rate decreases significantly.

    • When N = K:

    • Population growth ceases as it reaches carrying capacity.

Logistic Growth Visualization

  • The model produces a sigmoid (S-shaped) curve:

    • Rapid population increase occurs at intermediate population sizes.

    • Growth rate decreases as N approaches K.

Examples of Logistic Growth

Real Populations

  • Laboratory studies of populations, such as paramecium, display S-shaped growth curves when environmental factors like predators and competitors are constant.

  • Experimental observation:

    • Example: Paramecium growth over time under controlled conditions.

Overshoot and Stability

  • Some populations may overshoot their K before stabilizing.

  • Other populations may exhibit fluctuations making defining K challenging.

Life History Traits

Definition and Importance

  • Life History Traits: Products of natural selection that affect an organism's schedule of reproduction and survival.

  • Traits reflect evolutionary outcomes in development, physiology, and behavior.

Key Components of Life Histories

  1. Age at first reproduction (maturity)

  2. Frequency of reproduction

  3. Number of offspring produced per reproductive event

Reproductive Strategies

  • Semelparity:

    • Definition: Big-bang reproduction; species reproduce once before dying.

  • Iteroparity:

    • Definition: Species reproduce multiple times throughout their lifetime.

Trade-offs in Reproduction

  • Organisms may face trade-offs in resource allocation between reproduction and survival:

    • Example: In European kestrels, there is a trade-off between survival rates of parents and the size of their brood.

    • Observation: Variations in brood size affect the survival rate of parent birds over winters.

Seed Strategy in Plants

  • Selection pressures lead to trade-offs between the number and size of offspring (e.g., seeds):

    • Some plants produce many small seeds to ensure some germinate.

    • Other plants produce fewer but larger seeds to give seedlings a better start.

Selection Pressures: K-Selection vs. r-Selection

Definitions

  • K-selection:

    • Selection for life history traits that give advantages at high population densities.

  • r-selection:

    • Selection for life history traits that maximize reproductive success in low-density populations.

Population Density and Growth Regulation

Density-dependent vs. Density-independent Regulation

  • Density-independent populations:

    • Birth and death rates do not change with population density.

  • Density-dependent populations:

    • Birth rates decrease and death rates increase as population density rises.

    • Only density-dependent factors are capable of regulating population sizes.

Mechanisms of Population Regulation

  • Density-dependent factors:

    • Competition for resources

    • Disease

    • Predation

    • Territoriality

    • Toxic wastes

    • Intrinsic factors (behavioral & physiological changes)

Population Dynamics Visualization

  • Basic relationship between birth and death rates at differing population densities to find equilibrium density (Q).

    • A graph may illustrate population density against birth and death rates, showing equilibrium levels based on population density variations.