ES2303 Week 4: Populations and Population Growth

Key Concepts in Population Growth

Mathematical Characteristics of Population Growth

  • Exponential Growth: Model where populations increase rapidly when resources are unlimited.

    • Exponential growth equation: Nt= N0 e^{rt}

    • $N_t$: Number of individuals at time t

    • $N_0$: Number of individuals at start (t = 0)

    • $r$: Intrinsic growth rate

Density-Dependent vs Density-Independent Factors

  • Density-Dependent Factors: These factors affect population growth in relation to population density.

    • Examples include:

    • Availability of resources (food, nutrients)

    • Increased stress, disease spread, and predation at higher densities.

  • Density-Independent Factors: Factors that affect populations regardless of density levels.

    • Examples include:

    • Natural disasters (e.g., fires, storms)
      -Weather changes (temperature, rainfall)

The Logistic Growth Model

  • More realistic than exponential; accounts for carrying capacity (K)

    • Logistic growth equation:
      \frac{dN}{dt} = rN \left(1 - \frac{N}{K}\right)$$

    • At low densities, growth is exponential; at high densities, growth slows, approaching K.

Population Dynamics and Real-World Observations

  • Population examples illustrate growth:

    • Monarch Caterpillars: Show intra-specific competition for food.

    • Fruit Flies (Drosophila melanogaster): Lower reproductive output and lifespan at higher densities.

    • Common Terns: Population trends monitored across different islands indicate the effects of density on success.

Life Tables in Population Study

  • Life Tables: Tools to analyze survival rates and fecundity of different age classes within a population.

    • Constructed by listing age classes, survival rates ($sx$), and reproductive outputs ($bx$).

    • Net reproductive rate calculated as $R0 = \sum (lx \cdot b_x)$

    • Important to assess population viability; enables ecologists to predict growth patterns.

  • Pros and cons Static life table vs Cohort life table

    • Static life table

      • Potentially less effort (shorter study duration)

      • Environmental variation affects all age classes

      • Good for mobile/long lived species

      • May not be representative of data of other periods

    • Cohort life table

      • Long study period, man repeat surveys

      • Environmental variation and age-specific variation hard to disentangle

      • Best for sessile/ short-lived species

      • Potentially more representative by surveying multiple years

Age Structure and Survivorship Curves

  • Age structure impacts population dynamics.

  • Survivorship Curves: Graphical representation of survival rates:

    • Type I: High survival in early life (e.g., humans)

    • Type II: Constant mortality rate (e.g., songbirds)

    • Type III: High early mortality (e.g., frogs)

Methodologies for Measuring Population Size

  • Various approaches used in population studies:

    • Direct Observation: Simply count individuals.

    • Capture-Mark-Recapture: Estimate population size based on captured and tagged individuals.

    • Quadrat Sampling: Count individuals within designated areas.

    • Camera Trapping: Use technology to track wildlife without direct observation.