Notes on Population Growth & Age Structure

Population Distribution Patterns

• Clumping Patterns
  • Individuals clump around patchy resources.
  • Negative interactions among individuals in a population suggest an intraspecific competition impact.
  • Some plants are distributed based on animal dispersal.
  • Others may be affected by gravity dispersal.

Learning Objectives of the Lecture

1. Define all key terms (highlight in red).
2. Assess how births, deaths, emigration, and immigration influence population size.
3. Calculate population size using the exponential growth rate equation.
4. Differentiate between exponential growth and logistic growth.
   • Understand the effect of population size on growth rate as it approaches carrying capacity.
5. Explain the significance of age structure in relation to potential population size.
   • Identify different survivorship curves based on examples.
6. Discuss trade-offs in life history traits and differentiate between r and K species.

Population Growth Models

Open vs. Closed Systems

• In an open system, the population size equation is:
  $N<em>{t+1} = N</em>{t} + B<em>{t} + I</em>{t} - D<em>{t} - E</em>{t}$
  where:

  • $N_t$ = Population size at time t
  • $B_t$ = Total births
  • $I_t$ = Immigrants
  • $D_t$ = Total deaths
  • $E_t$ = Emigrants

• In a closed system, the equation is:
  $N<em>{t+1} = N</em>{t} + B<em>{t} - D</em>{t}$

  • Focus: births and deaths only, no immigration/emigration.

Exponential Growth

• Exponential growth occurs under unlimited resource environments:
  • Population growth rates depend on $r$ (intrinsic growth rate):
    $\Delta N \Delta t = rN$
  • Example: Rabbits introduced in late 1800s
  • Became invasive due to lack of natural enemies; populations thrived.

Logistic Growth

• Logistic growth reflects density-dependent factors: $\Delta N \Delta t = rN\left(1 - \frac{N}{K}\right)$ where:
  • $K$ = Carrying capacity of the environment.
  • Growth rate decreases as $N$ approaches $K$.

Survivorship Curves

1. Type I: High survival in early life (e.g., humans), declining at older age.
2. Type II: Steady decline in survivorship throughout life (e.g., birds).
3. Type III: High mortality at early life stages but if survived, then steady declines (e.g., many fish).

Life History Traits

• Life History Strategy: Overall patterns of growth, development, survival, and reproduction in populations:
  1. Age and size at sexual maturity.
  2. Timing and quantity of reproduction.
  3. Survivorship rates.
• Trait Trade-offs Example:
  • Growth vs. reproduction: Early maturity yields more offspring but may lead to less survival.
• R vs. K Strategists:
  • r-strategists: Focus on reproduction (e.g., dandelions).
  • K-strategists: Focus on survival and resource acquisition (e.g., elephants).

Calculations and Examples

• To calculate intrinsic growth rate $r$ for exponential growth given:
  1. Initial and final population sizes over a period.
  2. Formula: $N<em>t = N</em>0e^{rt}$.

Important Remarks

• Population Demography: Studies factors determining size and structure over time. Age structure significantly influences growth and reproductive rates.
• Changes in age structure due to factors like fishing can lead to reduced population growth rates and sustainability issues.
• As populations approach their carrying capacity, fluctuations in size may occur, leading to potential regular cycles.

Application in Real Scenarios

• Understanding population dynamics is crucial for managing ecosystems, fisheries, and conserving biodiversity. Knowledge of both growth models and life history traits can inform effective conservation strategies.