Study Notes on Population Size and Growth Patterns

Population Size and Survivorship Curves

Survivorship Curves

• Definition: Survivorship curves are graphical representations of the number of individuals in a population that survive to different ages.

Types of Survivorship Curves

1. Type I (Humans)

   • Characteristic: High survival rates during early and middle life, with a steep decline in survivorship as age increases.
   • Implication: Indicates a population with lower mortality rates early in life and significant mortality at later ages.
   • Example: Humans exhibit Type I survivorship curves, where most individuals live to adulthood, but mortality increases sharply in older age.

2. Type II (Birds)

   • Characteristic: A constant mortality rate regardless of age; individuals are equally likely to die at any age.
   • Implication: Reflects an intermediate survival strategy, ensuring some individuals survive to old age while others may die young.
   • Example: Many bird species demonstrate type II curves, maintaining a steady death rate across their lifespan.

3. Type III (Trees)

   • Characteristic: High mortality rates in early life stages with relatively low rates for those who survive youth.
   • Implication: This strategy reflects high offspring production with the expectation that many will not survive to maturity.
   • Example: Trees produce numerous seeds; however, only a small fraction survive to maturity due to environmental factors.

Exponential and Logistic Growth

• Definition: These terms refer to the patterns of population growth over time, influenced by factors such as resources and carrying capacity.

Exponential Growth

• Characteristics: A rapid increase in population size when resources are unlimited.
• Graphical Representation:
  • Population size increases sharply over time.
  • Visual representation shows the curve rising steeply, indicating growth without constraints.
• Formula: $N(t) = N_0 e^{rt}$
  • Where:
    • $N(t)$ = population size at time $t$
    • $N_0$ = initial population size
    • $e$ = base of the natural logarithm
    • $r$ = rate of growth
    • $t$ = time

Logistic Growth

• Characteristics: Growth that occurs when resources are limited, leading to a stabilization of population size at carrying capacity.
• Graphical Representation:
  • Initially resembles exponential growth but begins to level off as it approaches the carrying capacity.
  • The population grows quickly, then slows down, stabilizing around a certain maximum size.
• Carrying Capacity:
  • Definition: The maximum number of individuals that an environment can sustain due to limitations in resources (food, space, etc.).
  • Visual representation shows a horizontal asymptote as the population reaches this capacity.
• Formula: $N(t) = \frac{K}{1 + \frac{K-N<em>0}{N</em>0} e^{-rt}}$
  • Where:
    • $K$ = carrying capacity
    • Other variables are as described above.