Population Dynamics

Populations are dynamic entities.
Size and composition fluctuate in response to numerous factors:
     — seasonal and yearly changes in the environment
     — natural catastrophic events:
          forest fires, volcanic eruptions, hurricanes, drought, etc.
     — competition for resources between and within species.
Demography: statistical study of populations
     — Set of mathematical and graphical tools which describe populations and how they change.
     — Many of these tools were designed to study human population. (these will examined in more detail in another lecture)

Survivorship Curves

Graph of number of individuals surviving at each age interval versus time.
Type I:
     — Low mortality in early & middle years.
     — High mortality in older individuals.
     — Few offspring. Provide good care.
     — Humans and large mammals
Type II:
     — Mortality relatively constant; equally likely to occur at any point in life span.
     — Birds and small mammals
Type III:
     — Early ages experience highest mortality
     — Produce large numbers of offspring.
     — Provide little or no care.
     — Fish, trees and marine invertebrates

Population Growth

Deterministic equations to describe rate of change in size of population over time.
     — does not account for random events
Two basic models:
     — Exponential growth
     — Logistic growth
Neither model perfectly describes natural population growth.
     — provides points of comparison

Exponential Growth

Early pattern of accelerating population size
     — populations with abundant natural resources grow very rapidly
Growth Rate: number of organisms added in each reproductive generation
     — Often expressed as a multiplier factor (1x, 1.5x, 2x, 2.3x)
Exponential Population Growth: N_f = N_i + rN_i
     — N_f is the final population number
     — N_i is the initial population number
     — r is the growth rate
          — Can be positive: growing population
          — Can be zero: unchanging population size
          — Can be negative: shrinking population
Exponential Growth Curves

American Plains Bison

Plains region of U.S. originally supported 15 to 100 million bison.
1800’s: hunters decimated the wild bison populations.
     — aided by advancements in transportation and weaponry
1889: estimated 1,000 bison.
Early 1900’s: Programs to save bison from extinction.
Establishment of protected herds.
Herds started small, but grew quickly.
     — Due to plentiful resources and few predators.
Bison population in National Bison Range increased from 37 in 1909 to 577 in 1922.

Logistic Growth

Limited resources means that exponential growth cannot continue indefinitely.
Exponential growth may occur in environments where there are few individuals and plentiful resources.
When number of individuals grows large:
     — Resources will become depleted or limited by replacement processes.
     — Growth rate will slow down.
Growth rate will plateau or level off.

Carrying Capacity

The maximum population size that a particular environment can sustain.
     — K = carrying capacity
     — number of individuals that can be added to a population and supported by the environment.
Population growth can be express with the equation:
Logistic Population Growth: N_f = N_i + rN_i × [(K − N_i)/K]
For small populations, growth will be close to exponential.
But as population increases, the limiting factor becomes greater, slowing growth.
Growth rate then levels off as population numbers approach the carrying capacity.

Logistic Growth

Logistic Growth Curves

Flour Beetle (Tribolium confusum)

8 pairs of beetles were placed in 16 grams of flour.
32 pairs of beetles were placed in 64 grams of flour.
Flour was renewed every 13 to 23 days (17 days average), and the number of beetles were counted.
Limited food supply, limits number of beetles that can survive.
Notice that population size exceeds carrying capacity a short periods of time and then falls below the carrying capacity.
Population size then tends to oscillate above and below the carrying capacity.

Intraspecific Competition

Logistic model assumes that every individual within a population will have equal access to resources.
     For plants: water, sunlight, nutrients, space to grow
     For animals: food, water, shelter, nesting space, mates
Carrying capacity can also be reduced by the accumulation of waste.
Phenotypic variation among individuals means some individuals will be better adapted to their environment than others.
Intraspecific competition: Competition for resources among population members of the same species.

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