AEC 360  Ecology

Lecture 13:  Population size and growth

I.  Populations
    A.  Fundamentals
        -- Definition: All the individuals of a species that live in an area
        -- Question:  how large is the population?
        -- Question: how is population size changing?

    B.  Properties of populations
        1. Population size
          - Number of individuals
          - Density
          - Biomass

        2.  Rate of change
            -Additions to the population
              Birth rate
              Immigration rate 

            -Subtractions from the population
              Death rate
              Emigration rate

    C.  Estimating population size

       1.   Census: all individuals in population counted

       2.  Estimate of local density (= individuals/area): count all individuals in particular area then multiply by total area of population

       1.  Mark-recapture studies
                -Capture and mark as many animals as possible
                -Release them back into the population
                -Capture as many animals as possible, determine proportion marked

    D.  Lincoln-Peterson index:  Marked animals in 2nd sample/Total caught in second sample  =  # individuals originally marked/Total population size (N)
        1.  Assumptions
            -- All individuals equally likely to be captured
            -- No change in population size
            -- No marked individuals are lost

III.  Population growth
    A.  Simplest models assume:

        1. All individuals are identical
        2. No age differences
        3. No genetic differences
        4. No evolution
        5. Birth and death rates are constant
        6. No immigration or emigration
        7. Habitat is perfectly uniform

    B.  Is there every unlimited growth?  Examples

        - Best approximates population growth when a population is small 

   C.  Discrete, or geometric population growth
        1.  Lambda is the geometric rate of increase, or the ratio of population size in one year to that in the preceding year
        2.  N(t+1)/N(t) = lambda 

        3.  N(t) = N(0)*lambda^t 

    E.  Continuous population growth
        1.  Change in population size per unit time equals the population size times the growth rate
        2.  dN/dt = rN
        3.  r equals the birth rate minus the death rate
        4.  r is the per capita rate of increase
        5.  Rate of increase is proportional to the population  size
        6.  In unlimited growth, r never changes
        7.  N(t) = N(0)*e^rt

    G.  Intrinsic growth rate determined in part by the environment