Population Growth Analyses

I) Discrete Population Models (Nt to Nt+1)

1. Discrete Generations:

         a. Single annual breeding season & life span of one year

         b. Nt+1 = RoNt where:

                     Nt = pop. size females at generation t

                     Nt+1 = pop. size females at generation t+1

                     Ro = net reproductive rate, # female offspring/female/generation

2. Multiplication Rate Constant

         a. Geometric Growth

3. Multiplication Rate Dependent on Population Size

         a. Density dependence

         b. Population dynamics

                     i. fluctuate little

                     ii. fluctuate chaotic manner (unpredictable)

                     iii. cycles (up and down)

         c. Simplest relationship- pop. increase, reprod. decrease

                     i. linear relationship

                     ii. Equilibrium: Point where line crosses Ro=1

         d. Population density in terms of deviation from equilibrium:

         e. Change slope or B in model

                     i. Relationship between density and reproductive rate

                     ii. Very different patterns of population change

         h. Simple population model produce diversity trajectories

II) Overlapping Generations Population Models

         1. Continuous breeding season

         2. Continuous form model: Differential equations

         3. Multiplication rate constant where r = b-d

         4. Use equation estimate doubling time population� t = 0.69315/ r

5. Most populations do not follow geometric increase

6. Multiplication rate is a function of population size

            a. Density-dependent

            b. Limiting factors such as space etc.

            c. Logistic or S-shaped or Sigmoid curve

7. Differential Form basic logistic curve: dN/dt = rN((K-N)/K)

            K = carrying capacity

8. Integral Form of basic logistic curve:

9. Laboratory test fit data to logistic curve:

10. Reject notion � logistic is the �law� governs population growth