Overview (see Mills 91 - 99)
Exponential Growth Model
Unlimited, constant, favorable environment (i.e., population growth rate remains constant).
Age-specific birth and death rates remain constant (i.e., population has a stable-age distribution).
Constant unfavorable environment. Survival and/or reproduction are consistently below sustainable levels.
Stochastic Exponential Growth Models (see Humbert et al. in review):
Stochastic: involving a random variable; a random outcome
A random variable (e.g., number of offspring) is one that can take more than one value in which the values are determined by probabilities.
Statistical Distributions and random outcome (Examples: uniform, normal, log-normal)
a. Observation Error
b. 'Process' variation: environmental stochasticity bumps the population around
c. 'State-space' model (both observation error and process variation)
Limited environments cause age-specific birth and/or survival rates to decline with increasing population size.
Logistic (Ricker) Growth Model
Growth rate (i.e., birth rate and mortality rate) is a decreasing linear function of population size
Other Density-dependent Growth Models
Gompertz
Theta-logistic
Allee (W.C. Allee 1931)