How populations grow, reproduce and distribute themselves Population Ecology How populations grow, reproduce and distribute themselves

Mathematical modeling principles Models are a gross simplification of reality. Models are only as accurate as your: Equations – variables included in model Data used for model Consider weather prediction: Accurate only to a few days. Often right for big picture, wrong for details. Best models have dozens and dozens of variables. Real world is still much more complicated.

Population growth What factors increases the size of a population? Decreases a population? How can we represent this mathematically?

Population growth Births (B) Deaths (D) ΔN = B – D

r = B – D

Exponential growth Continuous Nt = N0ert Discrete Nt+1 = λNt

Carrying capacity Are there limits to population size? How do we represent such limits?

Logistic growth More realistic than exponential growth Includes carrying capacity variable (K) Nt = K/1+[(K-N0)/N0]e-rt

Other missing variables What other variables are missing in effectively modeling population growth? ?

Leslie matrix modeling Includes many factors ignored in other models. Based on 2 matrices (boxes of numbers). 1 - Number of individuals in each age group/stage. 2 - Survival/fertility probabilities Now Future

Add carrying capacity of environment EXPONENTIAL Add ages/stages Predation/Competition/Disease, etc. LOGISTIC MATRIX MODELS

Life history (r/K)

Human demography