Simple Population Model Consider a very simple population

Simple Population Model • Consider a very simple population – Closed (no emigration, no immigration) – No fishing (no fishing mortality) – Only examine numbers (i. e. , growth not examined) Natural Mortality Recruitment Population Numbers Immigration Fishing Mortality Emigration Growth Popn Models 1

Simple Population Model • Define the following: § § Nt = Population size (numbers) at time t N 0 = Initial (time=0) population size b = Per capita recruitment (birth) rate d = Per capita mortality (death) rate Recruitment b Population Numbers d Natural Mortality Nt Popn Models 2

Simple Population Model Recruitment b • Consider this … Population Numbers d Natural Mortality • Draw this … Popn Models 3

Simple Population Model Recruitment b Population Numbers • Now consider this … d Natural Mortality • And draw this … Popn Models 4

Simple Population Model Recruitment b Population Numbers d Natural Mortality Nt • Define the following: § b. Nt § d. Nt • Construct a model for estimating Nt+1 from Nt • Construct a model for estimating Nt from N 0 Popn Models 5

Simple Population Model • What is r? • What are the population dynamics if … – … r = 0 – … r > 0 – … r < 0 • Are these dynamics realistic? Why? Popn Models 6

More Complex Population Model • If not realistic … • Then what is … Popn Models 7

More Complex Population Model • Consider this … • Draw this … Popn Models 8

More Complex Population Model • Consider this … • Sketch this (assume low N 0) … Popn Models 9

More Complex Population Model • Define equation for r • Substitute into exponential growth model and simplify Popn Models 10

Continuous Models • Popn Models 11

Continuous Models • Popn Models 12

Density Independent Popn Growth • Rate of change does not depend on population size (i. e. , density) Popn Models 13

Density Dependent Popn Growth • Rate of change does depend on population size (i. e. , density) Popn Models 14

Density Dependent Popn Growth • Rate of change does • … but not always in a linear fashion depend on population size (i. e. , density) … Popn Models 15