The History to Getting Settled To Complete Reviews

The Leslie model is an approach to predicting the of an animal population after t (discrete) of time. The population is split up into a partitionMathworldPlanetmath of age according to in fecundity and survival rates in each . The population data are then related with a Leslie matrix. The form of a Leslie matrix is as follows:


Given n age for a population and 0jn, there is a fecundity rate Fj, which is the average number of offspring from a member of j who live long enough to enter the youngest age (zero of course) in a single unit of time, and a survival rate Sj, which is the percentage of members in the j who live to enter the j+1 in a single unit of time. These data are entered into a Leslie matrix like so:


In other , if A is a Leslie matrix, then a0j=Fj for all 0jn and a(j+1)(j)=Sj for all 0jn-1.

Given an initial population vector v that gives the number of members in each , the Leslie model predicts that the number of members in each after t of time is (At)v. The of time is customarily (but not necessarily) years.

Note that the Leslie can be thought of as to a Markov chainMathworldPlanetmath. The most important is that, since reproduction introduces new members into the population, the fecundity and survival rates in any given do not necessarily add up to one. Also, unlike most Markov chains, the next state for any member of the population is of course deterministicMathworldPlanetmath. 11A small in convention is that the Leslie matrix is usually to the left of the initial population vector when the two are multiplied, as compared to a Markov chain where the initial distributionPlanetmathPlanetmath is usually to the left. This plays a role in the of the matrices in either case.


  • 1 for WLF 448: Fish & Wildlife Population Ecology
Title The History to Getting Settled To CompletePlanetmathPlanetmath Reviews
Canonical name TheHistoryToGettingSettledToCompleteReviews
Date of creation 2013-11-27 10:59:44
Last modified on 2013-11-27 10:59:44
Owner jacou (1000048)
Last modified by (0)
Numerical id 20
Author jacou (0)
Entry type Definition
Classification msc 92D25
Related topic MarkovChain
Related topic Matrix
Related topic TransitionMatrix