An important model that is used in population biology and ecology is the Ricker model

Chapter 13, Problem 65

(choose chapter or problem)

An important model that is used in population biology and ecology is the Ricker model. The Canadian biologist William E. Ricker introduced this model in his paper Stock and Recruitment (Journal of the Fisheries Research Board of Canada, 11 (1954) 559 623). For information on Ricker himself, see the web page http://www.science.ca/scientists/scientistprofile.php?pID=17 The general form of the Ricker model that we will use here is defined by a recursive sequence of the form are positive constants 0. (a) Suppose that the initial size of a population is P0 300 and that the size of the population at the end of year t (continues)is given byUse a graphing utility to compute the population sizesthrough the end of year t 5. (As in Example 5, roundthe final answers to the nearest integers.) Then usethe graphing utility to draw the population scatter plotfor t 0, 1, . . . , 5. Describe in complete sentenceshow the size of the population changes over this period.Does the population seem to be approaching anequilibrium level?(b) Using a graphing utility, compute the sizes of the populationin part (a) through the end of the year t 20,and draw the corresponding scatter plot. Note that thepopulation seems to be approaching an equilibriumlevel of 1609 (or 1610).(c) Determine the equilibrium population algebraically bysolving the following equation for Pt1. For the final answer,use a calculator and round to the nearest integer.Hint: Divide both sides of the equation by Pt1, andthen use the techniques of Chapter 5.