Exercise 4. Recruitment of game birds. (9 points total) Imagine that in 2016, you were appointed to run a wildlife management area in Southwestern Oregon At this same time, an upland game bird stocking program transplanted 8 wild turkeys and 14 ruffed grouse into your area. You are in charge of determining the management target population sizes, with the intention of maximizing yield in the long term, as well as the sustainable harvest targets. A graduate student at OSU has recently determined that wild turkey population growth on your management area closely follows a Ricker curve. She estimates is 7 and is 0.003448. She also estimated that the grouse have Beverton-Holt recruitment dynamics. In this case, is 0.0012 and is 0.35 using the form of Beverton-Holt from the PPT not the form used in the video. ##The Ricker function: Recruits = alpha*N*exp(-beta*N) ##The Beverton-Holt function has various equivalent forms. ##In this problem use Recruits = 1/(alpha + beta/N)

C. What is the population size where sustainable yield (harvest) is expected to be maximized for each species? (3 points) Hint: to figure this out, you will first need to find the largest distance between the replacement line and each of the other lines. For each species, you can subtract the Y values of the replacement line from the recruitment function and save them as a vector. Then use the function which.max() to find the value of N where the difference is maximized. This will be the number of fowl producing the MSY.