ASU MAT 294 - INSTRUCTIONS FOR MODULE IV LAB

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INSTRUCTIONS FOR MODULE IV LAB • This will be a free-form lab. The instructions explain how to use the program and give some guidelines on values to try, but the questions are much less explicit than in previous labs. o Use the program to play with the population growth models o Examine how changing parameters change the outcomes o Ask specific questions. When you write up your lab report, be specific about what questions you asked and what answers you found. o Ask questions about all 3 models (described below). • The questions listed for each model are examples; you do not have to do all (or even any) of these. You do have to ask (and at least try to answer) some questions for each model though. • Hint: Model #3 will likely be the most interesting • Go to the following website: http://lsweb.la.asu.edu/rosenberg/bio294 o Download and extract the zip file containing the material for Module IV o The program has 4 parts: 1 part for choosing parameters, and 3 parts displaying graphs of the results of the simulation • The upper right window displays population size vs. time • The lower right window displays log population size vs. time • The lower left window displays population size at time t+1 vs. the population size at time t. This is a “cobweb” graph as demonstrated in class.o Individual graphs can be copied to the clipboard or saved to a file by pressing the appropriate button in the corner of each graph. You may want to use some graphs in your lab report. • Model # 1 – Single age class, unlimited population growth o Do not check “Multiple Age Classes” or “Enforce Carrying Capacity” o Examine how changing the growth rate effects the growth curve o Some suggestions (you can do anything you want, but these may make it a bit easier) • Keep the number of time steps low (< 50) • Keep growth rates low (< 1.5). • Try negative values of R (e.g., -0.2)? o Given what we learned in class, can you predict the final population size given the set of parameters? Does your prediction from a formula give the same value as the program? • Model # 2 – Multiple age classes, unlimited population growth o Check “Multiple Age Classes” • F1, F2, F3 are the fecundities of each age class, i.e., how many offspring are produced per individual of each age class • Si-j is the proportion of individuals from age class i that turn into class j. • Note: the lower left (cobweb) graph is not displayed for this model o Play with a variety of values in the matrices (starting population sizes, fecundities, survivorships). o How long does it take the population to reach a stable structure? Does changing the parameters make a big difference in how long it takes for this stability to be reached? Which parameters have the largest affect on the time it takes the population to become stable? • Try changing the # of time steps if you’re having problems seeing the graphs • Model # 3 – Single age class, limited population growth o Do not check “Multiple Age Classes”; Check “Enforce Carrying Capacity” o Examine how changing the growth rate effects the growth curve • Try a variety of growth rates over different ranges, e.g., < 1, 1 – 2, 2 – 2.5, 2.5 – 3, > 3 o For what parameters does the population reach the carrying capacity? Can you find cases where the population goes into periodic cycles? What happens if you’re initial population size is larger than the carrying capacity? Can you get a periodicity of 2? 4? 8? Can you find chaos? Does it stay chaotic forever (make # time steps a lot larger)? Can you drive the population extinct? Can you prevent extinction by changing the initial population


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ASU MAT 294 - INSTRUCTIONS FOR MODULE IV LAB

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