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  3. lets consider this very simple population dynamics matrix 08 02...

Question: lets consider this very simple population dynamics matrix 08 02...

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Lets consider this very simple population dynamics matrix. 0.8 0.2 Think of this as 교 model for a very simp c form where the population is divided into young and mature The first row says that during each time pe o cung member eads on average to .8 young members at the beginning 0 the next life cycle and cac 0.2 mature members (i.e. some of them qrow into the mature stage. 5o, for example, it we started with 100 young, atter one time period we would have 80 young surviving as young and 10 having orown into mature specimen. The others died) The second row ot the matrix tells us that the mature specimen each time period produce on average) 1 young specimen, but they themselves die out. 5o it there were 100 mature individuals at the beginning of a time period, trom those we would have 100 young at the end of the period but no matures. (rhey all died) Suppose we started with 10U young and 10U mature individuals, what would the model predict at the end of une time period? Number of young- After two time perods, what does the model predict? Number ot young- Notice that as time passes, the population appears to stabilize. Run thizs model into the distant future and give the ratio of young individuals to mature individuals. orexample, if the population stabilized at around 5D young and zo0 mature, that would be a ratio of number of mature- number of mature - 3.75 to 1 The asymptotic ratio of young to mature is about to 1

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