Ecology midterm Pt 1 answer key - Name Student ID 1 When...

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Name: Student ID: 1. When the first 1000 humans settled in California there was a resident population of 45,000 saber-toothed cats (= time t), and whose overall population carrying capacity (K) was estimated to be 50,000. The humans and cats competed for mammoths as prey. The per capita reproductive rate of cats is unknown. Assume the cat population is accurately described by a Lotka-Volterra competition equation, how large must have been the competition effect ( α ) of humans on the cats for the cat population to decline in t+1 rather than increase? Please show your work. (30 points) Note that the LV equations contain two terms: the size of the present population and the expected change over the next generation. If that change will be a decline, then the following must be true (independent of what value r would be): 𝐾 1 𝑁 1 𝛼𝑁 2 < 0; substituting from the given values, we can solve for alpha. 50000 45000 𝛼 (1000) < 0 5000 𝛼 (1000) < 0 −𝛼 (1000) < 5000 −𝛼 < 5 𝜶 > 𝟓 2. An acre of tropical rainforest may contain over 100 species of trees.
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