EEB 3408W Lecture 2: ecology lecture 2

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Birth rate ,death rate ,emigration and immigration determine population size. Assumptions for simple model: population is closed or immigration and emigration balance (no net movement) Birth and death determin popn density: individuals are identical (have the same birth/death rate, parthenogenetic females (do not worry about different reproduction, paradise: infinite resources. N(t) = popn size as a continuous function of time (t) B = instantaneous birth rate per individual. D = instantaneous death rate per individual. R = intrinsic growth rate per individual dn / dt = (b-d)n. Per capita growth rate = dn/ndt = r; growth rate / population. Integrating the differential population growth equation over time. R = intrinsic growth rate of individual (birth - death rate) Gives a number instead of a rate. Reminder: integral of 1/x = log x + c (1/n)dn = rdt. Integrate nt to n0 = integral of t to t0 rdt ln(a) - ln(b) = ln(a/b)

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