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The questions in this section contribute to your assignment grade. Stars indicate the di'tcutty of the questions, as described on Canvas. Some species reproduce continuously while other populations reproduce on a more restricted schedule. For example, rodents generally reproduce during any season whereas deer mate only in the late fall. For the latter type of species, especially those with a relatively high annual mortality rate, discrete time models are often effective at describing how the population changes from year to year. A discrete time model is one in which the population size in one year determines the population size in the following year. A simple case is one in which resources are plentiful so that individuals never die and the population has a consistent average number of offspring a each year: Pn+l = (1 + OJPYL' (1) year. The 1 - P.\" on the right side is all the individuals that were around in the nth year and a . P\" is all of their offspring. Because a is an average it can be any positive integer. We can write down a general form where the next year's population size is an arbitrary function of the current year's population size: Here, R, is the population size in the nth Punt-1 = .f(P.)' (2) Model is referred to as a linear model because 9(a) = (l + (1)3: is a linear function. A more complicated population model is the general model with f(:r) = med1 T). (3) Here K, in units of population size, and 7", having no units, are both positive parameters. Because :2? is a population size, we add the domain restriction a: 2 0. We have not specied the units for population as it depends on the type of species which we do not specify at this point. Keep in mind that population size could be measured in units of thousands or millions of individuals so, for example, K 2. Describe in words how your graph would have to change if 1