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ESPM-EEP%202010%20Lecture%2021

ESPM-EEP%202010%20Lecture%2021 - ESPM 104/EEP 115 Fall 2010...

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ESPM 104/EEP 115 Fall 2010: Lecture 21 1. Stochasticity (the influence of random processes and events). demographic : whether individuals live or die depends on the throw of a biased die, so does the size of a litter environmental : effects of the environment on individuals have a random component—e.g. good and bad years for food resources measurement errors : counts of individuals alive, of newborns, of deaths are subject to errors process errors : models do not include all the process that affect population change (e.g. migration may be ignore, or deaths from disease) 2. Consider: x i + 1 ( k + 1) = s i x i ( k ) If x i ( k ) = 3 individuals and s i = 2 / 3 then we expect x i ( k + 1) = 2 However, in reality, x i ( k + 1) = 0,1,2, or 3 each with a different probability: x i ( k + 1) = 2 is only the most likely of the four possible outcomes each of which is given by the binomial distribution with p =2/3 and n =3; P ( r ; p , n ) = Pr{ x i ( k + 1) = r | x i ( k ) = n , s i = p } x i ( k + 1) = 3 P (3;2/3,3) = (2/3) 3 =8/27=0.30 x i ( k + 1) = 2 P (2;2/3,3) = 3(1/3)(2/3) 2 =12/27=0.44 x i ( k + 1) = 1 P (1;2/3,3) = 3(1/3) 2 (2/3) =6/27=0.22 x i ( k +
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