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

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 +