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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 Fall '10
 WayneM.Getz
 Poisson Distribution, Probability theory, Method Euler starttime, answer xi +1

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