From this we obtain the residual standard deviation:
σ=0.04
The likelihood calculation for the theta logistic model is calculated in a similar man-
ner as we did for the Ricker model, except that we modify the expected value and
the residual variance:
Λ 2 =1.681 × 1013
p 2 = 4
Note that we now have four parameters (rmax, K, θ, and the standard deviation of the
residuals around the linear regression line), necessary for the more complex, non-
linear model:
AIC 2 =−49.573
AIC 222
2
22
1
log ( )
=− +
−−
⎛
⎝⎜
⎞
⎠⎟
e p
n
np
Λ
−− −
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rr
N
i K
i
max^1
2
2
2
θ
σ
Λ 2
0
(^11)
2
= exp
−
∏
i σ π
n
σ = MSE
MSE
(^) max
−−
⎛
⎝⎜
⎞
⎠⎟
⎡
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=
−
∑
rr
N
K
n
i
i
i
n
1
2
0
1
θ
260 Chapter 15
0.1
0
- 0.1
- 0.2
- 0.3
0 500 1000 1500
N
r
Fig. 15.4Predicted
(line) and observed
(circles) exponential
rates of increase shown
by Serengeti wildebeest
in relation to population
density, based on the
theta logistic model.