untitled

There are three parameters, because we estimated α, β, and the residual variation in r:

p 3 = 3

AIC 3 =−38.236

As our final model, we consider an old standby, the geometric growth model

(Chapter 6). This model assumes that there is no change in growth rates as the

population increases over time (Fig. 15.6):

rmax=mean(r)

The residual variance or mean-squared error is:

σ=0.085

The likelihood calculation for the geometric growth model is:

Λ 4 =5.24 × 107

Λ 4

0

(^12)
2

1

2 2

exp

( )max

=

⎡−−

⎣

⎢

⎤

⎦

⎥

=

−

∏

i σ π σ

n

rri

σ = MSE

MSE

( )max

=

−

=

−

∑

rr

n

i

i

n 2

0

1

AIC 3 log ( )

=− +

−−

⎛

⎝⎜

⎞

⎠⎟

22

1

33

3

e p

n

np

Λ

262 Chapter 15

• 0.2
  0 500 1000 1500
  N

r

0.2

0

0.1

• 0.1

Fig. 15.6Predicted
(line) and observed
(circles) exponential
rates of increase shown
by Serengeti wildebeest
in relation to population
density, based on the
geometric growth
model.

15.4.4Geometric
growth model