untitled

Scaling the wolf consumption rate to a yearly time frame yields estimates of

A=12.3 moose /wolf / year and B=0.47 moose / km^2. According to Fuller and Keith

(1980), each wolf needs to eat 0.06 kg of meat per day to meet maintenance require-

ments, whereas a population whose individuals eat 0.13 kg each day can grow at the

maximal rate. This yields estimates of D=0.6 and E=0.1.

Combining these parameter values together, the outcome is a complex series of oscil-

lations in moose and wolf abundance, which never quite repeat themselves (Fig. 12.11).

This is a mild form of deterministic chaos, common in tri-trophic systems (Hastings

and Powell 1991; McCann and Yodzis 1994). Even though the fluctuations are

non-repetitive, the time between successive peaks tends to be several decades – a

very protracted pattern of fluctuation.

The manner by which parameters for the wolf–moose–woody plant model were

derived, using a set of observations gathered around the globe, makes it fairly

unlikely that we can predict the dynamics of any given system. It does suggest, none-

theless, that this system should exhibit an inherent tendency towards protracted

fluctuations that recur over a decade-long time scale. Moreover, the model suggests

CONSUMER–RESOURCE DYNAMICS 209

10

1

0.1

0.01

1·10–3

1·10–4

1·10–3

1·10–5

1·10–7

1·10–9

1·10–11

1·10–13

1·10–15

1

0.1

0.01

0 100 200 300 400 500

Year

0 100 200 300 400 500

Year

Wolves / km

2

Moose / km

2

Fig. 12.11Predicted
population dynamics
of moose (top) and
wolves (bottom) based
on Turchin’s (2003)
tri-trophic model,
described in the text.

12.6.3Dynamics of
the wolf–moose–
woody plant system