the density gradient, which we have already suggested fuels a high rate of diffusion.
The net result is a population that explodes over both time and space.
Another interesting feature of the diffusion +exponential growth model is that a
standing wave of animals spreads over time across the landscape (Fig. 7.6), rather than
the gradually eroding “mountain” seen in the pure diffusion model (Fig. 7.5). This
wavelike form of spread is echoed in most models that incorporate population growth
as well as diffusive movement, such as those with logistic growth or predator–prey
models. The velocity with which this wave rolls across the landscape is identical in
virtually all such models: v= 2 √(λD).We should be able to discriminate between alternative models of population spread
by looking at population range versus time. If the rate of increase of the radius of
population distribution becomes less over time, then this deceleration would be
consistent with a pure diffusion process, in which population growth is not involved.
On the other hand, constant increase in radial spread of the population would be
most consistent with the diffusion +exponential growth model.
Skellam (1951) made this comparison using data on a population starting with five
muskrats (Ondatra zebithica) translocated into the countryside near Prague in 1905
(Fig. 7.7). Skellam’s analysis, supported by more rigorous analysis by Andow et al.
(1990), clearly demonstrated that the radial spread of muskrats increased linearly
over time, at a rate of 11 km/year (Fig. 7.8), thus supporting the exponential diffu-
sion model.
Similar analysis of the naturally recovering population of California sea otters
also supports the diffusion +exponential growth model (Lubina and Levin 1988),
although the pattern is more complex. Radial spread to the north was slower than
that to the southern California coast. Moreover, there seemed to be a dramatic jump
in the distance dispersed per year as the otters moved into sandy coastal areas with
less of their preferred rocky habitat.
Since those early days, there has been considerable development of alternative
models of population spread. These recognize directional bias on the part of theDISPERSAL, DISPERSION, AND DISTRIBUTION 103
7.6.3Empirical tests
of diffusion theory
(^1927) Breslau
Vienna
Münich
(^19201915)
1911
1909
1905
X
Fig. 7.7Spatial spread
over time of a small
population of muskrats
introduced into the
countryside near Prague.
(After Elton 1958.)