untitled

and morphological varieties that differ from central populations (Lesica and

Allendorf 1995).

Many species of wildlife have been eliminated from their traditional range, for one

reason or another. This can even happen to common species, like the plains bison

(Bison bison). Europeans arriving in North America encountered millions of bison on

the Great Plains. In remarkably short order, this massive population was nearly extir-

pated, through a combination of commercial hunting by Europeans and subsistence

hunting by aboriginal groups, competition with livestock, and fencing off of migra-

tion routes (Isenberg 2000). Since the turn of the century, the plains bison has been

re-established by wildlife authorities to parts of its former range, though in nothing

like its former abundance. Such reintroductions are becoming ever more common.

In other cases, species have naturally recovered from catastrophic decline, expand-

ing into their former range. A well-documented example is the California sea otter

Enhydra lutris (Lubina and Levin 1988). This species was nearly exterminated

throughout its Pacific coast range through overharvesting by fur traders in the late

nineteenth century, before a moratorium on harvesting was signed in 1911. A small

relict population of otters survived in an inaccessible part of the California coast south

of Monterey Bay. This small population provided the nucleus for gradual spread of

the population both northwards and southwards along the coast.

Whether intentional or accidental, such reintroductions have some fascinating char-

acteristics that have important bearing on their successful conservation. Key among

these is the interplay between demography and patterns of movement.

Although there are many elegant ways to model patterns of movement by invasive or

reintroduced species (Turchin 1998), simple random walk models can often predict

the pattern of spread surprisingly well. We first consider what is meant by a random

walk, then use this algorithm to develop a simple model of population distribution.

What pattern would emerge over time, for a single individual that moves randomly

every day of its life? We will assume that this hypothetical animal can only move

forwards, backwards, or sideways, one step at a time. We further assume that each

of these events is as probable as remaining where it is. To model this, we need to

sample randomly from a uniform probability distribution (see Box 7.1).

DISPERSAL, DISPERSION, AND DISTRIBUTION 99

7.6 Species reintroductions or invasions

7.6.1Diffusive
spread of
reintroduced species

We first need to randomly sample a large number of values uniformly distributed between 0 and 1,

assigning each random number on this interval to either the variable por the variable q. We then use

these probabilities to mimic forwards versus backwards movement using the variable xand side-

to-side movements using the variable y, using the logic shown below. As a result of this logic, an

animal would move left one-third of the time, right one-third of the time, and stay on track one-third

of the time. Similar probabilities correspond to forwards, backwards, and stationary outcomes.

y

yq

yq

y

t q

tt

tt

t

+= t

−<

1 +>∧<

1 0 333

1 0 333 0 667

.

.

.

if

if

otherwise

x

xP

xP P

x

t

tt

tt t

t

+=

−<

1 +>∧<

1 0 333

1 0 333 0 667

.

..

if

if

otherwise

Box 7.1Modeling a
random walk in space.