does not arise because no quadrats are involved, but no simple measure is presently
available for distributions of distances that clearly differentiates classes of dispersions,
one from the other, given the wealth of possible dispersions. However, J.M. Cullen
and M. Bulmer (in Patterson 1965) provide a formula for calculating the random dis-
tribution of inter-individual (or intergroup) distances in a known area. Given the
same number of individuals N, distributed randomly with respect to each other in
the same area A, then the proportion (p) of individuals having their nearest neigh-
bor at a distance xis given by the expression:
px=exp[(−πN/A)(x−0.5a)^2 ] −exp[(−πN/A)(x+0.5a)^2 ]
where ais the unit of measurement used. The number at distance xis Npx. Thus, if
one observes 200 birds in an area of 2 km radius (A=12.57 × 106 m^2 ), and obser-
vations are in units of 50 m (=a), then the expected frequency of distances at the
nearest interval (x 1 =25 m) is 23.5, that at the next interval (x 2 =75 m) is 55.2, and
so on until the sum of Npxequals 200. We see that the increments of xmust start
with the first one equal to 0.5a(midpoint of the first interval) and then increase
in increments of a(thus 25, 75, 125, 175, etc.). By comparing this frequency of
distances with the observed frequency one can identify clumped or overdispersed
distributions.
Dispersion is affected by the home rangeof individuals, that is the area used
during the normal daily activities. Traditionally, home ranges are estimated from
radiotelemetry locations (usually >30 locations are required) using computer soft-
ware packages. Habitat type affects range area (Relyea et al. 2000), as does the
gender of the individual (McCullough et al. 2000). Some species have tight habitat
preferences, their dispersion reflecting where that habitat is to be found. Others are
more catholic in their requirements and will therefore be distributed more evenly
across the landscape. The ecology of the dispersion is important. Dispersion can be
measured more directly, however, by the average distance between locations (Conner
and Leopold 2001). We considered the concept of home range in Chapter 5, in which
we outline methods of determining the key determinants of home range use.
When we design surveys to count wildlife (see Chapter 13) we have to pay atten-
tion to its dispersion and allocate our sampling units accordingly. We explore this
practical aspect of dispersion more fully in Section 13.4.
Krebs (2001) considered that “the simplest ecological question one can ask is sim-
ply: Why are organisms of a particular species present in some places and absent in
others?” There are several interesting ways that this question can be answered. We
start with a consideration of the ultimate limits of a species’ range, before going on
to consider the distribution of introduced or invading species and finally to consider
patterns of occupancy in spatially subdivided populations (metapopulations).
Figure 7.2 shows three hypothetical distributions, not as a map but as a plot within
a range of mean annual temperature and mean annual rainfall. For species A, tem-
perature and rainfall act independently of each other in setting limits to distribution.
A single mean temperature and a single mean annual rainfall is all one needs to pre-
dict whether or not the species will be in a given area.
The distribution of species B is also determined by temperature and rainfall but
this time in an asymmetric interactive manner. Distribution is determined absolutely
DISPERSAL, DISPERSION, AND DISTRIBUTION 93
7.4 Distribution
