Biology Reference
In-Depth Information
Using the uniform null model, the average
P
mean
of the adults is
2
0.267 and the range is
0.1689, an interval that excludes zero. This result also suggests a non-random
distribution, with distances being smaller than expected under a random uniform model.
Using the Gaussian model,
2
0.3365 to
2
the average
P
mean
52
0.2636 and the range is
0.3312
2
to
0.2036, an interval that also excludes zero. As we found for the juveniles, the data
argue against the null hypothesis of a random distribution, and also against over-
dispersion. Therefore, we now explicitly test the hypothesis of clustering.
We now test the hypothesis of clustering using the narrower estimate of the range. For
the juveniles, based on the uniform model, the average
P
mean
52
2
0.3172 with a range
of
0.2247, an interval that excludes zero and supports the hypothesis of
clustering. Analyzing the data under the null Gaussian model, the average
P
mean
52
0.3813 to
2
2
0.3006
with a range from
0.2372, an interval that again excludes zero. Taking
these results altogether, they suggest that juvenile piranha body shapes are more tightly
clustered than expected under either null model.
For the adults, the uniform null model yields an average
P
mean
52
0.3700 to
2
2
0.2537 and a range
of
0.1788, an interval that excludes zero. These results again support the infer-
ence of clustering. Analyzing the data under the Gaussian null model,
0.3092 to
2
2
the average
P
mean
52
0.1598, an interval that also excludes zero.
Taking these results altogether, they suggest that adult piranha body shapes are more
tightly clustered than expected under either null model.
Nearest-neighbor analysis can be used to examine patterns of variation as well as
disparity. To exemplify this, we return to the ontogenetic variation in mouse skulls.
Considering that each sample comprises individuals from a single homogeneous popula-
tion, we would expect random variation to follow a Gaussian distribution. Results of
analyses based on both range estimators (i.e. the parameter values estimated using the
Strauss
Sadler estimate of the range (SS), and those estimated from the data (DP)) are
given in
Table 10.3
. It is difficult to argue that the data suggest a departure from random
variation. When the parameter estimates are based on an expanded range, the two
youngest samples seem to be more clustered than expected under the null hypothesis of a
Gaussian distribution. That expansion seems appropriate in light of the small sample sizes,
but using it could be considered an overly liberal test of clustering. When estimates are
0.2388 with a range from
0.3091 to
2
2
TABLE 10.3
Nearest-Neighbor Analysis of Skull Shape Variation in M. m. domesticus, Sampled at 5-Day
Intervals (Average P
mean
and the Range of P
mean
Obtained from 100 Monte Carlo Simulations)
Age
SS (P
mean
)
DP (P
mean
)
Average
Range
Average
Range
10
0.0929
(
0.1356)
(
0.0276)
0.0028
(
0.0425)
(0.0377)
2
2
2
2
2
15
0.0944
(
0.1503)
(
0.0334)
0.0153
(
0.0326)
(0.0598)
2
2
2
2
20
0.0409
(
0.0963)
(
0.0178)
0.0126
(
0.0313)
(0.0658)
2
2
2
2
25
2
0.0745
(
2
0.1343)
(
2
0.0051)
0.0122
(
2
0.0495)
(0.0654)
Parameter estimates are based either on the Strauss
Sadler estimators (SS) or on the parameters of the data (DP).
