Geoscience Reference
In-Depth Information
ships. This test is based on Landau's linearity index, but takes the unknown
and tied relationships into account. An unknown relationship commonly
arises because two members of a dyad simply were not seen to interact. This
can occur for at least four reasons: sampling may be inappropriate, linearity of
the dominance hierarchy may be an artifact of experimental circumstances
(e.g., dispersal cannot occur in captivity), the formation of coalitions may lead
to mutual protection or mutual avoidance, and linearity may not be a feature
of the group's social structure (ultimately because the ecological circumstances
offer no selective advantage to linear dominance with regard to, for example,
resource holding potential). However, papers acknowledging the first two cat-
egories of problem are inevitably few.
The problems of elucidating a hierarchy and revealing its consequences are
illustrated by wood mice (
Apodemus sylvaticus
). Although some aspects of this
species' behavior can be studied in the wild (Tew and Macdonald 1994), their
small body size and large ranges thwart many studies and make them strong
candidates for observation in arenas (Plesner Jensen 1993) or seminatural
enclosures (Bovet 1972a, 1972b). Bovet (1972b) found that male wood mice
of different statuses tended to be active at different times. Therefore, they
rarely met, which thwarts study of their encounters. Such problems can be
partly circumvented by the use of sociometric matrices. Because it illustrates
the use of matrices, we will go step by step through Stopka and Macdonald's
(in press) sociometric study of wood mice. Based on videotaped interactions of
nine mice observed over 3 months, the frequencies of transition between fight
or chase and avoidance for all individuals in the colony were ranked (table
10.1).
Each of these matrices can be analyzed for linearity in the relationships
between the mice (a task swiftly performed by options in the package
MATMAN
).
In the case of avoidance (table 10.1), this provides a statistic (Kendall's linear-
ity index
K
= 0.775), which indicates that the null hypothesis that avoidance
relationships are randomly distributed can be rejected in favor of the alterna-
tive that they are linearly ordered (
c
2
= 43.76,
df
= 20.16,
p
= 0.005). Similarly
for allogrooming (
K
= 0.592), there is significant linearity (
c
2
= 34.96,
df
=
20.16,
p
= 0.03). However, linearity in avoidance relationships is stronger (
p
=
0.005) than that in allogrooming relationships (
p
= 0.03), raising the possibil-
ity that linearity in grooming merely reflects that in avoidance. The statistical
tool to test this hypothesis is the
Kr
row-wise matrix correlation test (de Vries
et al. 1993; de Vries 1995). When applied to the avoidance and allogrooming
matrices (in which the rows and columns are identically ordered), this reveals a
