107 chapter 5 structural equation models sem

107
Chapter 5
Structural Equation Models (SEM) Predicting Species Recurrence-index
SEMs were used to predict each species’ recurrence-index, a continuous response
variable that measures both how many times a species was observed in an occupied cell and a
measure of its abundance in the cell. In general, the SEMs explain more of the observed
variation in the spatial distribution of smaller grazers than larger grazers (Fig. 5). The SEM for
Thomson’s gazelle explains 39% of the overall observed variance in their recurrence-index,
whereas the SEM for buffalo explains only 3%.
The correlations between exogenous environmental variables (i.e. variables on the far
left of Fig. 5) are less than 0.35 for all SEM’s, with the exception of rainfall, woody cover, and
distance to drainage beds for the Thomson’s gazelle SEM and the Grant’s gazelle SEM only. The
small correlation between the exogenous variables suggests that the unique variation of the
variables is high and therefore the conceptual nature of the composite variable is not
confounded by other variables. The correlations between exogenous variables change between
the SEM’s for each species because they occupy different areas. The SEM reflects the real corre-
lation among the variables in the habitats the species occupies.
Previous SEM’s included proximity to humans and water as additional variables
accounting for the variation in the recurrence-index, however these models were not supported
by the data. This suggests that the factors that predict a species recurrence-index are a subset
of those predicting presence/absence.
The chi-square associated with the SEM describing the buffalo recurrence-index
suggests the data supports our a priori interpretation ( χ
2
=5.99, df=7, p=0.540), however the
model explains very little of the overall observed variance (3%) (Fig. 5a). Only the abundance
of food (as estimated by rainfall and the topographic wetting index) is significant in explaining
the variation in the buffalo recurrence-index (standardized path strength = 0.14). The exposure
to predation risk (as estimated by the amount of woody cover available to ambush predators,
the distance to riverbeds, and the landscape curvature) is not significant in explaining the
buffalo recurrence-index. The amount of nitrogen available in the grass (i.e. forage quality) only
explains 0.02 of the variation in the buffalo recurrence-index and was also not significant.
The data on the recurrence of Coke’ hartebeest support the structural equation model
(χ
2
=6.52, df=7, p=0.480). The SEM describes 8% of the variation in Coke’s hartebeest recur-
rence-index, which is negatively related to food quality (standardized path strength = -0.13),
food abundance (-0.19) and risk of predation (-0.17) approximately equally (Fig. 5b).
The recurrence-index of topi is positively related to the abundance of food (0.36),
while the risk of predation and food quality had non-significant negative trends. The SEM
describing the topi recurrence-index is supported by the data (χ
2
=9.57, df=6, p=0.144), and
accounts for 14% of the overall observed variance (Fig. 5c).