Dissertation - HQ

76 Spatial distribution of larvae
Non-explicitly spatial
regressions
agreement or dissimilarity between the two is assessed, taking spatial
autocorrelation (i.e. the fact that two neighbouring points are more
likely to have similar properties) into account (following the method of
Dutilleul et al. 183 ).
Even if we are interested in the spatial distribution of fish larvae,
what we are looking for ultimately are correlations with explanatory
factors (e.g. are larvae more abundant where temperature is higher?).
These correlations do not need to be explicitly spatial. Therefore, such covariations
between the abundance of larvae and environmental factors
were first examined with Principal Component Analysis (PCA) and
regression trees, considering each station as an independent data point.
PCA allows to examine several families in parallel in a multivariate
procedure. Regression trees hierarchise explanatory factors and allow
to use discrete and continuous explanatory variables together. The
variables tested to explain larval fishes abundance were taxonomic
(family), ontogenetic (flexion stage), temporal (rotation, time of day),
geographic (latitude, longitude, location with respect to the island,
i.e. windward, leeward), and hydrographic (depth of thermo-, halo-,
pycnoclines, and of the fluorometry maximum, temperature, salinity,
density, and fluorometry in the mixed layer — above the clines —, mean
current speed in the same layer). For correlated explanatory variables
(such as the depths of clines) each factor was assessed independently
and only the most explanatory one was kept in the final analysis.
Besides these general, exploratory analyses, some specific relationships
between larval fishes abundance and various physical factors were
tested using Generalised Linear Models (GLM) with a quasi-Poisson
error distribution family (which is appropriate for data expressed as
counts). Eventually, a multiple regression model, with the same error
distribution, was built to summarise the global picture. As a first step, all
physical but non-geographic variables were introduced in the model and
it was reduced to (1) keep only the most informative variable among
each set of correlated variables (e.g. one of the clines only), taking
in account the effect of interactions, (2) keep only significant factors.
In a second step, geographic variables (e.g. location) were added to
investigate whether some spatial trends remain and were not explained
by spatially varying physical variables.
All analyses were performed in R, with the additional packages
FactoMineR (PCA), mvpart (trees), akima and fields (spatial interpolation).
4.3 Results
4.3.1 Highly variable physical environment
Wind regime shift
The wind is usually quite steady in the region and this should have
allowed to repeatedly study the same location under equivalent physical
conditions. However the regime shift between trade winds and Northerly