2.5. Discussion
To predict how the spatial distribution of marine species may
change with climate, it is essential to understand the factors that limit their
distributions. One way to achieve this is to use ecological niche models.
However, only a limited number of models can deal with presence-only data. The
models BIOCLIM and HABITAT use a rectilinear volume and a convex envelope
(i.e. a closed polygonal chain), respectively (Carpenter et al. 1993).
The drawbacks to these simple models are the imposed shapes, which can be the
cause of a non-justified exclusion or inclusion of a geographical point from
the predicted distribution (Carpenter et al. 1993). The model DOMAIN can solve
this problem by the use of a point-to-point similarity metric. However, the
metrics used (e.g. the Gower metric; Carpenter et al. 1993, Legendre
& Legendre 1998) does not take into account the correlation between
descriptors (Legendre & Legendre, 1998). Furthermore, a threshold is used
to map the modelled distribution of the species. The RES model (Kaschner et al.
2006) uses a trapezoid shape that constitutes a good compromise between species
with a shorter or a unimodal ecological niche and migratory species with larger
or a bimodal niche (Kaschner et al. 2006). However, the bounds of this
trapezoid need to be precisely defined, implicating often arbitrary choices and
thus it requires a good knowledge of the species. While the Ecological Niche
Factor Analysis (ENFA; Hirzel et al. 2002) could be adapted for our study, this
technique requires the multinormality of the ecogeographical variables to
extract the eigenvectors to calculate the marginality and the specialization
factors and thereby a transformation of the ecogeographical variables is often
needed (e.g. Box-Cox) prior to the analysis. Finally, the statistical technique
MAXENT (Philips et al. 2006), which is based on the maximum-entropy principle,
also requires accurate threshold definition and showed some application
restrictions.
NPPEN offers a number of advantages on the above existing
methods. Firstly, contrary to models such as RES (Kaschner et al. 2006) or the
mixed model of Cheung and colleagues (Cheung et al. 2008a), our simple model
does not need an a priori knowledge of the species biology. Our
technique is also based on a non-parametric test that does not require the
multinormality of the ecogeographical variables. Although the use of the
Generalised Mahalanobis distance is not new in this kind of model (Farber &
Kadmon 2003, Cayuela 2004, Etherington et al. 2009), this is the first time
that this distance metric is embedded into a non-parametric test. For example,
Cayuela (Cayuela 2004) rescaled the Mahalanobis distance into quantiles to
produce a map of probability and Nogués-Bravo et al.
(Nogués-Bravo et al. 2008) converted the distance into quartiles.
Ibañez (Ibañez 1981) or Farber & Kadmon (Farber & Kadmon
2003) tested this distance by approximating this measure by a ÷²
distribution with n-1 degrees of freedom. Legendre & Legendre (Legendre
& Legendre 1998) also described the conversion of the D² by the
Hotelling T² (Hotelling 1931) statistic and its test by the F statistic.
These tests require the distribution to be multinormal. Although these authors
stated that the test can tolerate some degrees of deviation from this
assumption, it can be seen from histograms that the bathymetry data (Fig. II.5)
were very far from the normality. Finally, the procedure does not need the
selection of arbitrary thresholds and is fully statistical. The technique
simply tests whether an observation belongs to a group of observations called
here a training set or a reference matrix. NPPEN therefore can be used very
quickly as an exploratory analysis to give a first approximation of the spatial
distribution of a species. The test is also appropriate for many species for
which no information on the physiology exists. The only caveat is that our
model, as others, does not fully resolve the problem of autocorrelation (SAR).
The spatial autocorrelation can inflate significantly the probabilities
inferred from ENMs (Bahn & McGill 2007). We think that presence-only
technique of ENMs are much less subject to this problem than other types of
ENMs (e.g. GLM). The problem is that only few studies considered local
functions of autocorrelation (Beaugrand & Ibañez 2002, Dormann et
al. 2007). Most corrections applied are based on global function of
autocorrelation with underlying assumption of isotropy (e.g. the
Moran' index, global semivariograms), which is rarely the case in
biogeography (Beaugrand & Ibañez 2002).
Our technique is currently restricted to presence-only data.
Although some adjustments could be made to apply the method (e.g.
calculate the test for different category of abundance), it is probably
preferable in such a case to use other techniques such as Generalised Linear
Model (GLM; McCullagh & Nelder 1983) or Generalised Additive Models (GAM;
Hastie & Tibshirani 1990). Guisan & Zimmermann (Guisan & Zimmermann
2000) provided an extended review on the different techniques used to assess
the spatial distribution of a species. Perhaps, another limitation of the
technique lies in the fact that it should only be employed with a limited
number of ecogeographical variables. If a high number of variables are used it
would be preferable to use a principal component analysis prior to the
application of the test, or use the Mahalanobis distance factor analysis
(MEDIFA; (Calenge et al. 2008) to better understand the contribution of the
ecogeographical variables; this can also be done a posteriori by
calculating the correlation (here, the rank correlation coefficient of Spearman
or Kendall (Legendre & Legendre 1998) between the modeled probability and
each environmental factor. NPPEN might also be subjected to what could be
described as a «border effect». Indeed, the modelling of the niche of
Atlantic cod (see Fig. II.6) showed a reduction in the probability of cod
occurrence towards shallow regions, which is unexpected based upon our
knowledge of the species (Sundby 2000). Indeed, the technique works in such a
way that maximum probability is concentrated towards the middle of the niche.
Therefore some borders of the multidimensional niche might be underestimated.
Although this problem is difficult to circumvent, it could be overcome
partially by modelling the absence of the species (i.e. estimate the
probability of the absence of the species). Probabilities issued from such a
modelling approach would be less sensitive to the border effect discussed above
and would be complementary, i.e. by assessing the
fundamental niche whereas the ENMs applied on presence data estimate the
realized niche (Pulliam 2000, Helaouët & Beaugrand 2009).
Modelling the absence of a species has never be done, as far
as we know, however, this could be as interesting as modelling the presence of
a species, especially in the case of an exploited species such as Atlantic cod.
Indeed, modelling the probability of absence is very informative for
policymakers and fisheries scientists. It should not be assessed from map of
probability of presence however, but instead should be based on physiological
evidence (Bigg et al. 2008, Helaouët & Beaugrand 2009). When
presence-only data are available to model the spatial distribution of cod,
several known scientific facts and physiological evidence exist that could be
used in NPPEN. First, the species is generally found where the bathymetry is
shallower than 800 m (see Fig. II.5). While some authors found a sharp decrease
in the frequency of occurrence of this species at 400 m and an absence from 600
m (Bigg et al. 2008), this not a sharp constraint and so we can be
conservative. From field and experimental studies, we know that cod are unable
to reproduce at salinities below 11 because their sperm become immobile and
their eggs sink (Brander, Personal Communication), therefore we can predict
confidently that cod will cease to reproduce in areas where salinity falls
below these levels. For temperature, different thresholds could be used.
Beaugrand et al. (Beaugrand et al. 2008) found a pronounced increase
in the variance of the Atlantic cod when the thermal regime was between 9 and
12°C with maximum variance between 9 and 10°C. Brander (2005) in a
synthesis report on this species found maximum spawning temperatures of
12.7°C in Georges Bank. Pepin et al. (1997) found a sustained decrease in
the percentage of egg survival in laboratory between 10° and 12°C.
Here also, it would be logical to select the threshold of 12.7°C (as
monthly SST) in order to remain conservative.
Our model explains in part the pronounced decrease observed in
the abundance of cod in the North Sea (Brander et al. 2006) although the
decline modelled from our study seems less pronounced. Two main phenomena could
explain this result. First, our model does not incorporate information on
plankton. Recent studies have shown however that plankton amplifies the effect
of temperature change (Beaugrand & Kirby 2010b, a). If plankton exacerbates
the effect of climate, our model could be too conservative. Second, overfishing
has exerted a sustained pressure on the stock that has probably increased its
sensitivity to climate change (Hsieh et al. 2006). It is also expected that
these two phenomena act in synergy to reduce the size of the stock (Kirby &
Beaugrand 2009). Our model only explains in part the collapse of cod observed
in eastern part of North America (e.g. The Georges Bank, the Eastern Scotian
Shelf and Newfoundland). This is mainly observed when our model is based on
modelled SST data (Fig. II.8). Recently, Beaugrand & Kirby (Beaugrand &
Kirby 2010a) also show that some plankton indicators decreased at the same time
than the observed collapse of cod stocks in these regions. However, the region
is complex and some other plankton variables were unable to explain completely
this collapse. Here also, overfishing has had a well-documented effect (Myers
et al. 1996, Hsieh et al. 2006). The stock may resist sustained pressure up to
a point when environmental conditions become less favorable and trigger the
collapse of the stock. While it is impossible to compensate directly for both
the direct and indirect effects of global warming on the ocean, the
consideration of change in the carrying capacity of the ecosystem in the
management of the species should be made more explicit in ecosystem fisheries
based management (Pikitch et al. 2004).
Finally, projections suggest substantial changes in the
spatial distribution of cod at the scale of the North Atlantic Ocean. Our
projections indicate that cod should decrease to the level of commercial
extinction in the North Sea and in regions on the eastern side of North America
(e.g. Georges Bank, the Scotian Shelf and Newfoundland) where collapses have
already been detected. These results tend to suggest that the rebuilding of cod
stocks in the North Sea might be difficult. Instead, our effort should perhaps
be made on what resource is likely to present or to develop over the next
decades to enable fishermen to anticipate changes in the resources should
climate continue to warm.
Acknowledgements
We thank Dr Richard R Kirby for helpful comments on an early
version of the manuscript. We are grateful to past and present members and
supporters of the FishBase website
(http://www.FishBase.org), whose continuous efforts have
allowed the establishment of the fish data set. We thank Dr Keith Brander for
helpful comments on an early version of the manuscript. The research was
supported by the French Agency of Research and Technology (ANRT, grant CIFRE
862/2007).
CHAPITRE III
Distribution spatiale modélisée des
poissons marins et projections des changements dans l'océan Atlantique
Nord
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