@article{
 title = {Variation partitioning of species data matrices: estimation and comparison of fractions},
 type = {article},
 year = {2006},
 pages = {2614-2625},
 volume = {87},
 id = {373d2091-fa38-37c5-84c1-4278db5f52b0},
 created = {2010-11-03T21:13:25.000Z},
 file_attached = {true},
 profile_id = {976aa121-3316-304c-8340-7ca54d70abe6},
 last_modified = {2017-03-16T14:38:37.564Z},
 read = {true},
 starred = {false},
 authored = {true},
 confirmed = {true},
 hidden = {false},
 citation_key = {Peres-Neto2006a},
 source_type = {article},
 folder_uuids = {7e415411-ab1b-4ef7-9523-01b20e85991d},
 private_publication = {false},
 abstract = {Establishing relationships between species distributions and environmental
characteristics is a major goal in the search for forces driving
species distributions. Canonical ordinations such as redundancy analysis
and canonical correspondence analysis are invaluable tools for modeling
communities through environmental predictors. They provide the means
for conducting direct explanatory analysis in which the association
among species can be studied according to their common and unique
relationships with the environmental variables and other sets of
predictors of interest, such as spatial variables. Variation partitioning
can then be used to test and determine the likelihood of these sets
of predictors in explaining patterns in community structure. Although
variation partitioning in canonical analysis is routinely used in
ecological analysis, no effort has been reported in the literature
to consider appropriate estimators so that comparisons between fractions
or, eventually, between different canonical models are meaningful.
In this paper, we show that variation partitioning as currently applied
in canonical analysis is biased. We present appropriate unbiased
estimators. In addition, we outline a statistical test to compare
fractions in canonical analysis. The question addressed by the test
is whether two fractions of variation are significantly different
from each other. Such assessment provides an important step toward
attaining an understanding of the factors patterning community structure.
The test is shown to have correct Type I error rates and good power
for both redundancy analysis and canonical correspondence analysis.},
 bibtype = {article},
 author = {Peres-Neto, P R and Legendre, P and Dray, Stéphane and Borcard, D},
 journal = {Ecology},
 keywords = {R2}
}

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Canonical ordinations such as redundancy analysis\nand canonical correspondence analysis are invaluable tools for modeling\ncommunities through environmental predictors. They provide the means\nfor conducting direct explanatory analysis in which the association\namong species can be studied according to their common and unique\nrelationships with the environmental variables and other sets of\npredictors of interest, such as spatial variables. Variation partitioning\ncan then be used to test and determine the likelihood of these sets\nof predictors in explaining patterns in community structure. Although\nvariation partitioning in canonical analysis is routinely used in\necological analysis, no effort has been reported in the literature\nto consider appropriate estimators so that comparisons between fractions\nor, eventually, between different canonical models are meaningful.\nIn this paper, we show that variation partitioning as currently applied\nin canonical analysis is biased. 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Such assessment provides an important step toward\nattaining an understanding of the factors patterning community structure.\nThe test is shown to have correct Type I error rates and good power\nfor both redundancy analysis and canonical correspondence analysis.","bibtype":"article","author":"Peres-Neto, P R and Legendre, P and Dray, Stéphane and Borcard, D","journal":"Ecology","keywords":"R2","bibtex":"@article{\n title = {Variation partitioning of species data matrices: estimation and comparison of fractions},\n type = {article},\n year = {2006},\n pages = {2614-2625},\n volume = {87},\n id = {373d2091-fa38-37c5-84c1-4278db5f52b0},\n created = {2010-11-03T21:13:25.000Z},\n file_attached = {true},\n profile_id = {976aa121-3316-304c-8340-7ca54d70abe6},\n last_modified = {2017-03-16T14:38:37.564Z},\n read = {true},\n starred = {false},\n authored = {true},\n confirmed = {true},\n hidden = {false},\n citation_key = {Peres-Neto2006a},\n source_type = {article},\n folder_uuids = {7e415411-ab1b-4ef7-9523-01b20e85991d},\n private_publication = {false},\n abstract = {Establishing relationships between species distributions and environmental\ncharacteristics is a major goal in the search for forces driving\nspecies distributions. 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