Title: Canonical discriminant analysis of a larval fish lipid enrichment study Author
Submitted to: Aquaculture America Conference
Publication Type: Abstract Only
Publication Acceptance Date: May 3, 2009
Publication Date: July 27, 2009
Citation: Rawles, S.D. 2009. Canonical discriminant analysis of a larval fish lipid enrichment study [abstract]. Aquaculture America Conference. 71:224-228. Technical Abstract: The analysis of a fatty acid enrichment study for hybrid striped bass fry presents several statistical problems. Univariate analysis is limited to one or two responses at a time and it does not account for interrelationships (colinearity) among quantitative variables (fatty acids, fish proximate composition, or body indices) and class variables (enrichments, rotifers, fry). Canonical discriminant analysis (CDA), on the other hand, discerns the influence of multiple fatty acid (FA) enrichments in a multi-step food chain on the resulting fatty acid or compositional profiles of fry. In other words, CDA answers the questions: how do my continuous responses (FA's) differ as a function of group (enrichment, live feed, or fry) levels, and which responses "most" predict group identity? CDA begins by deriving new variables called canonical variates (CVs) which are linear combinations of all responses (say, FA abundances) in a particular group (treatment). In our example, the first CV for, say, the initial unfed fry would be denoted CAN1Fi=a1[14:0] + a2[14:1] +'''+ a23[22:6], where the numbers in brackets are the response variables, in this case log transformed FA concentrations in unfed fry samples. The canonical coefficients (a1…a23) are loading factors that denote the relative influence of responses (FAs) in determining the value of the canonical variate. Several successive CVs can be formed from a particular dataset and each subsequent variate is orthogonal (not parallel) to the previously formed variates. The number of CV’s that can be formed from a dataset depends on the number of response variables and groups (treatments) and will be discussed. However, five salient features of the variates are 1) they explain 100% of the variance in the data, 2) they are uncorrelated (orthogonal) even when response (FA) variables are correlated, 3) they define a location in n-space for a particular (treatment) group, 4) the distance between groups in n space is a measure of their similarity due to responses (FAs), and 5) the loading factors (coefficients) can be used to discern the relative influence of the responses to the identity (location) of a group. The example of differentially enriched rotifers fed to hybrid striped fry is extended to show the steps of CDA in a SAS context. Topics covered include judicious selection of meaningful variates, canonical correlations, Eigenvalues, explained error variance, plotting variates, distance statistic, and interpretation of canonical coefficients (loading factors). In the current example (see Ludwig, G. M., S. D. Rawles, and S. E. Lochmann. 2008. Effect of rotifer enrichment on sunshine bass Morone chrysops X M. saxatilis larvae growth and survival and fatty acid composition. JWAS 39 (2): 158-173), CDA allowed determination of the rotifer enrichment combination that maximized essential fatty acid profile and hybrid striped bass fry condition, but minimized labor.