Application of two tests of multivariate discordancy to fisheries data sets

Abstract

The generalized (Mahalanobis) distance and multivariate kurtosis are two powerful tests of multivariate discordancies (outliers). Unlike the generalized distance test, the multivariate kurtosis test has not been applied as a test of discordancy to fisheries data heretofore. We applied both tests, along with published algorithms for identifying suspected causal variable(s) of discordant observations, to two fisheries data sets from Lake Erie: total length, mass, and age from 1,234 burbot, Lota lota; and 22 combinations of unique subsets of 10 morphometrics taken from 119 yellow perch, Perca flavescens. For the burbot data set, the generalized distance test identified six discordant observations and the multivariate kurtosis test identified 24 discordant observations. In contrast with the multivariate tests, the univariate generalized distance test identified no discordancies when applied separately to each variable. Removing discordancies had a substantial effect on length-versus-mass regression equations. For 500-mm burbot, the percent difference in estimated mass after removing discordancies in our study was greater than the percent difference in masses estimated for burbot of the same length in lakes that differed substantially in productivity. The number of discordant yellow perch detected ranged from 0 to 2 with the multivariate generalized distance test and from 6 to 11 with the multivariate kurtosis test. With the kurtosis test, 108 yellow perch (90.7%) were identified as discordant in zero to two combinations, and five (4.2%) were identified as discordant in either all or 21 of the 22 combinations. The relationship among the variables included in each combination determined which variables were identified as causal. The generalized distance test identified between zero and six discordancies when applied separately to each variable. Removing the discordancies found in at least one-half of the combinations (k=5) had a marked effect on a principal components analysis. In particular, the percent of the total variation explained by second and third principal components, which explain shape, increased by 52 and 44% respectively when the discordancies were removed. Multivariate applications of the tests have numerous ecological advantages over univariate applications, including improved management of fish stocks and interpretation of multivariate morphometric data.

Genetic and morphometric differences demonstrate fine‐scale population substructure of the yellow perch Perca flavescens: need for redefined management units

“…Multivariate outlier analysis was conducted to identify discordant fish and to determine if any particular morphometric was causal in the discordancy using Scout software (Stapanian et al ., 2008). Fish identified as discordant were re-measured.…”

Effects of freezing on white perch Morone americana (Gmelin, 1789): implications for multivariate morphometrics

“…The poor re‐classification results for 100 days fish frozen may have been due to random error resulting from an unbalanced assortment of fresh and iced fish to the 100‐days and 200‐days groups, or because fish were outliers ( sensu Stapanian et al., ). Conversely, the observed misclassification might be expected because most 100 days frozen fish were misclassified as 200 days frozen fish.…”

“…Whole‐body morphometrics were analyzed using Discriminant Function Analysis (DFA). Prior to analysis all variables were tested for univariate normality using the Shapiro‐Wilk test (although not a true test of multivariate normality, it is unusual for data to not be multivariate normal if a large proportion of the contributing variables are univariate normal; see Stapanian et al., ). Discriminant Function Analysis was chosen because group identity was known a priori and so thus to be able to assess re‐classification success, which is a means of assessing practical effects of the observed differences.…”

Morphological evidence of discrete stocks of yellow perch in Lake Erie

“…Multivariate outlier analysis was conducted to identify discordant fish and to determine if any particular morphometric was causal using Scout software (Stapanian et al, 2008). Fish identified as discordant were re-measured.…”

“…1) sampled in at least two years: Cleveland 2007 and2008;Perry, Chagrin, Erie, andDunkirk 2007-2009;andMonroe 2008-2009. Year was nested within each site for ANOVA to avoid constraining annual differences in morphology to be the same for all sites. This analysis permitted examination of spatial versus temporal variation for the broadest range of sites.…”