Multivariate analyses of the concordance between environmental variables and growth in smallmouth bass populations

Multivariate statistics were used to assess the concordance between climate and growth variables in 125 North American populations of smallmouth bass. Patterns in the growth-climate relationships were compared between native and introduced populations.

Methods - Principal components analysis (PCA) was performed separately on the climate and growth data using a correlation matrix (Figure 1). A Procrustes analysis was run with the scores of the first two principal components for both the climate and growth PCAs as inputs. The first two PCA components were used as inputs to the Procrustes analysis in order to reduce the multiple, often correlated variables down to two independent variables that explain most of the variation.

A Procrustes test is used to analyze the concordance between two data sets (climate and growth in this case). In a Procrustes analysis, one of the data configurations (i.e., the climate matrix) is rotated and scaled against a reference configuration (i.e., the growth matrix) until the residual sum-of-squares is minimized. To evaluate the significance of the Procrustes rotation and the concordance between the climate and growth datasets, we used the Procrustes randomization test PROTEST (Jackson 1995).

Results - Positive relationships were found between air temperatures and growth at earlier ages, while growth at later ages was less influenced by climate. The concordance between climate and growth was higher for native populations than for introduced populations. Procrustes superimposition plots indicated interesting contrasts between native and introduced Ontario populations (Figure 2). The residual vectors had clumped apexes in both native and introduced populations but the clump for the native populations was located close to the origin while the clump for the introduced populations was located well above and to the left of the origin (Figure 2). This indicated a similar within category (i.e., native or introduced) climate but a different between category climate. This difference in climate between native and introduced populations was probably related to the more northern distribution of introduced relative to native populations in Ontario. The orientation of native Ontario residual vectors was more varied than that of the introduced populations, which were generally oriented in directions opposite to those defined by the early growth vectors (Figure 2). This indicated a varied growth response in native populations but generally faster observed growth in many of the introduced populations than was predicted by their climate characteristics.

Figure 1. Results of a principal components analysis (PCA) of smallmouth bass climate and growth data. Panel (a) presents variable scores (i.e. correlations) for a PCA of climate data (SumTemp = summer temperature, DD10 = ln transformed degree days above 10oC, and MaxTemp, MeanTemp, and MinTemp = the maximum, mean, and minimum temperatures, respectively. Panel (b) shows the variable scores for the PCA of growth data. Age 1, Age 2, Age 3, Age 4 are growth increments for ages 1 through 4, respectively. Reproduced from Dunlop and Shuter (2006).

Figure 2. PROTEST residuals of smallmouth bass populations in Ontario. Panel (a) shows a Procrustes superimposition plot for native populations. The arrows in the primary plot represent the magnitude (length of arrow) and direction of PROTEST residuals for individual populations (the origin of each arrow represents the observed position of the population in the growth matrix while the arrowhead represents the position of the population in the configured climate matrix). The insert shows the growth vectors from the PCA (reading from top to bottom, growth at ages 4, 3, 2, and 1). The arrows in the primary plot moving away from the growth vectors in the insert indicate growth that is faster than that predicted by climate. Other panels are as follows: (b) Procrustes superimposition plot for introduced populations. (c) frequency distribution of PROTEST residual vector direction for native populations (the insert illustrates quadrant assignments – A, B, C, D – based on the direction of the residual vector), and (d) frequency distribution of the PROTEST residual vector direction for introduced populations. Reproduced from Dunlop and Shuter (2006).

References

Dunlop, E.S., and Shuter, B.J. 2006. Native and introduced populations of smallmouth bass differ in the concordance between climate and somatic growth. Transactions of the American Fisheries Society 135:1175-1190.

Jackson, D. A. 1995. PROTEST: A PROcrustean Randomization TEST of community environment concordance. Ecoscience 2:297-303.