Evol Ecol Res 8: 295-308 (2006)     Full PDF if your library subscribes.

The biological and statistical significance of life-history invariants in walleye (Sander vitreus)

Craig F. Purchase,1* Jeffrey A. Hutchings1 and George E. Morgan2

1Department of Biology, Dalhousie University, Halifax, Nova Scotia B3H 4J1 and  2Cooperative Freshwater Ecology Unit, Department of Biology, Laurentian University, Sudbury, Ontario P3E 2C6, Canada

Author to whom all correspondence should be addressed.
e-mail: purchasecraig@hotmail.com


Questions: Do life-history invariants exist in walleye (Sander vitreus) and do they differ between the sexes? How does the probability of detecting life-history invariants vary with sample size? How much error is created if invariance is incorrectly assumed when using the relationships to predict one trait from another?

Data description: Sex-specific data, obtained from standardized research surveys, on growth, age and size at maturity, and mortality for 435 populations of walleye from Ontario, Canada.

Search method: Invariance in four life-history relationships (Lm /Linf, M/k, Tm · M and Tm /Lm) was assessed using linear slopes. We examined sample and effect sizes to determine the extent to which life-history invariants are influenced by statistical power. Errors in estimating traits from predicted invariants were obtained from random samples of 50 populations.

Conclusions: Life-history invariants did not exist among populations of walleye. The value of each ratio and the extent of invariance differed between the sexes. The number of populations required to generate variance in Lm /Linf was high for males (200) and females (41), suggesting that this potential life-history invariant may be statistically robust. However, none of the other ratios examined (M/k, Tm · M and Tm /Lm) was invariant at sample sizes of 10 or more populations for either sex. For walleye, Lm can be predicted from Linf if comparisons are from populations ranging widely in Linf. Estimates of either k or Tm are unlikely to yield reliable estimates of M; similarly, Tm cannot be reliably estimated from Lm.

Keywords: covariation, life-history invariants, inter-population, statistical power, walleye.

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