Measuring Probabilistic Reaction Norms for Age and Size at Maturation

Heino, M. ORCID: https://orcid.org/0000-0003-2928-3940, Dieckmann, U. ORCID: https://orcid.org/0000-0001-7089-0393, & Godoe, O.R. (2002). Measuring Probabilistic Reaction Norms for Age and Size at Maturation. IIASA Interim Report. IIASA, Laxenburg, Austria: IR-02-017

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Abstract

We present a new probabilistic concept of reaction norms for age and size at maturation that is applicable when observations are carried out at discreet time intervals. This approach can also be used to estimate reaction norms for age and size at metamorphosis or at other ontogenetic transitions. Such estimations are critical for understanding phenotypic plasticity and life-history changes in variable environments, for assessing genetic changes in the presence of phenotypic plasticity, and calibrating size- and age-structured population models. We show that previous approaches to this problem, based on regressing size against age at maturation, give results that are systematically biased when compared to the probabilistic reaction norms. The bias can be substantial and is likely to lead to qualitatively incorrect conclusions; it is by failing to account for the probabilistic nature of the maturation process. We explain why, instead, robust estimation of maturation reaction norms ought to be based on logistic regression, or on other statistical models that treat the probability of maturing as a dependent variable. We demonstrate the utility of our approach with two examples. First, the analysis of data generated for a known reaction norm highlights some crucial limitations of previous approaches. Second, application to the Northeast Arctic cod ("Gadus morhua") illustrates how our approach can be used to shed new light on existing real-world data.

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