Multiple working hypotheses for hyperallometric reproduction in fishes under metabolic theory

Abstract

Hyperallometric reproduction, whereby large females contribute relatively more to the renewal of the population than small females, is purported to be widespread in wild populations, especially in fish species. Bioenergetic models derived from a sufficiently general metabolic theory should be able to capture such a relationship but it was recently stated that no existing models adequately capture hyperallometric reproduction. If this were true it would seriously challenge our capacity to develop robust predictions of the life history and population dynamics in changing environments for many species. Here, using the European sea bass (Dicentrarchus labrax) as a test case, we demonstrate multiple ways that hyperallometric reproduction in a population may emerge from the Dynamic Energy Budget (DEB) theory, some inherently related to the metabolism and life history and others related to plastic or genetically based intraspecific variation. In addition, we demonstrate an empirical and modelled hypoallometric scaling of reproduction in this species when environment is controlled. This work shows how complex metabolic responses may underlie apparently simple relationships between weight and reproduction in the wild and provides new and testable hypotheses regarding the factors driving reproductive scaling relationships found in the wild.

Introduction

Hyperallometric reproduction, defined as a more than proportional increase of the fecundity relative to the body mass of individuals within a species, has a wide range of consequences for our understanding of population dynamics, our predictions in a changing environment and ultimately our conservation policies (Marshall et al., 2019). Such a reproductive scaling pattern has recently been described for a wide range of fish species (Barneche et al., 2018) and implies that large females contribute more to the renewal of the population than do small females, relatively to their body mass. Large females therefore have a higher conservation value and their protection should be prioritized over small females to increase the sustainability of the population (Birkeland and Dayton, 2005).

Ideally, population dynamics models should be driven by an underlying model of bioenergetic processes that can explicitly capture the observed scaling of reproduction. A number of ‘growth models’ now exist, including some derived from general theories of how metabolism works, i.e. ‘metabolic theories’ (van der Meer, 2006). It was recently argued that the observed hyperallometric scaling of reproduction could not be explained using current bioenergetic models (Marshall and White, 2019). If this were true, and hyperallometric reproduction is indeed widespread, it would call into question the generality of existing theory and limit our capacity to develop robust models of the life history and population dynamics for many species.

However, a pattern of hyperallometric reproduction observed in wild populations is challenging to interpret when the age, environmental life history and genetic background of the individuals displaying this relationship are unknown (Kearney, 2019). This is the case for the data underlying hyperallometric reproduction in fish which derive almost entirely (>98%) from observations of wild individuals (Barneche et al., 2018). Investigating a fecundity to body mass scaling naturally results from the comparison of different sized individuals. But what is driving this variability? Why are large individuals larger? Multiple biological explanations are possible.

First, in nature, there is no reason to believe that all animals encounter the same environmental conditions over their life history. This is particularly true for species with wide geographical and habitat ranges (Riede, 2004; Wheeler, 1975), including the Atlantic cod and European sea bass. Comparing the weight and reproductive output of wild-harvested individuals of such species necessarily involves confounding effects related to environmental history. These effects are amplified when investigating the variability in weight without evaluating the age, since large animals are more likely to have encountered better environments compared to small individuals of the same age.

Second, whether it is the consequence of predation, of sudden environmental challenges or of human activities, selective pressures in the wild are particularly numerous and diversified. These multiple sources of selection are considered as the primary mechanisms of polymorphism in nature (Orr and Smith, 1998). Metabolic capacities driving growth, maturation, reproduction and ultimately fitness are central phenotypic targets of selective pressures (Pettersen et al., 2018). Within a given population, one can expect genetically based variability in metabolic capacities resulting in intrinsic individual differences in assimilation and growth capacity (Besson et al., 2019). Thus, the life history patterns obtained from wild-harvested individuals may also reflect the action of selection.

The environmental and genetic variation inherent in samples from wild populations means that one should be cautious in attributing a pattern of reproductive hyperallometry to metabolic mechanisms involved at the individual level. Rather than using such an empirical observation to dismiss existing models of individual growth and metabolism, one can instead ask under what environmental and genetic circumstances the model would produce the empirical pattern in question. This then leads to clear and testable predictions about what might be occurring in nature. In parallel, detailed laboratory experiments are critical to control and evaluate selective pressures and environmental variabilities and thereby evaluate theoretical expectations.

A common point of contention and misunderstanding in modelling growth centers around the distinction between phenomenological and mechanistic models (White and Marshall, 2019). A phenomenological model provides a quantitative description of a process using a simple function thought to capture the essence of an underlying process; often these are allometric functions in the case of growth models. In contrast, mechanistic models are derived through the explicit representation of processes occurring at a lower level to the phenomenon in question. In growth models, these processes are the chemical transformations from food to biomass, which are modelled on the basis of physicochemical principles including energy and mass conservation. Successful mechanistic models can predict dynamics under complex sequences of environmental conditions with the same variables and parameters – something phenomenological models cannot do without adding parameters or changing their functional form. In this sense, mechanistic modeling can help reconstruct environmental history when they are inverted to fit growth data from the wild (Lavaud et al., 2019; Pecquerie et al., 2009).

In this paper, we explore the potential for reproductive hyperallometry under the framework of Dynamic Energy Budget (DEB) theory; a general, mechanistic metabolic theory that captures the environmental (food, temperature) and internal (chemical transformations and allocations) constraints on development, growth and reproduction from first principles (Kooijman, 2010, 1986). In particular, we consider three working hypotheses (Fig. 1) and illustrate them using the European sea bass, Dicentrarchus labrax, a species shown to exhibit hyperallometric reproduction in the wild (Mayer et al., 1990):

• the ‘ontogenetic hypothesis’ that hyperallometric reproduction can emerge for an individual simulated under DEB theory across its ontogeny;

• the ‘environmental variation hypothesis’ that hyperallometric reproduction can be produced by realistic variation in feeding rate and temperature environments among individuals with the same metabolic capacities;

• the ‘metabolic capacities variation hypothesis’ that inter-individual variation in DEB parameter values can lead to hyperallometric reproduction.

Finally, we provide empirical data on the allometric scaling of reproduction under controlled environmental conditions and limited selection pressure. We discuss our results in the light of DEB predictions under such environmental conditions. Since the DEB model is generic between fish species (only parameters vary), the results of our study are transposable to most other fish species.