Growing the biphasic framework: Techniques and recommendations for fitting emerging growth models

Abstract

Several new growth models have been proposed to account for the life‐history trade‐offs that occur when indeterminately growing species allocate energy between somatic growth and reproduction. These models can improve the understanding of lifetime growth and life history, but can be more difficult to fit than conventional growth models. Increased data demands, multiple growth phases and increased parameterization all serve as barriers to the adoption and proper use of these new models. We review and comment on confounding issues during model fitting for several of these models, and provide advice on surmounting such issues. We then simulation‐test an example model, the Lester biphasic growth model, using several common fitting approaches. We highlight the biases and precision of each approach and provide guiding documents using r and jags code. The Bayesian Markov chain Monte Carlo and likelihood profiling approaches generally provided the best fits. Simpler approaches can be unbiased and precise if sampled data are of relatively high quality (e.g. moderate sample sizes for juvenile and adult phases) and model assumptions are met. Bayesian hierarchical approaches can accommodate more complicated data scenarios (e.g. unbalanced design across multiple populations); we provide an example of such an approach by recovering growth trajectories and inferring growth‐associated trait variation and environmental effects across multiple populations. Conventional growth models provide limited inference on life history. Many biphasic growth models can provide direct inference on multiple life‐history traits, but can be difficult to fit. The recommended approaches herein provide a path forward for fitting biphasic growth models in a variety of scenarios, allowing for wider application and tests of life history and ecological theory.

Comparing three methods to estimate the average size at first maturity: A case study on a Curimatid exhibiting polyphasic growth

“…This method also highlights another use for the allometric factor obtained in the LWR. Unlike monophasic growth models that assume constant traits through individual lifespans, polyphasic models allow traits to vary in different growth phases most often caused by a shift in reproductive investment (Wilson et al, 2018). Unlike monophasic growth models that assume constant traits through individual lifespans, polyphasic models allow traits to vary in different growth phases most often caused by a shift in reproductive investment (Wilson et al, 2018).…”

“…Allometric changes in growth rates are well known for fish and starts at pre-larval and larval stages (Gisbert, 1999;Osse & van den Boogaart, 1995) and endures until adulthood due to shifts in energy intake and allocation, according to reproductive investment reflecting environmental and food availability changes (Boukal, Dieckmann, Enberg, Heino, & Jørgensen, 2014;Quince et al, 2008a). Polyphasic models can be readily incorporated into future studies, but the specific model structure chosen (e.g., change in growth at size at maturity, migration or habitat use) will depend on the ecological hypothesis explaining the change in growth (Wilson et al, 2018). Hence, the reproductive strategy of studied species should be considered when using polyphasic models because reproductive investment could start a year before first spawning, as observed in longer-lived fishes.…”

“…LWR considers that the relationship between weight and length is constant throughout life, meaning that body dimensions increase relative to each other according to an allometric coefficient constant (b) in a monophasic growth. A fundamental change in somatic growth patterns of most fish species is the change in energy allocation when individuals of a population reach sexual maturity, since there is an investment in gonadal development (Quince, Abrams, Shuter, & Lester, 2008a,b;Shuter et al, 2005;Wilson, Honsey, Moe, & Venturelli, 2018). A fundamental change in somatic growth patterns of most fish species is the change in energy allocation when individuals of a population reach sexual maturity, since there is an investment in gonadal development (Quince, Abrams, Shuter, & Lester, 2008a,b;Shuter et al, 2005;Wilson, Honsey, Moe, & Venturelli, 2018).…”

Life‐history variation along environmental and harvest clines of a northern freshwater fish: Plasticity and adaptation

“…We simultaneously estimated biphasic growth and maturity models following Wilson, Honsey, Moe, and Venturelli (). We explored relationships among juvenile growth rate, size at maturity and reproductive allocation and related these traits to environmental covariates such as climate, productivity, prey fish occurrence and exploitation gradients (Table ).…”

The growth of juvenile native mussels (Elliptio complanata) in lakes varies with sediment characteristics and site exposure

“…They quickly bury into the sediments, where they first pedal feed on deposited organic matter (Gatenby et al, 1996;Mistry & Ackerman, 2017;Yeager et al, 1994), and then gradually metamorphose and develop their capacity for suspension feeding (Araujo et al, 2018;Lavictoire et al, 2018). The simplest model of juvenile growth is to assume constant (linear) growth (Wilson et al, 2017). Juvenile and adult mussels are quite mobile and can quickly bury when exposed to physical disturbances or otherwise unfavourable conditions (Balfour & Smock, 1995;Nichols & Wilcox, 1997;Schwalb & Pusch, 2007).…”