Metabolic theories in ecology interpret ecological patterns at different levels through the lens of metabolism, typically applying allometric scaling to describe energy use. This requires a sound theory for individual metabolism. Common mechanistic growth models, such as 'von Bertalanffy', 'dynamic energy budgets' and the 'ontogenetic growth model' lack some potentially important aspects, especially regarding regulation of somatic maintenance. We develop a model for ontogenetic growth of animals, applicable to ad libitum and food limited conditions, based on an energy balance that expresses growth as the net result of assimilation and metabolic costs for maintenance, feeding and food processing. The most important contribution is the division of maintenance into a 'non-negotiable' and a 'negotiable' part, potentially resulting in hyperallometric scaling of maintenance and downregulated maintenance under food restriction. The model can also account for effects of body composition and type of growth at the cellular level. Common mechanistic growth models often fail to fully capture growth of insects. However, our model was able to capture empirical growth patterns observed in house crickets.

Metabolic theories in ecology interpret ecological patterns at different levels through the lens of metabolism, typically applying allometric power scaling laws to describe rates of energy use. This requires a sound theory for metabolism at the individual level. Commonly used mechanistic growth models lack some potentially important aspects and fail to accurately capture a growth pattern often observed in insects. Recently, a new model (MGM–the Maintenance-Growth Model) was developed for ontogenetic and post-mature growth, based on an energy balance that expresses growth as the net result of assimilation and metabolic costs for maintenance and feeding. The most important contributions of MGM are: 1) the division of maintenance costs into a non-negotiable and a negotiable part, potentially resulting in maintenance costs that increase faster than linearly with mass and are regulated in response to food restriction; 2) differentiated energy allocation strategies between sexes and 3) explicit description of costs for finding and processing food. MGM may also account for effects of body composition and type of growth at the cellular level. The model was here calibrated and evaluated using empirical data from an experiment on house crickets growing under ad libitum conditions. The procedure involved parameter estimations from the literature and collected data, using statistical models to account for individual variation in parameter values. It was found that ingestion rate cannot be generally described by a simple allometry, here requiring a more complex description after maturity. Neither could feeding costs be related to ingestion rate in a simplistic manner. By the unusual feature of maintenance costs increasing faster than linearly with body mass, MGM could well capture the differentiated growth patterns of male and female crickets. Some other mechanistic growth models have been able to provide good predictions of insect growth during early ontogeny, but MGM may accurately describe the trajectory until terminated growth.

A growing animal ingests food from the environment and distributes the assimilated energy between chemical energy stored in synthesized biomass and energy spent on metabolic processes, including food processing, maintenance, activity and overhead costs for growth. Under food restriction, the growth rate is usually decreased. However, the extent of this reduction may be influenced by a potential trade -off with maintenance metabolism. The latter seems to be down-regulated under food restriction in some animals and up-regulated in others. Recently, the Maintenance-Growth Model (MGM) was developed for ontogenetic and post-mature growth, including several aspects not considered by common mechanistic growth models, most importantly the division of maintenance costs into non-negotiable and negotiable parts, where the latter can be up- or downregulated under food restriction. Using empirical data, MGM has been calibrated and successfully applied to an insect growing under ad libitum conditions. Here, the model is further calibrated to newly collected individual data for the same species growing under two different regimes of food restriction, complemented with previously collected data for food-limited cohorts. We find that two alternative model scenarios of MGM are able to generate rather good predictions of observed growth under food restriction, assuming either upregulated maintenance or decreased effective assimilation (assimilation minus energy spent on processing and searching food). We find the latter scenario least plausible, implying that the current study provides the first indication for the occurrence of upregulated maintenance in an insect species when food is scarce, an unexpected result that requires further investigation. The inclusion of maintenance regulation in MGM enables the new growth model to be used in the modelling of life-history dependent trade-offs between maintenance, growth and maturation for various other species.

Empirical evidence has shown that historical exposure of polychlorinated biphenyls (PCBs) to Baltic grey seals not only severely affected individual fitness, but also population growth rates and most likely caused the retarded recovery rate of the depleted population for decades. We constructed a new model which we term a toxicokinetic–toxicodynamic (TKTD) population model to quantify these effects. The toxicokinetic sub-model describes in detail the bioaccumulation, elimination and vertical transfer from mother to offspring of PCBs and is linked to a toxicodynamic model for estimation of PCB-related damage, hazard and stress impacts on fertility and survival rates. Both sub-models were linked to a Leslie matrix population model to calculate changes in population growth rate and age structure, given different rates of PCB exposure. Toxicodynamic model parameters related to reproductive organ lesions were calibrated using published historical data on observed pregnancy rates in Baltic grey seal females. Compared to empirical data, the TKTD population model described well the age-specific bioaccumulation pattern of PCBs in Baltic grey seals, and thus, the toxicokinetic parameters, deduced from the literature, are believed to be reliable. The model also captured well the general effects of PCBs on historical population growth rates. The model showed that reduced fertility due to increased PCB exposure causes decreased vertical transfer from mother to offspring and in turn increased biomagnification in non-breeding females. The developed TKTD model can be used to perform population viability analyses of Baltic grey seals with multiple stressors, also including by-catches and different hunting regimes. The model can also be extended to other marine mammals and other contaminants by adjustments of model parameters and thus provides a test bed in silico for new substances.