A new mechanistic model for individual growth applied to insects under ad libitum conditions

Abstract

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.

Fig 1. Energy balance and resulting growth equation of the Maintenance-Growth Model (MGM).

Arrows represent fluxes of energy through a growing (non-reproducing) animal. Some of the energy ingested as food (S) disappears as losses through egestion or excretion. The assimilated energy (eS) is distributed between feeding costs (R_F), maintenance costs (R_M), growth overhead costs (R_G) and energy becoming bounded in reproductive and somatic biomass (G). Maintenance costs are divided between basal (R_MB) and negotiable (R_MN) maintenance costs.

Fig 2. Components of MGM for house crickets under ad libitum growth.

a) Ingestion rate (S) as a function of body mass (W), initially a power function that breaks at maturity (W = W_mat). b) Feeding costs (R_F) as a function of ingestion rate (S), shaped as a ‘hockey-stick’. c-d) Maintenance costs (R_M) as a function of body mass (W) for (c) males and (d) females, including basal maintenance costs (R_MB) and negotiable maintenance costs (R_MN). In males, basal maintenance costs increase linearly with total body mass. In females, basal maintenance costs increase linearly with somatic body mass until maturity (W = W_mat) and then increase linearly with reproductive body mass. Negotiable maintenance costs increase superlinearly with body mass in both sexes.

Fig 3. Observed and predicted ingestion rate, growth rate and body mass as functions of age.

Data points represent individual empirical data for house crickets reared under ad libitum conditions at 28.6°C. Dashed curves are age-wise average values of individual empirical data. Model predictions (red curves) were obtained from numerical solutions to the growth equation (Eq (4)) with insertion of estimated fixed parameter values (SI9 Table in S1 File).

Fig 4. Observed and predicted ingestion and growth rate as functions of growth rate and body mass.

Data points represent individual empirical data for house crickets reared under ad libitum conditions at 28.6°C. Dashed curves are age-wise average values of individual empirical data. Model predictions were obtained from numerical solutions to the growth equation (Eq (4)) with insertion of estimated fixed parameter values (SI9 Table in S1 File).

Fig 5. Observed and predicted metabolic rates.

a-b) Total metabolic rate R_tot versus body mass (logarithmic scales) for male (a) and female (b) house crickets reared under ad libitum conditions at 28.6°C, predicted by MGM (Eq (SI5) in S1 File, solid curve) and calculated based on empirical data and literature estimates (Eq (SI37) in S1 File, dashed curve). Points represent calculated values for individuals. Dashed curves are average values of individual empirical data. Vertical dashed lines indicate mass at break point for feeding costs (S = S₁). Vertical dash-dotted lines indicate mass at maturity. Predictions were obtained by inserting the numerical solution to the MGM growth equation (Eq (4) with estimated fixed parameter values from SI9 Table in S1 File) into model specifications of contributing metabolic components and summing (R_tot = R_F + R_G + R_M). c-d) Predicted components of total metabolic rate versus body mass (linear scales) for males (c) and females (d). R_F: Feeding costs (Eq (SI14) in S1 File). R_G: Growth overhead costs (Eq (SI6) in S1 File). R_M: Maintenance costs (Eqs (SI25) & (SI27) in S1 File). R_MB: Basal maintenance costs (Eq (SI24) in S1 File). R_MN: Negotiable maintenance costs (Eq (SI15) in S1 File). Filled circles (•) indicate break point for feeding costs (S = S₁). Unfilled circles (o) indicate maturity.