Technical Comments

Comment on “Energy Uptake and Allocation During Ontogeny”

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Science  04 Sep 2009:
Vol. 325, Issue 5945, pp. 1206
DOI: 10.1126/science.1169523


Hou et al. (Reports, 31 October 2008, p. 736) presented a model for energy uptake and allocation over an organism’s growth and development. However, their model does not account for allocation to reproduction (essential to adults) and growth without assimilation (essential to embryos) and is therefore only applicable to organisms growing with abundant food in the juvenile stage.

Hou et al. (1) proposed a modification of the ontogenetic growth model (OGM) to explain how food is transformed into biomass and metabolic energy during development. However, their model describes biomass with one state variable and therefore cannot explain the variable chemical composition of organisms growing with variable food. Also, if biomass had a variable chemical composition, growth would correspond to a varying aggregated chemical reaction. Thus, parameters like the combustion energy content of a unit of biomass (Ec), the energy required to synthesize a unit of biomass (Em), or the maintenance metabolic rate (Bm) would no longer be constant. These problems disappear if biomass is composed of more than one aggregated compound with constant chemical compositions. This is the case of the dynamic energy budget (DEB) framework (25), in which biomass is composed of two compounds, structure and reserve, each with a constant chemical composition. Growth, that is, the transformation of reserve into structure, is characterized by an aggregate chemical reaction with a constant stoichiometry, which is consistent with the assumption of constant parameters Ec and Em. Only structure has maintenance needs, because reserve is being constantly replenished and used, which is consistent with a constant parameter Bm. Also, the organism’s chemical composition changes with the reserve density (the ratio between reserve and structure). Thus, the Hou et al. model is only applicable to constant food conditions where the chemical composition of biomass tends to a constant value.

The Hou et al. model is also restricted to the description of growth in juveniles and cannot be applied to embryos or adults. A single state variable for biomass implies direct formation of biomass from assimilation. This cannot describe the energetics of embryos since they do not ingest food (but do grow). With two state variables, in the context of DEB, embryos use their initial endowment of reserve for growth and all other metabolic activities. In addition, energy allocation to maturation and reproduction is not explicit in the Hou et al. model, which therefore cannot be applied to adults. In DEB, energy is allocated to maturation in juveniles and to reproduction in adults.

The model proposed by Hou et al. (1) specifies that the resting metabolic rate, Brest, is proportional to m3/4 and that the total metabolic rate, Btot = fBrest, which includes movement and other activities, is also proportional to m3/4. This is based on the empirical scaling of dioxygen consumption with mass in resting organisms. However, energy use is only proportional to dioxygen consumption in aerobic organisms when the overall metabolic activity is characterized by a constant stoichiometry. To relate mass and energy measurements, the Hou et al. model requires an explicit chemical description of metabolism. A simple way to proceed is to have processes with aggregate fixed stoichiometries, like assimilation, dissipation, and growth in DEB (4, 5).

The assumptions for Brest and Bmaint together with the energy allocation scheme in figure 1 in (1) predict that the normalized growth rate has a maximum value for relative mass μ = 0.316 [figure 3 in (1)]. In itself, this prediction does not validate the Hou et al. model because it is indistinguishable from that of the von Bertalanffy growth model, dμ/dt = 3rB2/3 – μ), where rB is a species-specific constant. The maximum value for dμ/dt occurs when d2/3 – μ)/dμ = 0, i.e., for μ = (2/3)3 ≈ 0.296. The von Bertalanffy growth model, the limiting case of DEB at constant food, has been thoroughly tested. In table 8.3 in (4), a compilation of rB and its standard deviation is presented for more than 250 species, including fish, reptiles, amphibians, mollusks, crustaceans, fungi, chromista, and protozoa, among others. Of these, 132 are bird and mammal species [the only taxa considered in (1)] and more than 70% have an rB with coefficient of variation below 10%.

In the model proposed by Hou et al., the assimilation rate of food is such that it matches the needs imposed by Brest and Bmaint. Thus, assimilation is completely independent of food availability. This might be a good approximation for demand systems that can ingest whatever they need, but never for supply systems (in fact, Hou et al. present good fits to assimilation rates of mammals, which are typically demand systems). A more realistic assumption is to consider that the assimilation rate is both supply and demand driven. This can be achieved, as in DEB, by considering that assimilation depends both on organism surface area and on food availability. Hou et al. state incorrectly that the intraspecific assimilation rate in DEB follows a simple power law scaling relation with mass. This is the case only for constant food level; otherwise, surface area (a power law of structure) is not a power law of biomass (equal to structure plus reserve) because the ratio of reserve to structure is not constant.

Hou et al. further use their model to make interspecies comparisons. In this case, the specific maintenance rate, Bm, is taken proportional to M3/4 (where M is the body mass of fully grown adults). However, neither Hou et al. nor previous papers adequately explain the reason for this (6). Their modified OGM therefore has a seemingly weak connection between parameters and biological processes. In contrast, DEB presents a rationale for the covariation of parameter values among species: Parameters that characterize cellular-based processes (constant primary parameters), e.g., the specific maintenance rate, are similar across related species because cells are similar; all other parameters depend on the maximum size of each species in predictable ways because they can be written as a function of constant primary parameters and/or the maximum size (5).

In conclusion, the Hou et al. model (1) needs to make explicit the link between dioxygen consumption and the resting metabolic rate. Also, it must include a theory for parameter values that explains in a consistent way why some parameters are constant and others are not. Even solving these issues, their model would be applicable only to demand systems in the juvenile stage growing at abundant food. To widen its scope, we suggest that the proposed model (i) include allocation to reproduction; (ii) provide a way for organisms to obtain energy when food is not ingested, e.g., the embryonic stage; and (iii) set an assimilation rate that depends on food availability.

References and Notes

  1. This work was supported by Fundação para e a Tecnologia through grant SFRH/BPD/27174/2006 (to G.M.M.) and project PPCDT/AMB/55701/2004.
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