# The importance of body size - scaling of physiological traits in insects

The following summarises work conducted as part of my PhD from 2011-2015.

Biological phenomena occur across wide scales in space, time, and organisational complexity. Molecules, which are small, simple, quickly transforming units, exhibit new emergent properties when they are arranged into ecosystems. These properties of ecosystems, such as species diversity, distribution, standing biomass, or rates of nutrient turnover involve large spatial and temporal scales, and many underlying processes that make their study inherently complex. Integration across disciplines and across levels of biological organisation is one of the grand challenges in biology. Towards this end, novel methods are required so that cross-disciplinary phenomena can be quantified using a common metric. One universal currency that is able to cut through the hierarchy of biology is the currency of mass and energy, which must be conserved irrespective to the scale of inquiry.

Dynamic Energy Budget (DEB) theory builds upon the laws of energy and mass conservation by identifying other universal constraints on the metabolic organisation of diverse species. While, DEB theory has been used with great success at fine biological resolutions, particularly the individual level, the application of DEB theory to higher level processes has received less attention. Thus, the relevance of DEB theory at coarser scales of analysis has remained less evident. We bring principles of DEB theory to bear against several current problems in biology that each span multiple organisational levels. The cross-disciplinary nature of these problems suits interpretation in a framework that yields predictive synthesis, in place of classical reductionism.

The first of these problems surrounds a theoretical underpinning to the famous pattern of metabolic scaling. Metabolic scaling is the observation that as organisms increase in size, the energy turnover in a fixed unit of biomass decreases. This pattern has great biological importance and now forms the basis of the emerging field of metabolic ecology. Much of the current interest and controversy in metabolic scaling relates to recent ideas about the role of supply networks in constraining energy supply to cells. I show that an alternative explanation for physicochemical constraints on individual metabolism, as formalised by DEB theory, can contribute to the theoretical underpinning of metabolic ecology, while increasing coherence in the topic of metabolic scaling. In particular, I emphasise how DEB theory considers constraints on the storage and use of assimilated nutrients, and illustrate how this explains the frequently observed quarter-power scaling of many biological rates without relying on optimisation arguments or implying cellular nutrient supply limitation. Because the DEB theory mechanism for metabolic scaling is based on the universal process of acquiring and using pools of stored metabolites, it applies to all organisms irrespective of the nature of metabolic transport to the cells, but without necessarily excluding insights from transport-based models.

Thus, design constraints imposed by increasing size cause metabolic rate in animals of different species to increase more slowly than mass. However, mechanistic explanations for interspecific metabolic scaling do not apply for ontogenetic size changes within a species implying different mechanisms for scaling phenomena. Next, I show that the DEB theory approach of compartmentalizing biomass into reserve and structural components provides a unified framework for understanding both ontogenetic and interspecific metabolic scaling. We formulate the theory for the insects and show that it can account for ontogenetic metabolic scaling during the embryonic and larval phases, as well as the U-shaped respiration curve during pupation. After correcting for the predicted ontogenetic scaling effects, which we show to follow universal curves, the scaling of respiration between species is approximated by a ¾ power law, supporting past empirical studies on insect metabolic scaling and our theoretical predictions. The ability to explain ontogenetic and interspecific metabolic scaling effects under one consistent framework suggests that the partitioning of biomass into reserve and structure is a necessary foundation to a general metabolic theory.

The uptake of resources from the environment is a basic feature of all life. Consumption rate has been found to scale with body size with an exponent close to unity across diverse organisms. However, like metabolic rate, past analyses have ignored the important distinction between ontogenetic and interspecific size comparisons. I present a mechanistic model, based on DEB theory, for the body mass ($m$) scaling of consumption, which separates interspecific size effects from ontogenetic size effects. The model predicts uptake to scale with surface-area ($m^{2/3}$) during ontogenetic growth but more quickly (between $m^{3/4}$ and $m^1$) for interspecific comparisons. Available data for 41 insect species on consumption and assimilation during ontogeny provides strong empirical support for the theoretical predictions. Specifically, consumption rate scaled interspecifically with an exponent close to unity (0.89) but during ontogenetic growth scaled more slowly with an exponent of 0.70. Assimilation rate (consumption minus excretion) through ontogeny scaled more slowly than consumption due to a decrease in assimilation efficiency as insects grow. Again, these results highlight how body size imposes different constraints on metabolism depending on whether the size comparison is ontogenetic or inter-specific.

Finally, I use the principles of DEB theory to explore the universality of growth patterns in insects. Insects are typified by their small size, large numbers, impressive reproductive output, and rapid growth. However, insect growth is not simply rapid; rather, insects follow a qualitatively distinct trajectory to many other animals. I present a mechanistic growth model for insects and show that the up-regulation of assimilation during the growth phase can explain the near-exponential growth trajectory of insects. The presented model is tested against growth data on 50 insects, and compared against other mechanistic growth models. Unlike the other mechanistic models, our growth model predicts energy reserves per biomass to increase with age, which implies a higher production efficiency and energy density of biomass in later instars. These predictions are tested against data compiled from the literature whereby it is confirmed that insects increase their production efficiency (by 25 percentage points) and energy density (by 3 J/mg) between hatching and the attainment of full size. The model suggests that insects achieve greater production efficiencies and enhanced growth rates by up-regulating assimilation and increasing energy reserves per biomass, which are less costly to maintain than structural biomass. Our findings illustrate how the explanatory and predictive power of mechanistic growth models comes from their grounding in underlying biological processes.

These applications of DEB theory highlight novel insights on some well-studied, but unresolved issues in biology. More importantly, the theoretical basis of these insights demonstrates the value of a quantitative framework for metabolic organisation, which I confirm holds true even at coarser scales of analysis. While the grand challenge of unification across scales in biology still remains, the results of this thesis hold much promise for metabolic theory as a platform for synthesis.

## Publications

. Mechanistic models for predicting insect responses to climate change. In COIS, 2016.

. Testing mechanistic models of growth in insects. In Proceedings of the Royal Society B, 2015.

. The effect of egg size on hatch time and metabolic rate: theoretical and empirical insights on developing insect embryos. In Functional Ecology, 2015.

. Ontogenetic and interspecific scaling of consumption in insects. In Oikos, 2015.

. Ontogenetic and interspecific metabolic scaling in insects. In American Naturalist, 2013.

. Reconciling theories for metabolic scaling. In JAnE, 2013.