Optimisation and constraint: explaining metabolic patterns in biology

Authors: Craig R White and Dustin J Marshall

Published in: Journal of Experimental Biology


Constraint-based explanations have dominated theories of size-related patterns in nature for centuries. Explanations for metabolic scaling — the way in which metabolism changes with body mass — have been based on the geometry of circulatory networks through which resources are distributed, the need to dissipate heat produced as a by-product of metabolic processes, and surface-area-to-volume constraints on the flux of nutrients or waste.

As an alternative to these constraint-based approaches, we recently developed a new theory that predicts that metabolic allometry arises as a consequence of the optimisation of growth and reproduction to maximise fitness within a finite life. Our theory is free of physical geometric constraints that limit the possibilities available to evolution, and we therefore argue that metabolic allometry can be explained without the need to invoke any of the assumed constraints traditionally imposed by metabolic theories. Our findings also suggest that metabolism, growth and reproduction have co-evolved to maximise fitness (i.e. lifetime reproduction) and that the observed patterns in these fundamental characteristics of life can similarly be explained by optimisation rather than constraint.

In this Centenary Commentary, we present an overview of our approach and a critique of its limitations. We propose a suite of empirical tests that we hope will move the field forward, discuss the dangers of model overparameterisation and highlight the need to remain open to non-adaptive hypotheses for the origin of biological patterns.

White CR, Marshall DJ (2023) Optimisation and constraint: explaining metabolic patterns in biology. Journal of Experimental Biology PDF DOI 

Fish live faster in the tropics and slower in the poles because of mortality risks

Biological organisms must acquire resources to enable them to grow, mature and reproduce before they die. The study of how organisms allocate resources to each of these requirements is known as life history theory. Organisms with a ‘fast’ life history grow to smaller sizes, mature early and reproduce at both smaller sizes and younger ages before dying. A ‘slow’ life history suggests the opposite end of the spectrum; organisms have slower growth, mature and reproduce later and live for much longer than their ‘faster’ counterparts.

A new study from The Centre for Geometric Biology at Monash University and international collaborators has found that fish in tropical regions suffer high mortality and so optimise their fitness by diverting energy into reproduction earlier in life — their fast life histories are driven by mortality risk.

The research team led by Dr Mariana Álvarez-Noriega have used life history optimisation models to predict global patterns in the life histories of marine fish. They then tested and confirmed these predictions with a global dataset of marine fish life histories.

They found fish in polar regions have a lower chance of dying and therefore optimise their life history by growing longer and larger, and delaying maturity and reproduction. But when they do start reproducing they have a disproportionately greater investment in reproduction in relation to their size. That is, the relationship between body mass and reproductive output increases much more steeply for fish living in colder waters than those in warmer environments.

The model predicted that fish would mature later at the poles (higher latitudes) (graph a) and the real-life data the team collated from existing records confirmed this relationship (graph b).

So, for example a 10-kilogram fish is predicted to produce approximately 2.2 million eggs in the tropics and 3.5. million eggs in polar regions. But a 20-kilogram fish is predicted to produce approximately 4 million eggs in the tropics and 8.1 million eggs at the poles. The difference is greater as the fish get bigger.

Bigger fish produce more eggs and bigger fish at higher latitudes (polar regions) produce more eggs than fish of the same size at lower latitudes (tropical regions)

Dr Álvarez-Noriega emphasises that these global patterns have important consequences: “the impacts of fishing and Marine Protected Areas will be different in different latitudes”.

What is more, the team modelled the impacts of climate change and found that if CO2 emissions remain high their model predicts that a 25-kilogram fish at 60° latitude will produce 300,000 fewer eggs by the end of the century.

Our model predicts that global warming will profoundly reshape fish life histories, favouring earlier reproduction, smaller body sizes and lower mass-specific reproductive outputs, with worrying consequences for population persistence

Dr Álvarez-Noriega

This research was published in PLOS Biology.

Life history optimisation drives latitudinal gradients and responses to global change in marine fishes

Authors: Mariana Álvarez-Noriega, Craig R White, Jan Kozłowski, Troy Day, and Dustin J Marshall

Published in: PLOS Biology


Within many species, and particularly fish, fecundity does not scale with mass linearly; instead, it scales disproportionately. Disproportionate intraspecific size–reproduction relationships contradict most theories of biological growth and present challenges for the management of biological systems. Yet the drivers of reproductive scaling remain obscure and systematic predictors of how and why reproduction scaling varies are lacking.

Here, we parameterise life history optimisation model to predict global patterns in the life histories of marine fishes. Our model predicts latitudinal trends in life histories: Polar fish should reproduce at a later age and show steeper reproductive scaling than tropical fish.

We tested and confirmed these predictions using a new, global dataset of marine fish life histories, demonstrating that the risks of mortality shape maturation and reproductive scaling.

Our model also predicts that global warming will profoundly reshape fish life histories, favouring earlier reproduction, smaller body sizes, and lower mass-specific reproductive outputs, with worrying consequences for population persistence.

Álvarez-Noriega M, White CR, Kozłowski J, Day T, Marshall DJ (2023) Life history optimisation drives latitudinal gradients and responses to global change in marine fishes. PLOS Biology PDF DOI

Response to comments on “Metabolic scaling is the product of life-history optimization”

Authors: Craig R White, Lesley A Alton, Candice L Bywater, Emily J Lombardi, and Dustin J Marshall

Published in: Science


Froese and Pauly argue that our model is contradicted by the observation that fish reproduce before their growth rate decreases.

Kearney and Jusup show that our model incompletely describes growth and reproduction for some species.

Here we discuss the costs of reproduction, the relationship between reproduction and growth, and propose tests of models based on optimality and constraint.

White CR, Alton LA, Bywater CL, Lombardi EJ, Marshall DJ (2023) Response to Comments on “Metabolic scaling is the product of life-history optimization.” Science PDF DOI 

Fundamental niche narrows through larval stages of a filter-feeding marine invertebrate

Authors: Emily L Richardson and Dustin J Marshall

Published in: The Biological Bulletin


Ontogenetic niche theory predicts that resource use should change across complex life histories.

To date, studies of ontogenetic shifts in food niches have mainly focused on a few systems (e.g., fish), with less attention on organisms with filter-feeding larval stages (e.g., marine invertebrates). Recent studies suggest that filter-feeding organisms can select specific particles, but our understanding of whether niche theory applies to this group is limited.

We characterized the fundamental niche (i.e., feeding proficiency) by examining how niche breadth changes across the larval stages of the filter-feeding marine polychaete Galeolaria caespitosa. Using a no-choice experimental design, we measured feeding rates of trochophore, intermediate-stage, and metatrochophore larvae on the prey phytoplankton species Nannochloropsis oculata, Tisochrysis lutea, Dunaliella tertiolecta, and Rhodomonas salina, which vary 10-fold in size, from the smallest to the largest.

We formally estimated Levins’s niche breadth index to determine the relative proportions of each species in the diet of the three larval stages and also tested how feeding rates vary with algal species and stage.

We found that early stages eat all four algal species in roughly equal proportions, but niche breadth narrows during ontogeny, such that metatrochophores are feeding specialists relative to early stages. We also found that feeding rates differed across phytoplankton species: the medium-sized cells (Tisochrysis and Dunaliella) were eaten most, and the smallest species (Nannochloropsis) was eaten the least.

Our results demonstrate that ontogenetic niche theory describes changes in fundamental niche in filter feeders. An important next step is to test whether the realized niche (i.e., preference) changes during the larval phase as well.

Richardson EL, Marshall DJ (2023) Fundamental niche narrows through larval stages of a filter-feeding marine invertebrate. The Biological Bulletin PDF DOI 

Interspecific interactions alter the metabolic costs of climate warming

Authors: Lesley A Alton and Vanessa Kellermann

Published in: Nature Climate Change


Climate warming is expected to increase the energy demands of ectotherms by accelerating their metabolic rates exponentially. However, this prediction ignores environmental complexity such as species interactions.

Here, to better understand the metabolic costs of climate change for ectotherms, we reared three Drosophila species in either single-species or two-species cultures at different temperatures and projected adult metabolic responses under an intermediate climate-warming scenario across the global range of Drosophila.

We determined that developmental acclimation to warmer temperatures can reduce the energetic cost of climate warming from 39% to ~16% on average by reducing the thermal sensitivity of metabolic rates. However, interspecific interactions among larvae can erode this benefit of developmental thermal acclimation by increasing the activity of adults that develop at warmer temperatures.

Thus, by ignoring species interactions we risk underestimating the metabolic costs of warming by 3–16% on average.

Alton LA, Kellermann V (2023) Interspecific interactions alter the metabolic costs of climate warming. Nature Climate Change DOI

Mapping the correlations and gaps in studies of complex life histories

Authors: Emily L Richardson and Dustin J Marshall

Published in: Ecology and Evolution


For species with complex life histories, phenotypic correlations between life-history stages constrain both ecological and evolutionary trajectories.

Studies that seek to understand correlations across the life history differ greatly in their experimental approach: some follow individuals (“individual longitudinal”), while others follow cohorts (“cohort longitudinal”). Cohort longitudinal studies risk confounding results through Simpson’s Paradox, where correlations observed at the cohort level do not match that of the individual level. Individual longitudinal studies are laborious in comparison, but provide a more reliable test of correlations across life-history stages.

Our understanding of the prevalence, strength, and direction of phenotypic correlations depends on the approaches that we use, but the relative representation of different approaches remains unknown.

Using marine invertebrates as a model group, we used a formal, systematic literature map to screen 17,000+ papers studying complex life histories, and characterized the study type (i.e., cohort longitudinal, individual longitudinal, or single stage), as well as other factors.

For 3315 experiments from 1716 articles, 67% focused on a single stage, 31% were cohort longitudinal and just 1.7% used an individual longitudinal approach.

While life-history stages have been studied extensively, we suggest that the field prioritize individual longitudinal studies to understand the phenotypic correlations among stages.

Richardson EL, Marshall DJ (2023) Mapping the correlations and gaps in studies of complex life histories. Ecology and Evolution PDF DOI

Macroevolutionary patterns in marine hermaphroditism

Authors: George C Jarvis, Craig R White, and Dustin J Marshall

Published in: Evolution


Most plants and many animals are hermaphroditic; whether the same forces are responsible for hermaphroditism in both groups is unclear. The well-established drivers of hermaphroditism in plants (e.g., seed dispersal potential, pollination mode) have analogues in animals (e.g., larval dispersal potential, fertilization mode), allowing us to test the generality of the proposed drivers of hermaphroditism across both groups.

Here, we test these theories for 1,153 species of marine invertebrates, from three phyla. Species with either internal fertilization, restricted offspring dispersal, or small body sizes are more likely to be hermaphroditic than species that are external fertilizers, planktonic developers, or larger.

Plants and animals show different biogeographical patterns, however: animals are less likely to be hermaphroditic at higher latitudes — the opposite to the trend in plants.

Overall, our results suggest that similar forces, namely, competition among offspring or gametes, shape the evolution of hermaphroditism across plants and three invertebrate phyla.

Jarvis GC, White CR, Marshall DJ (2022) Macroevolutionary patterns in marine hermaphroditism. Evolution PDF DOI

Changing lanes: can we reconcile the ways we measure reproduction so we can make meaningful comparisons across animal species?

Reproduction is perhaps the only truly unambiguous measure of fitness and yet we measure it in different ways. Biologists working on birds tend to measure clutch size as number of eggs per clutch, while mammal biologists focus on litter size measured in mass. These differences only become obvious when researchers want to move out of their accustomed lanes and ask broader questions applicable to a wide range of animal species. One unequivocal measure of reproduction is reproductive mass per year but how often do researchers measure this?

Reproductive mass per year combines the number of offspring per reproductive bout with the mass of the offspring and, importantly, the number of reproductive bouts per year. We know that some species can have a few large offspring and only reproduce once per year whilst other species can produce many small offspring numerous times per year. So which species puts in the most resources to reproduction? Only by combining measures of offspring mass over time can we really compare reproductive effort across species.

How often are all three components of reproductive mass per year – number of offspring per reproductive bout, offspring mass, and the number of reproductive bouts per year – provided for animals?

PhD student, Sam Ginther, is interested in the energetic costs of reproduction and wondered how feasible it would be to collate reproduction data for a wide range of species. Could he translate the existing data into a consistent and biologically relevant measure of reproductive mass per year?

Sam and supervisors Dustin Marshall, Craig White and Hayley Cameron created a ‘systematic map’ of reproductive trait data that exist in online databases. They used this unbiased approach to collate and describe:

  1. how common is the measure reproductive mass per year in databases, and
  2. how well did more ambiguous reproductive measures (i.e., fecundity per bout, fecundity per year, and reproductive mass per bout) represent a truly comparable measure of reproductive effort – reproductive mass per year.

So, can we use other measures as proxies for reproductive mass per year? While most reproductive measures are poor predictors of reproductive effort, reproductive mass per bout is the exception.

Reproductive databases are amazing resources and represent centuries of work in the field of reproductive biology. However, to unlock their full potential Sam and his colleagues feel that the best way forward is to encourage researchers to measure reproduction in a way that allows us to reconstruct reproductive mass per year; that is, tie reproductive measures to temporal- and volumetric-dimensions. But where this is unrealistic in terms of time and effort then measuring reproductive mass per bout is the next best thing.

This research is published in the journal Global Ecology and Biogeography.

Avoiding growing pains in reproductive trait databases: the curse of dimensionality

Authors: Samuel C Ginther, Hayley Cameron, Craig R White, and Dustin J Marshall

Published in: Global Ecology and Biogeography


Aim: Reproductive output features prominently in many trait databases, but the metrics describing it vary and are often untethered to temporal and volumetric dimensions (e.g., fecundity per bout). The use of such ambiguous reproductive measures to make broad-scale comparisons across taxonomic groups will be meaningful only if they show a 1:1 relationship with a reproductive measure that explicitly includes both a volumetric and a temporal component (i.e., reproductive mass per year). We sought to map the prevalence of ambiguous and explicit reproductive measures across taxa and to explore their relationships with one another to determine the cross-compatibility and utility of reproductive metrics in trait databases.

Location: Global.

Time period: 1990–2021.

Major taxa studied: We searched for reproductive measures across all Metazoa and identified 19,785 vertebrate species (Chordata), and 440 invertebrate species (Arthropoda, Cnidaria or Mollusca).

Methods: We included 37 databases, from which we summarized the commonality of reproductive metrics across taxonomic groups. We also quantified scaling relationships between ambiguous reproductive traits (fecundity per bout, fecundity per year and reproductive mass per bout) and an explicit measure (reproductive mass per year) to assess their cross-compatibility.

Results: Most species were missing at least one temporal or volumetric dimension of reproductive output, such that reproductive mass per year could be reconstructed for only 4,786 vertebrate species. Ambiguous reproductive measures were poor predictors of reproductive mass per year; in no instance did these measures scale at 1:1.

Main conclusions: Ambiguous measures systematically misestimate reproductive mass per year. Until more data are collected, we suggest that researchers should use the clade-specific scaling relationships provided here to convert ambiguous reproductive measures to reproductive mass per year.

Ginther SC, Cameron H, White CR, Marshall DJ (2022) Avoiding growing pains in reproductive trait databases: the curse of dimensionality. Global Ecology and Biogeography PDF DOI