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 

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 

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

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

Carry-over effects and fitness trade-offs in marine life histories: The costs of complexity for adaptation

Authors Dustin J Marshall and Tim Connallon

Published in Evolutionary Applications


Most marine organisms have complex life histories, where the individual stages of a life cycle are often morphologically and ecologically distinct. Nevertheless, life-history stages share a single genome and are linked phenotypically (by “carry-over effects”). These commonalities across the life history couple the evolutionary dynamics of different stages and provide an arena for evolutionary constraints. The degree to which genetic and phenotypic links among stages hamper adaptation in any one stage remains unclear and yet adaptation is essential if marine organisms will adapt to future climates.

Here, we use an extension of Fisher’s geometric model to explore how both carry-over effects and genetic links among life-history stages affect the emergence of pleiotropic trade-offs between fitness components of different stages. We subsequently explore the evolutionary trajectories of adaptation of each stage to its optimum using a simple model of stage-specific viability selection with nonoverlapping generations.

We show that fitness trade-offs between stages are likely to be common and that such trade-offs naturally emerge through either divergent selection or mutation. We also find that evolutionary conflicts among stages should escalate during adaptation, but carry-over effects can ameliorate this conflict.

Carry-over effects also tip the evolutionary balance in favor of better survival in earlier life-history stages at the expense of poorer survival in later stages. This effect arises in our discrete-generation framework and is, therefore, unrelated to age-related declines in the efficacy of selection that arise in models with overlapping generations.

Our results imply a vast scope for conflicting selection between life-history stages, with pervasive evolutionary constraints emerging from initially modest selection differences between stages. Organisms with complex life histories should also be more constrained in their capacity to adapt to global change than those with simple life histories.

Marshall DJ, Connallon T (2023) Carry‐over effects and fitness trade‐offs in marine life histories: The costs of complexity for adaptation. Evolutionary Applications PDF DOI

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


Organisms use energy to grow and reproduce, so the processes of energy metabolism and biological production should be tightly bound. On the basis of this tenet, we developed and tested a new theory that predicts the relationships among three fundamental aspects of life: metabolic rate, growth, and reproduction.

We show that the optimization of these processes yields the observed allometries of metazoan life, particularly metabolic scaling. We conclude that metabolism, growth, and reproduction are inextricably linked; that together they determine fitness; and, in contrast to longstanding dogma, that no single component drives another.

Our model predicts that anthropogenic change will cause animals to evolve decreased scaling exponents of metabolism, increased growth rates, and reduced lifetime reproductive outputs, with worrying consequences for the replenishment of future populations.

White CR, Alton LA, Bywater CL, Lombardi EJ, Marshall DJ (2022) Metabolic scaling is the product of life-history optimization. Science DOI

Long-term experimental evolution decouples size and production costs in Escherichia coli

Authors: Dustin J Marshall, Martino Malerba, Thomas Lines, Aysha L Sezmis, Chowdhury M Hasan, Richard E Lenski, and Michael J McDonald

Published in: Proceedings of the National Academy of Sciences (PNAS) of the United States of America 


Populations of larger organisms should be more efficient in their resource use, but grow more slowly, than populations of smaller organisms.

The relations between size, metabolism, and demography form the bedrock of metabolic theory, but most empirical tests have been correlative and indirect.

Experimental lineages of Escherichia coli that evolved to make larger cells provide a unique opportunity to test how size, metabolism, and demography covary. Despite the larger cells having a relatively slower metabolism, they grow faster than smaller cells. They achieve this growth rate advantage by reducing the relative costs of producing their larger cells.

That evolution can decouple the costs of production from size challenges a fundamental assumption about the connections between physiology and ecology.


Body size covaries with population dynamics across life’s domains. Metabolism may impose fundamental constraints on the coevolution of size and demography, but experimental tests of the causal links remain elusive.

We leverage a 60,000-generation experiment in which Escherichia coli populations evolved larger cells to examine intraspecific metabolic scaling and correlations with demographic parameters.

Over the course of their evolution, the cells have roughly doubled in size relative to their ancestors. These larger cells have metabolic rates that are absolutely higher, but relative to their size, they are lower.

Metabolic theory successfully predicted the relations between size, metabolism, and maximum population density, including support for Damuth’s law of energy equivalence, such that populations of larger cells achieved lower maximum densities but higher maximum biomasses than populations of smaller cells. The scaling of metabolism with cell size thus predicted the scaling of size with maximum population density. In stark contrast to standard theory, however, populations of larger cells grew faster than those of smaller cells, contradicting the fundamental and intuitive assumption that the costs of building new individuals should scale directly with their size.

The finding that the costs of production can be decoupled from size necessitates a reevaluation of the evolutionary drivers and ecological consequences of biological size more generally.

Marshall DJ, Malerba M, Lines T, Sezmis AL, Hasan CM, Lenski RE, McDonald MJ (2022) Long-term experimental evolution decouples size and production costs in Escherichia coli. Proceedings of the National Academy of Sciences of the United States of America PDF DOI