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

Are larvae picky eaters?

A study by recent PhD graduate Emily Richardson and her supervisor Dustin Marshall found that the larvae of a filter-feeding marine worm move from being feeding generalists to specialists as they develop.

We know that many organisms experience dietary shifts as they grow bigger or after undergoing dramatic changes in body shape and structure (e.g. metamorphosis). But what happens across larval stages? Some species can increase in size by several orders of magnitude during larval development, and yet, few studies have looked at how diet changes within the larval phase.

Emily and Dustin tested how fundamental ‘niche’ (or, in this case, the ideal diet in the absence of competition or other environmental influences) changes during larval development. Their filter-feeding study species Galeolaria caespitosa is included in a group overlooked in classic niche theory — filter feeders were once assumed to have no diet changes during their life cycle. Overall, the study targeted two knowledge gaps of niche theory: whether diet changes

  1. across larval stages and
  2. for filter feeders.
Emily and Dustin looked at feeding rates of four different species of algae that differed in size, in three larval stages of a marine filter-feeder.

They assumed that smaller larvae would be limited to feeding on the smallest phytoplankton (i.e. algae) species, whilst larger larvae would eat more algae and enjoy a wider range of species. In other words, the fundamental niche would broaden as the larvae grew and were able to eat a wider range phytoplankton species of variable sizes.

This was not what they found. They offered the three different larval stages four different algal food species that vary in size. Each algal species was offered on its own so that there was no choice of food available and feeding rates were calculated from the difference in algal concentrations at the start of each run and after six hours of larval feeding.

The smallest larvae ate all four algal species in approximately equal proportion, although they did consume slightly less of the biggest species, which is roughly the same size as the mouth gape. As the larvae got bigger, they consumed large amounts of the two medium-sized algal species and barely touched the smallest species, despite its availability in high concentrations. Overall, small larvae had a broad niche that ultimately narrowed across the stages, because medium-sized cells made up the majority of the diet for large larvae.

While the bigger larvae were not constricted by algal size they may have concentrated on a narrower range of algae because it is more nutritious at the stage of development where they are preparing to settle and metamorphose into adult worms. Alternatively, the medium sized algae may have represented the most efficient food source, in that capture success was maximized in relation to encounter rate.

There was little difference in the four different algae species consumed by the smallest larval phase – the trochophore – while the largest larval phase (metatrochophore) consumed very little of the smallest algae (Nannochloropsis) but instead consumed lots of the intermediate sized algae. Note the y-axis is final biovolume so higher final biovolumes indicate less was consumed. The starting biovolumes are the figures below each data group.

While this study doesn’t elucidate the reasons for this narrowing of the fundamental niche in developing larvae, it does suggest that the relationship between fundamental niche and body size may be more complicated than classic theory suggests.

A previous study from our lab has shown that benthic filter feeders have the potential to impact on phytoplankton communities through their feeding; the same may be true of filter feeding larvae.

This research was published in the journal The Biological Bulletin.

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 

The Conversation: ‘Let’s get real’: scientists discover a new way climate change threatens cold-blooded animals

This article is republished from The Conversation under a Creative Commons license. Read the original article.

All animals need energy to live. They use it to breathe, circulate blood, digest food and move. Young animals use energy to grow, and later in life, to reproduce.

Increased body temperature increases the rate at which an animal uses energy. Because cold-blooded animals rely on the thermal conditions of their environment to regulate their body temperature, they’re expected to need more energy as the planet warms.

However, our new research, published today in Nature Climate Change, suggests temperature is not the only environmental factor affecting the future energy needs of cold-blooded animals. How they interact with other species will also play a role.

Our findings suggest cold-blooded animals will need even more energy in a warmer world than previously thought. This may increase their extinction risk.

Young animals use energy to grow, and later in life, to reproduce.

What we already know

The amount of energy animals use in a given amount of time is called their metabolic rate.

Metabolic rate is influenced by a variety of factors, including body size and activity levels. Larger animals have higher metabolic rates than smaller animals, and active animals have higher metabolic rates than inactive animals.

Metabolic rate also depends on body temperature. This is because temperature affects the rate at which the biochemical reactions involved in energy metabolism proceed. Generally, if an animal’s body temperature increases, its metabolic rate will accelerate exponentially.

Most animals alive today are cold-blooded, or “ectotherms”. Insects, worms, fish, crustaceans, amphibians and reptiles – basically all creatures except mammals and birds – are ectotherms.

As human-induced climate change raises global temperatures, the body temperatures of cold-blooded animals are also expected to rise.

Researchers say the metabolic rate of some land-based ectotherms may have already increased by between 3.5% and 12% due to climate warming that’s already occurred. But this prediction doesn’t account for the animals’ capacity to physiologically “acclimate” to warmer temperatures.

Acclimation refers to an animal’s ability to remodel its physiology to cope with a change in its environment.

But rarely can acclimation fully negate the effect of temperature on metabolic processes. For this reason, by the end of the century land-based ectotherms are still predicted to have metabolic rates about 20% to 30% higher than they are now.

Having a higher metabolic rate means that animals will need more food. This means they might starve if more food is not available, and leaves them less energy to find a mate and reproduce.

As climate change raises global temperatures, the body temperatures of cold-blooded animals are also expected to rise.

Our research

Previous research attempts to understand the energetic costs of climate warming for ectotherms were limited in one important respect. They predominantly used animals studied in relatively simple laboratory environments where the only challenge they faced was a change in temperature.

However, animals face many other challenges in nature. This includes interacting with other species, such as competing for food and predator-prey relationships.

Even though species interact all the time in nature, we rarely study how this affects metabolic rates.

We wanted to examine how species interactions might alter predictions about the energetic costs of climate warming for cold-blooded animals. To do this, we turned to the fruit fly (from the genus Drosophila).

Fruit fly species lay their eggs in rotting plant material. The larvae that hatch from these eggs interact and compete for food.

Our study involved rearing fruit fly species alone or together at different temperatures. We found when two species of fruit fly larvae compete for food at warmer temperatures, they were more active as adults than adults that didn’t compete with other species as larvae. This means they also used more energy.

From this, we used modelling to deduce that species interactions at warmer global temperatures increase the future energy needs of fruit flies by between 3% and 16%.

These findings suggest previous studies have underestimated the energetic cost of climate warming for ectotherms. That means purely physiological approaches to understanding the consequences of climate change for cold-blooded animals are likely to be insufficient.

Previous studies have underestimated the energetic cost of climate warming for ectotherms.

Let’s get real

Understanding the energy needs of animals is important for understanding how they’ll survive, reproduce and evolve in challenging environments.

In a warmer world, hotter ectotherms will need more energy to survive and reproduce. If there is not enough food to meet their bodies’ energy demands, their extinction risk may increase.

Clearly, we must more accurately predict how climate warming will threaten biodiversity. This means studying the responses of animals to temperature change under more realistic conditions.
The Conversation

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

Can we apply theory developed to understand hermaphroditism in plants, to animals?

Hermaphroditism — a condition where an organism can produce both male and female gametes — is very common in plants and many animals. While the ability to self-fertilise seems like an evolutionary ‘cunning plan’, there are drawbacks. If hermaphrodites only self-fertilise, they run the risk of inbreeding depression, but where survival or mating opportunities are slim, then self-fertilisation is better than not reproducing at all.

Theory does a good job of predicting when hermaphroditism will benefit plants. Interestingly, animals have not received the same attention. George Jarvis and his PhD supervisors Craig White and Dustin Marshall have found that the same theories predicting hermaphroditism in plants can also be applied to animals.

Essentially, strong competition among siblings for resources or among gametes for fertilisation may drive the evolution of hermaphroditism in both plants and animals.

Highly competitive environments can tip the balance towards hermaphroditism, because hermaphrodites can reallocate resources from male to female function (or vice versa) to increase their competitive advantage.

George and his supervisors considered the accepted evolutionary drivers for hermaphroditism in plants and looked for analogues in marine animals.

In plants, species with limited seed dispersal can experience strong competition among siblings for resources, and are more likely to be hermaphrodites. In marine animals, larval dispersal provides an analogous model to test if the same forces are at play.

Larvae released into the plankton travel further than non-planktonic larvae and feeding larvae travel even further than their non-feeding counterparts. Plant theory predicts that hermaphrodites are more common in species where local competition is greatest; in marine animals then, hermaphroditism should be more common in species with non-planktonic larvae.

Similarly, plants pollinated by specialist insects are more likely to be hermaphrodites. In animals, internal fertilisers are akin to plant species with specialist pollinators; competition between gametes is fierce and so an extra guarantee in the form of hermaphroditism should be more common.

George and his supervisors found other analogues between plant and animal theory as well. Smaller plants and plants at higher latitudes are more likely to be hermaphrodites due to increased competition between gametes and rarer mating opportunities respectively. If plant theory holds, the same patterns between hermaphroditism, size and biogeography will be true for animals as well.

The research team set about compiling data for reproductive mode, larval development mode, fertilisation mode, latitude and adult size for 1,153 species of marine annelids, echinoderms and molluscs.

They found theory developed to understand hermaphroditism in plants, predicts many patterns of hermaphroditism in marine animals. Overall, hermaphroditism is generally associated with limited offspring dispersal, internal fertilisation and small body size.

But just to complicate things, George and his supervisors also found that in annelids and molluscs, species that are external fertilizers are more likely to be hermaphrodites when large, but in internal fertilizers the opposite is true.

George, Craig and Dustin feel their results support Darwin’s supposition from over a century ago: hermaphroditism evolves in response to an organism’s life history and ecology —  not the other way around.

This research was published in the journal Evolution.

Theory developed to understand hermaphroditism in plants, predicts many patterns of hermaphroditism in marine animals. In these taxa (top to bottom: annelids, echinoderms and molluscs) hermaphroditism is generally associated with internal fertilisation, small body size and, with the exception of molluscs, limited dispersal. In each graph, the bars represent average (± SE) predicted probabilities of hermaphroditism from standard regressions, and numbers represent the number of species for each mode. Note that scales differ among taxa.