How does spawning frequency scale with body size in marine fishes?

Authors: Dustin J Marshall, Diego R Barneche, and Craig R White

Published in: Fish and Fisheries


How does fecundity scale with female size? Female size not only affects the number and size of offspring released in any one reproductive bout (i.e. batch fecundity) but also affects frequency of bouts that occur within a given spawning season (i.e. spawning frequency).

Previous studies have noted contrasting effects of female size on spawning frequency such that the effect of female size on reproductive output and total egg production of a population remains unclear. If smaller females spawn more frequently, this could effectively nullify hyperallometry—the disproportionate contribution of larger females to batch fecundity.

Here, we explore the relationship between female size and spawning frequency in marine fishes and test this relationship while controlling for phylogeny.

Within all of the species considered, spawning frequency scaled positively with body size. Comparing across species, the smallest species showed steeper scaling than the largest.

Considering only batch fecundity scaling probably underestimates the relationship between body size and absolute fecundity for many species; reproduction is likely to be more hyperallometric than is currently appreciated based on batch fecundity estimates. Second, an understanding of fecundity scaling depends on estimates of batch fecundity, spawning frequency and spawning duration—we have far more estimates of the first parameter than we do the others, and more studies are required.

Marshall DJ, Barneche DR, White CR (2021) How does spawning frequency scale with body size in marine fishes? Fish and Fisheries PDF DOI 

Does metabolic rate drive population size?

All organisms must eat to sustain themselves, but some more so than others. Metabolic rates should determine how much food an organism needs and how quickly it can convert that food into growth. We have long suspected the reason mice populations grow faster than elephant populations has something to do with their different metabolisms – for their size, mice have much higher metabolisms. While higher metabolisms might mean faster population growth, there is a supposed downside – populations with relatively higher metabolisms should exhaust resources at a much lower population biomass due to their higher resource demands. Thus, mice populations can sustain more individuals (have larger population sizes) than elephants, but on a per gram basis, mice have far lower population biomasses. That’s the theory at least – in reality no-one really knows.

Remarkably, despite years of interest in this topic, there have been no experimental tests of how metabolism affects populations – instead we relied on mouse-and-elephant-type comparisons – looking for patterns across organisms of very different sizes. While these comparisons are useful, obviously, mice and elephants differ in far more than their metabolisms alone, and these other factors could easily be driving any differences we observe. What’s needed is an experiment that manipulates the metabolism of whole populations, without changing anything else – a difficult task.

Lukas Schuster and Hayley Cameron along with Craig White and Dustin Marshall, set out to do just that. Using more than 1000 individuals of a common fouling marine creature – which feeds by filtering food particles from the water column – the team created 172 experimental populations that differed in their metabolic rates and population densities. These populations were then hung from plastic panels at a local marina where they were left to grow. The team then followed these populations for their entire lifetimes; measuring survival, growth and reproduction.

As anticipated, populations with higher metabolisms grew more rapidly – but what was unexpected was that populations with moderately high metabolic rates actually supported more individuals than those with lower metabolic rates. The reasons are unclear, but what seems to be happening is that higher metabolisms result in more feeding activity, which allows these populations to access relatively more resources, sustaining a larger number of individuals than expected. Metabolic rates can get too high, however, such that populations with the highest metabolic rates showed the expected decline in population size – probably because they exhausted local resources at a greater rate than these resources could be replenished, such that further increases in metabolism had no effect on resource intake.

The results have some surprisingly far-reaching implications. Many of the assumptions about how climate change will affect the resource consumption of future populations are based on classic, but untested theory. Likewise, fisheries are sometimes managed based on expectations about metabolic rate and resource demands. This research shows that the fundamental theory on how metabolism affects population demography needs revision. Higher metabolisms don’t invariably lead to lower population densities and a key rule of life seems to partially broken – higher metabolism populations can have their cake (grow fast) and eat it too (achieve high densities) – up to point at least.

This research was published in Proceedings of the National Academy of Sciences of the United States of America.

In biology we call the density at which a population stops growing the ‘carrying capacity’. Theoretical models predict that there will be a steady decline in carrying capacity as metabolic rates increases (blue line). But the research team found a more complicated relationship (black line). Initially carrying capacity increased with increasing metabolic rate before starting to decline. At higher metabolic rates the rate of decline in carrying capacity was the same for the team’s experimental data as for theoretical predictions.

Metabolism drives demography in an experimental field test

Authors: Lukas Schuster, Hayley Cameron, Craig R White, and Dustin J Marshall

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


Biology has long-standing rules about how metabolism and demography should covary. These rules connect physiology to ecology but remarkably, these rules have only ever been tested indirectly.

Using a model marine invertebrate, we created experimental field populations that varied in metabolic rate but not body size.

We show that metabolism qualitatively affects population growth and carrying capacity in ways predicted by theory but that scaling relationships for these parameters, as well as estimates of energy use at carrying capacity, depart from classic predictions.

That metabolism affects demography in ways that depart from canonical theory has important implications for predicting how populations may respond to global change and size-selective harvesting.


Metabolism should drive demography by determining the rates of both biological work and resource demand. Long-standing “rules” for how metabolism should covary with demography permeate biology, from predicting the impacts of climate change to managing fisheries.
Evidence for these rules is almost exclusively indirect and in the form of among-species comparisons, while direct evidence is exceptionally rare.

In a manipulative field experiment on a sessile marine invertebrate, we created experimental populations that varied in population size (density) and metabolic rate, but not body size. We then tested key theoretical predictions regarding relationships between metabolism and demography by parameterizing population models with lifetime performance data from our field experiment.

We found that populations with higher metabolisms had greater intrinsic rates of increase and lower carrying capacities, in qualitative accordance with classic theory. We also found important departures from theory—in particular, carrying capacity declined less steeply than predicted, such that energy use at equilibrium increased with metabolic rate, violating the long-standing axiom of energy equivalence.

Theory holds that energy equivalence emerges because resource supply is assumed to be independent of metabolic rate. We find this assumption to be violated under real-world conditions, with potentially far-reaching consequences for the management of biological systems.

Schuster L, Cameron H, White CR, Marshall DJ (2021) Metabolism drives demography in an experimental field test. Proceedings of the National Academy of Sciences of the United States of America PDF DOI

Fishing better to fish more

We have benchmarks for how to manage fisheries sustainably but what if the assumptions that go into setting those benchmarks are wrong?

In a previous study led by Diego Barneche and published in 2018, a research team looked at reproduction in more than 300 fish species. They found that contrary to a general perception, reproductive output did not increase in proportion with the size of the fish. Instead, the bigger the fish the disproportionately more eggs it produced. The mathematical term for this is hyperallometry.

This has clear implications for fisheries management and led Dustin and colleagues from Australia, USA and Germany to investigate assumptions around reproduction in fisheries management models.

Thirty-two of the world’s largest fisheries use management models that assume a proportional increase in reproductive output and fish size. These models estimate reproductive output from the total biomass of fish mature enough to spawn. This is because they are assuming that two 1 kg fish have the same reproductive output as one 2 kg fish. But the study led by Diego found that this was unlikely — 95% of the fish species they looked at had a hyperallometric relationship between size and reproduction — meaning the one big fish will produce many more eggs than the two smaller fish put together.

Does it matter? Well, yes. Dustin and his colleagues calculated that, for these fisheries, catches are set too high — in most cases, catches are twice what they should be in order to achieve the desired level of replenishment.

So, what happens when we get the biology right? Importantly, challenging assumptions about reproduction not only has ramifications for setting catch limits but has the potential to reset the way we manage fisheries. The team produced models that looked at retaining the largest and most reproductive members of the stock; through a temporary closure or protected area, or by setting size limits that focused on mid-size fish — leaving juveniles and the largest individuals unharvested.

The benefits of these different approaches vary depending on the species. Atlantic cod, for example, would benefit by switching to a fishery closure (either in space or time) with a predicted increase in long-term catch of ~25%

Dustin and his team acknowledge there are difficulties (both practical and social) with these approaches but also emphasise that any strategy that protects and retains larger fish in a population should provide a pay-off. Their models had some general assumptions of their own, however. When modelling fisheries that included protected areas where no fishing was allowed, they assumed that adult fish moved very little while larvae had the potential to replenish areas a long way away.

To check whether their results were too optimistic they did a more detailed study of the coral trout fishery in the Great Barrier Reef where they input data on larval movement. This reduced the catch increase from ~32% to ~16% suggesting that the more generic approach may overestimate benefits of fishery closures by ~12%.

A benefit of 16% is still non-trivial. Overall the results suggest that including hyperallometric reproduction in fisheries management models allows underused management tools such as marine protected areas to outperform traditional tools. This study highlights the role of reservoirs of large, highly reproductive individuals within a fishery.

This research is published in the journal Proceedings of the National Academy of Sciences of the United States of America.

Reproductive hyperallometry and managing the world’s fisheries

Authors: Dustin J Marshall, Michael Bode, Marc Mangel, Robert Arlinghaus, and EJ Dick

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


We find that a ubiquitous assumption in fisheries models for predicting population replenishment introduces systematic overestimates of replenishment in fished populations.

For 32 of the world’s major fisheries, these biases result in harvest thresholds being set too high: in most cases, reference points based on spawning potential ratios are more than 2.5 times higher than those necessary to achieve the desired level of replenishment.

When we use the more biologically appropriate assumption of reproductive hyperallometry, we find that management tools such as spatiotemporal closures and harvest slots can outperform traditional approaches in terms of yield.

Failing to consider reproductive hyperallometry overestimates the efficacy of traditional fisheries management and underestimates the benefits of approaches that create reservoirs of larger individuals.


Marine fisheries are an essential component of global food security, but many are close to their limits and some are overfished. The models that guide the management of these fisheries almost always assume reproduction is proportional to mass (isometry), when fecundity generally increases disproportionately to mass (hyperallometry).

Judged against several management reference points, we show that assuming isometry overestimates the replenishment potential of exploited fish stocks by 22% (range: 2% to 78%) for 32 of the world’s largest fisheries, risking systematic overharvesting.

We calculate that target catches based on assumptions of isometry are more than double those based on assumptions of hyperallometry for most species, such that common reference points are set twice as high as they should be to maintain the target level of replenishment.

We also show that hyperallometric reproduction provides opportunities for increasing the efficacy of tools that are underused in standard fisheries management, such as protected areas or harvest slot limits. Adopting management strategies that conserve large, hyperfecund fish may, in some instances, result in higher yields relative to traditional approaches.

We recommend that future assessment of reference points and quotas include reproductive hyperallometry unless there is clear evidence that it does not occur in that species.

Marshall DJ, Bode M, Mangel M, Arlinghaus R, Dick EJ (2021) Reproductive hyperallometry and managing the world’s fisheries. Proceedings of the National Academy of Sciences of the United States of America PDF DOI

Effects of light variation in algal cultures: a systematic map of temporal scales

Authors: Belinda Comerford, Nicholas Paul, and Dustin J Marshall

Published in: Journal of Applied Phycology


Algal aquaculture is a rapidly growing field, with a proliferation of studies exploring algal growth. The expansion of the field not only presents opportunities for synthesis, but also creates challenges in identifying where the strengths and knowledge gaps exist.

One tool for formally quantifying the state of knowledge is a systematic map, already useful in many fields, but underutilised in algal research. We used a systematic map to describe variable light regimes in algal cultures.

Light variation is ubiquitous in algal cultures and spans a range of temporal scales (microseconds to months), but it is unclear which scales have been explored.

We characterised 1393 experiments according to the temporal scale of light variation that was manipulated. Intensely studied light variation frequencies were either very short (< seconds) or long (diel cycles); the prominent gap was frequencies between these extremes (seconds to hours), especially for experiments that lasted for long durations (> months). Experiments that lasted for days were most common, while few studies lasted for months or more. Most studies were conducted in small culture vessels, used instantaneous changes in light regimes, and few studies reported initial stocking density metrics consistently.

Our map highlights that the field has accumulated a rich knowledge base that is ripe for synthesis in some areas, particularly very short or relatively long frequency light variation. The map indicates that the key priorities are explorations of intermediate frequencies and our understanding of their effects is limited. Similarly, our understanding of evolutionary responses to variable light regimes of all scales is lagging.

Comerford B, Paul N, Marshall D (2021) Effects of light variation in algal cultures: a systematic map of temporal scales. Journal of Applied Phycology PDF DOI

Mother-offspring conflicts: temperature can change selection on offspring size

We know offspring size varies enormously and understanding this variation is a long-standing goal of life history theoreticians and ecologists alike. A particularly interesting facet of offspring size is the fact it affects the fitness of both mothers and offspring simultaneously, so selection acts on both. This can lead to conflict over the amount of provisioning mothers provide to offspring. Selection on offspring usually favours bigger sizes, but mothers should only produce larger offspring where there is a marked benefit in performance for these offspring – there is a cost associated with this extra provisioning.

Temperature has a fairly reliable relationship with offspring size – higher temperatures are associated with smaller offspring. But what happens next? Does the relationship between offspring size and adult performance change with temperature?

There are few studies exploring these relationships in the field because it is an onerous undertaking. Repeated estimates of selection across multiple seasons and years are required to determine whether the relationship between offspring size and adult performance varies with natural temperature fluctuations

Professor Dustin Marshall designed a long-term study aimed at filling that gap. Using the model marine invertebrate species Bugula neritina, his research group deployed over 6000 individuals of known offspring size into the field over a period of 4 years. In total Dustin had 28 cohorts, each of approximately 240 individuals, where he had measures of survival, growth and reproduction of all individuals and water temperature data for the entire period.

Using the data collected in this study Dustin ran a simple ‘optimisation’ model which predicts cooler temperatures favour mothers producing larger offspring, while higher temperatures favour mothers producing smaller offspring. And, this works the other way around too. Larger offspring are favoured at cooler temperatures, smaller offspring are favoured at higher temperatures. In other words, at higher and lower temperatures, selection pressures on both mothers and offspring are the same; their interests are aligned.

But, there was a catch. At intermediate temperatures a conflict emerged. From around 18-22 degrees it is still better to be larger from the offspring’s perspective. Larger offspring had higher survival and growth than smaller offspring but the benefits were not enough to offset the costs to the mother of producing larger offspring. At these temperatures, mothers are better served by producing smaller offspring. This means at intermediate temperatures we would predict different offspring sizes to be favoured, depending on which perspective is taken.

Dustin also estimated the temporal autocorrelation of selection on offspring size among cohorts. In other words, knowing the selection coefficient on offspring size of one cohort, could he predict the selection coefficient of the next? Surprisingly, the answer was yes. But maybe even more surprising was that selection during one cohort was negatively correlated with selection two cohorts from now. So, it seems that selection varies from one generation to the next but this variation is not entirely random.

Estimating temporal autocorrelation is a notoriously data-hungry exercise which is exacerbated here because Dustin is interested in selection in each cohort. This means he only has selection estimates for 28 cohorts despite the scope of the study. Dustin plans to resume estimating selection on offspring size to see whether these patterns persist, as soon as Covid-19 obstacles are removed.

At the same time, he will see whether the relationships between offspring size, adult performance and temperature, change when offspring settle within a community. Does the presence of other species tip the balance in selection on offspring size?

This research is published in the journal Functional Ecology.

Temperature-mediated variation in selection on offspring size: A multi-cohort field study

Author: Dustin J Marshall

Published in: Functional Ecology


Offspring size is a key life-history trait that often covaries negatively with temperature. Most studies focus on how temperature alters selection on offspring size during early life-history stages such as embryos or larvae. The degree to which temperature alters the relationship between offspring size and post-metamorphic performance remains unclear as field studies across multiple temperature regimes are rare.

I deployed over 6,000 individuals of known offspring size, into the field across 28 cohorts spanning 4 years for the model marine invertebrate, Bugula neritina and monitored their survival, growth and reproduction.

Offspring size closely tracked the local environmental temperature across cohorts. This offspring size–temperature covariance appeared to be adaptive, at least from the perspective of mothers. When temperatures were warmer, the relationship between offspring size and performance was weak; when temperatures were cooler, the relationship was strongly positive.

The estimates of selection based on maternal fitness differed from those based on offspring fitness, suggesting temperature-mediated parent–offspring conflict over offspring provisioning exists. I also found evidence for temporal autocorrelation in temperature and selection on offspring size.

The fact that temperature affects the relationship between offspring size and post-metamorphic performance further complicates the challenge in understanding the ubiquitous covariance between offspring size and temperature.

Marshall DJ (2021) Temperature‐mediated variation in selection on offspring size: A multi‐cohort field study. Functional Ecology PDF DOI

Challenging the karyoplasmic ratio: bigger cells, smaller nuclei

A new publication finally puts paid to a long-held belief that the ratio between nucleus size and cell size (NS:CS) is approximately constant. This is called the karyoplasmic ratio and, while recently it has been recognised that nucleus size and cell size are not inexorably bound, the idea of a constant NS:CS ratio remains pervasive in biology. Not least in cancer biology where the karyoplasmic ratio is used in both diagnosis and prognosis for certain tumour types.

But, Dr Martino Malerba and Prof Dustin Marshall found that bigger cells have relatively smaller nuclei; as cells get bigger the karyoplasmic ratio actually gets smaller.

It all started when Martino and Dustin noticed that their evolved lines of different size algae didn’t show a constant karyoplasmic ratio. This piqued their curiosity; were these cells unusual or had this been observed in other cells? They started compiling data on cell size and nucleus size in a range of species and started reviewing publications for statements about the karyoplasmic ratio. To their surprise, they found many publications referring to a constant ratio between nucleus size and cell size, but the data didn’t support that. It was enough to compel Martino and Dustin to formally assess the karyoplasmic ratio across a wide range of cell types and species.

They continued amassing data on cell size and nucleus size across as many species as they could find. They collected measurements from 879 species, ranging from microbes to mammals. Then they looked for data within a species and assembled 7,929 observations of both nucleus size and cell size in a diverse range of species including yeast, plants and metazoans. Finally, they returned to the artificially size-selected algae (small and large) and tracked nucleus size and cell size across 500 generations of evolution.

What they found was that while, yes, bigger cells had bigger nuclei, in relative terms bigger cells had smaller nuclei. At all three scales of biological organisation that they looked at (among-species, within-species, and among evolved lineages of the same species) they saw a systematic decrease in the karyoplasmic ratio with increasing cell size.

Martino and Dustin measured nucleus size in two different ways to double check that their observation of decreasing karyoplasmic ratio with increasing cell size was not due to the methods they had used. Here we see that regardless of the method of calculating nucleus size the ratio decreases across a range of different species as well as the large and small evolved algal lines of the same species.

Why do larger cells have relatively smaller nuclei? The authors surmise it might tie into the fact that larger cells also have relatively lower metabolisms. So, is it because larger cells, with their lower relative metabolic rates are able to meet all of their functional needs with relatively smaller nuclei? Or, conversely, is it because larger cells, with relatively smaller nuclei are only capable of sustaining relatively lower metabolic rates? We don’t know.

What we do know is that the decreasing karyoplasmic ratio with increasing cell size is remarkably consistent across a wide variety of life forms. Martino and Dustin hope that a universal driver for this relationship will be identified.

This research was published in the journal Evolution Letters.

Larger cells have relatively smaller nuclei across the Tree of Life

Authors: Martino E Malerba and Dustin J Marshall

Published in: Evolution Letters


Larger cells have larger nuclei, but the precise relationship between cell size and nucleus size remains unclear, and the evolutionary forces that shape this relationship are debated.

We compiled data for almost 900 species – from yeast to mammals – at three scales of biological organisation: among-species, within-species, and among-lineages of a species that was artificially selected for cell size.

At all scales, we showed that the ratio of nucleus size to cell size (the ‘N: C’ ratio) decreased systematically in larger cells. Size evolution appears more constrained in nuclei than cells: cell size spans across six orders of magnitude, whereas nucleus size varies by only three.

The next important challenge is to determine the drivers of this apparently ubiquitous relationship in N:C ratios across such a diverse array of organisms.

Malerba ME, Marshall DJ (2021) Larger cells have relatively smaller nuclei across the Tree of Life. Evolution Letters PDF DOI