Growing pains: time to reassess models of growth?

A central aim of the Centre for Geometric Biology is understanding how and why organisms grow. In a recent opinion piece, published in the journal Trends in Ecology & Evolution, Dustin Marshall and Craig White suggest that it might be time to take another look at the ways we currently understand and model growth.

In the past, growth has mainly been considered in two different ways. Mechanistic models of growth emphasise identifying the physiological processes driving growth. This group of models includes the von Bertalanffy Growth Function, which is perhaps the best-known growth model. It estimates the rate of increase in mass (growth) as the difference between anabolism (energy-consuming processes) and catabolism (energy-producing processes). Other models of this type include the Ontogenetic Growth Model and the Dynamic Energy Budget model.

In contrast, phenomenological models of growth are based on life-history theory and work from the assumption that organisms evolve to maximise their fitness. Theories and models under this framework revolve around the trade-offs between maximising reproduction against the risk of mortality.

The von Bertalanffy Growth Function and more recent mechanistic models do an excellent job of describing how the growth of most organisms slows as they approach their final size. Models such as these assume that growth slows or stops because the organism cannot acquire, distribute or use resources faster than it has to expend them on self-maintenance.

There is a problem however. Mechanistic models do not adequately consider reproduction — an energetically expensive undertaking. Most mechanistic models make the simple but crucial assumption that reproduction is proportional to body size, and that allocation to reproduction begins at birth and remains a constant fraction of total body size throughout an individual’s life. While this assumption seems unrealistic, it is essential for these models to describe growth well.

Phenomenological models tend to have different dynamics for juvenile and mature phases; after maturity, increasing allocation of resources to reproduction reduces growth. But again, most of these models assume that reproductive output is directly proportional to body size.

We now know that, for marine fish at least, reproductive output is disproportionally higher in bigger females. Dustin and Craig suspect that this pattern is the rule for most taxa but that it has been overlooked (see Figure 1).  If this does occur more generally, what does it mean for our understanding of growth?

Figure 1. Data from a range of taxa (A = marine invertebrates and B = other taxa) showing the disproportionate increase in reproductive output at larger sizes. The dotted line in each case shows what a 1:1 (or isometric) scaling of reproduction with growth would look like.

Dustin and Craig argue that many of the mechanistic models of growth are trying to explain dynamics that are driven by increasing allocation to reproduction but they do not allow for it.  Instead, these models assume that resource supply decreases as individuals get bigger so that if the allocation to reproduction is allowed to increase then organisms will shrink once they start to reproduce.

A common feature of both theoretical approaches is that they assume that the relative amount of energy available for total production decreases with size.  If we instead assume that resource acquisition and usage both change in the same proportions in relation to size, and combine those parameters with the disproportionate increase in reproductive output (hyperallometry), then we can predict growth trajectories remarkably well (see Figure 2).

Dustin and Craig posit that the growth dynamics that biologists have long sought to understand emerge simply from hyperallometric scaling of reproduction.

Figure 2. Dustin and Craig propose a simple model that allows energy intake and expenditure to scale consistently with size, but reproductive output to increase disproportionately with size. To illustrate that this “hyperallometric reproduction” model describes growth patterns on par with well-known mechanistic models, Dustin and Craig have used data for cod Gadus morhua and have fitted model outputs for the van Bertanalaffy Growth Function (orange), the Ontogentic Growth Model (blue) and the hyperallometric reproduction model shown in red.


Have we outgrown the existing models of growth?

Authors: Dustin J Marshall and Craig R White

Published in: Trends in Ecology & Evolution

Theories of growth have a long history in biology. Two major branches of theory (mechanistic and phenomenological) describe the dynamics of growth and explain variation in the size of organisms. Both theory branches usually assume that reproductive output scales proportionately with body size, in other words that reproductive output is isometric.

A meta-analysis of hundreds of marine fishes contradicts this assumption, larger mothers reproduce disproportion- ately more in 95% of species studied, and patterns in other taxa suggest that reproductive hyperallometry is widespread.

We argue here that reproductive hyperallometry represents a profound challenge to mechanistic theories of growth in particular, and that they should be revised accordingly. We suspect that hyperallometric reproduction drives growth trajectories in ways that are largely unanticipated by current theories.

Marshall DJ, White CR (2018) Have we outgrown the existing models of growth? Trends in Ecology & Evolution PDF DOI

Parental environment influences the adaptive potential to global change

A new study indicates that parental environment can influence adaptation to projected increases in sea level temperatures, not only by altering the fitness of offspring but also by altering the genetic variance available to increase fitness.

Evatt Chirgwin, along with his PhD supervisors Dustin Marshall, Carla Sgro and Keyne Monro, were interested in how, in the face of global change, populations can maintain or recover fitness. Evatt used a small, marine tubeworm Galeolaria caespitosa to examine how parental exposure to projected ocean warming affects adaptive potential for survival during the most vulnerable early life stage.

Individuals faced with environmental stress can respond through ‘plastic’ changes to morphology, physiology and/or behaviour and these changes can persist in their offspring. But in order for populations to persist in the longer term, they will often require adaptive evolution, which rests on the availability of adequate genetic variation.

Galeolaria is an external fertiliser which allowed Evatt to manipulate fertilisation across different males and females as well as exposing parents and embryos to different temperatures. Evatt took sperm from each male parent and crossed it with eggs from multiple females and vice versa; a design that allowed him to estimate genetic variance and therefore adaptive potential to ocean warming.

Embryos and larvae are the life stages most sensitive to stress in marine invertebrates, and are key to assessing vulnerability to ocean warming. Evatt measured survival of 20,000 Galeolaria offspring as a measure of fitness where parents were exposed to two temperatures prior to spawning and offspring were then reared in the same two temperatures.

The team found that mean offspring survival was higher when offspring were reared at the same temperatures as their parents, but also that parental exposure to warming altered genetic variance.  This means that parental environments may have broader ranging effects on adaptive capacity to global warming than is currently appreciated. 

While effects were subtle, even this modest buffering may help natural populations to persist under rising ocean temperatures. This study is an important step towards understanding how plasticity and adaptation jointly shape population dynamics and extinction risks under global change.

This research was published in the journal Proceedings of the Royal Society B.

How does parental environment influence the potential for adaptation to global change?

Authors: Evatt Chirgwin, Dustin J Marshall, Carla M Sgrò, and Keyne Monro

Published in: Proceedings of the Royal Society B


Parental environments are regularly shown to alter the mean fitness of offspring, but their impacts on the genetic variation for fitness, which predicts adaptive capacity and is also measured on offspring, are unclear. Consequently, how parental environments mediate adaptation to environmental stressors, like those accompanying global change, is largely unknown.

Here, using an ecologically important marine tubeworm in a quantitative-genetic breeding design, we tested how parental exposure to projected ocean warming alters the mean survival, and genetic variation for survival, of offspring during their most vulnerable life stage under current and projected temperatures.

Offspring survival was higher when parent and offspring temperatures matched. Across offspring temperatures, parental exposure to warming altered the distribution of additive genetic variance for survival, making it covary across current and projected temperatures in a way that may aid adaptation to future warming. Parental exposure to warming also amplified nonadditive genetic variance for survival, suggesting that compatibilities between parental genomes may grow increasingly important under future warming.

Our study shows that parental environments potentially have broader-ranging effects on adaptive capacity than currently appreciated, not only mitigating the negative impacts of global change but also reshaping the raw fuel for evolutionary responses to it.

Chirgwin E, Marshall DJ, Sgrò CM, Monro K (2018) How does parental environment influence the potential for adaptation to global change?, Proceedings of the Royal Society B PDF DOI

Death is not the end, especially if you are a colonial organism

Colonial, or modular, organisms are fascinating because each module can experience its own life history while the colony as a whole shares resources. This means that when a module dies it can actually be beneficial to the whole colony. The death of an older module can mean resources are allocated to younger, more vital modules which, in turn, can increase colony reproduction and hence colony fitness. 

Most of our knowledge about these types of organisms comes from plants and although there are many marine examples of colonial organisms, there has been little testing of ideas about module mortality and its effects on colony fitness in these animals.

Karin Svanfeldt and her PhD supervisors Keyne Monro and Dustin Marshall have been working to redress the balance. Karin has been studying the colonial bryozoan Watersipora subtorquata as part of her PhD and she was interested in testing some ideas about selection on module longevity in this species and seeing how it compared with what we know about plants.

Karin used un-analysed data from a field experiment where she had manipulated food availability and flow rate. Karin also used data from another experiment where competition between different species was manipulated by settling Watersipora on either bare PVC plates or on plates where other animals were already growing.

Modules in colonial animals are called zooids and in the bryozoan Watersipora, growth and new zooids appear at the edge of the colony. Over time, the zooids in the centre of the colony lose colour and irreversibly senesce. Zooid senescence is visible as the appearance of a grey inner circle of older, dead zooids that expands as the colony grows. This meant that Karin was able to track individual zooids over time to provide measures of zooid longevity and also get data on the reproductive output of colonies to use as a measure of colony fitness. Karin measured reproductive output as either the number of new zooids or the number of ovicells per colony.

This data enabled Karin and her supervisors to ask the question: “does having a shorter zooid lifespan mean increased fitness for the colony as a whole?” Or, put another way: “is module longevity under selection?”

They found that, ‘Yes’ module longevity is under selection and that the strength of selection varies with environmental conditions, which is what has been found in numerous studies looking at modular plant species. 

This research has been published in the Journal of Evolutionary Biology.

Can we predict egg size of marine fish by looking at the predictability of the environment?

The size of eggs in marine fish has been observed to decrease with increasing temperatures and results from a new study support this finding but, more interestingly, suggest that the predictability of the environment is also important in shaping patterns in egg size.

Diego Barneche and Dustin Marshall from the Centre for Geometric Biology have collaborated with Scott Burgess of Florida State University to compile a dataset of 1078 observations of fish egg size taken from 192 studies that took place between 1880 and 2015 and which include 288 species. This enabled them to test multiple life history theories, including the prediction that in environments with stable food regimes the most effective strategy to maximise reproductive rates is to produce many small eggs.

When compiling this data, Diego and colleagues only included geo-located data so that they could use other existing datasets to estimate means and predictability of sea surface temperatures and chlorophyll a concentrations for the different locations.

The research team were interested, not only in testing how egg size responds to changes in average temperature, but how environmental productivity or food supply (using chlorophyll a as a proxy measure) will affect egg size. The team also formally tested how different components of environmental predictability would affect egg size; they looked at seasonality as well as temporal autocorrelation (how similar conditions at any one point in time are likely to be with previous conditions) to provide indices of environmental predictability.

Diego and colleagues found that egg size decreased as temperatures or chlorophyll a concentrations increased. In contrast, environments that were more seasonal in respect to temperature had larger eggs, but so did environments that were not seasonal in respect to chlorophyll a but were temporally autocorrelated.

These graphs show data from 192 studies and 1,078 observations of fish egg size where egg size decreased as both (a) temperature and (b) chlorophyll-a concentrations increased.

The findings from this study are consistent with a theory that suggests that in an unpredictable environment mothers employ a ‘bet-hedging’ strategy whereby they insulate their offspring from poor conditions through better provisioning, that is, they produce larger eggs.

Importantly this study demonstrated that different components of environmental variation – not just changes in the mean environmental state – contribute to observed patterns in egg size. As future changes to the ocean are expected to impact not only the average state but the degree of predictability, there may be profound effects on the distribution of marine life history traits.

This research is published in the journal Global Ecology and Biogeography

Global environmental drivers of marine fish egg size

Authors: Diego R Barneche, Scott C Burgess, and Dustin J Marshall

Published in: Global Ecology and Biogeography


Aim: To test long‐standing theory on the role of environmental conditions (both mean and predictability) in shaping global patterns in the egg sizes of marine fishes.

Location: Global (50° S to 50° N).

Time period: 1880 to 2015.

Major taxa studied: Marine fish.

Methods: We compiled the largest geo‐located dataset of marine fish egg size (diameter) to date (n = 1,078 observations; 192 studies; 288 species; 242 localities). We decomposed sea surface temperature (SST) and chlorophyll‐a time series into mean and predictability (seasonality and colour of environmental noise – i.e. how predictable the environment is between consecutive time steps), and used these as predictors of egg size in a Bayesian phylogenetic hierarchical model. We test four specific hypotheses based on the classic discussion by Rass (1941), as well as contemporary life‐history theory, and the conceptual model of Winemiller and Rose (1992).

Results: Both environmental mean and predictability correlated with egg size. Our parsimonious model indicated that egg size decreases by c. 2.0‐fold moving from 1 to 30 °C. Environments that were more seasonal with respect to temperature were associated with larger eggs. Increasing mean chlorophyll‐a, from 0.1 to 1 mg/m3, was associated with a c. 1.3‐fold decrease in egg size. Lower chlorophyll‐a seasonality and reddened noise were also associated with larger egg sizes – aseasonal but more temporally autocorrelated resource regimes favoured larger eggs.

Main conclusions: Our findings support results from Rass (1941) and some predictions from Winemiller and Rose (1992). The effects of environmental means and predictability on marine fish egg size are largely consistent with those observed in marine invertebrates with feeding larvae, suggesting that there are important commonalities in how ectotherm egg size responds to environmental change. Our results further suggest that anthropogenically mediated changes in the environment will have profound effects on the distribution of marine life histories.

Barneche DR, Burgess SC, Marshall DJ (2018) Global environmental drivers of marine fish egg size, Global Ecology and Biogeography PDF DOI