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.

 

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.

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

How does size affect the maintenance of a constant body temperature?

Staying warm is a subject close to many of our hearts during winter and we probably wouldn’t be surprised to hear that animals from colder climes have higher rates of energy expenditure.  But is this true for all species, or is it more complicated than that?

Researchers from Uruguay, Daniel Naya and Hugo Naya, have joined forces with Craig White from the Centre for Geometric Biology to investigate how body mass in mammals affects the relationship between energy expenditure and climate. They found that, yes, energy expenditure was greater for species that live in colder regions but only in mammals smaller than 100 g. The effect became less marked as the animals got bigger. 

The Basal Metabolic Rate (BMR) is a measure that represents the minimum amount of energy needed to maintain a relatively constant body temperature through active heat production.  It has been repeatedly demonstrated that there is a negative correlation between temperature and residual BMR in mammals and birds.

So where does body mass come into all this?  Over half of all mammals weigh less than 100 g although the range in body mass for mammals scales over 8 orders of magnitude. Also, smaller animals are generally easier to work with in the laboratory and so it is likely that much of our data on BMR in mammals comes from smaller species.

In order to untangle the effects of size on the ‘Temperature – BMR’ relationship, Daniel, Hugo and Craig looked at existing data on 458 mammal species. They compiled data on body mass, BMR and temperature from each collection site.  Their data set, as expected, included many more small species than big ones. What is more, their prediction that smaller species would be more dependent on adjustments in BMR to cope with lower temperatures, was confirmed.

There are other ways to maintain constant body temperatures apart from exerting more energy or increasing the Basal Metabolic Rate. Some examples include physiological adjustments, such as the separation of core and outer temperatures through peripheral vasoconstriction.  Behavioural adjustments, such as building / using shelters or changing activity levels can also help maintain body temperatures. Body shapes (surface to volume ratio), body colour, and the properties of body fat and skin can all affect heat retention, absorbance and loss.

Smaller species may have less scope for accessing these alternative solutions. This is because their smaller size may place restrictions on their adoption; including both physical restrictions (fur thickness is limited by body size) and biological restrictions (colour change or activity changes can increase predation risk). Such factors may mean that smaller mammals are more dependent on basal heat generation as a means of maintaining a constant temperature than are larger mammals.

The research team are keen to see if the same pattern of strong Temperature – BMR relationships at smaller body mass but not at bigger body mass, hold true with birds as well.

This research was published in The American Naturalist.

Student session: Applying for a postdoc

Not all PhD students want to pursue a career in academia; some definitely do, while others feel that they would like to further their academic training through doing a postdoctoral fellowship before moving into industry or other fields.

But how do you go about getting a postdoc? 

Professors Dustin Marshall and Craig White will be speaking about their experiences as academics looking for postdocs, and we invite students and interested early career researchers to join us armed with questions about how to go about getting a postdoc, what to expect from a postdoc and ‘conversations you should have’ when starting a postdoc.

When: 2 pm, Thursday 23 August 2018

Where: Sanson Room (22 G01/02) Rainforest Walk, Monash University Clayton

Sizing-up the impacts of fluctuating resources on body size

Recent work in the Centre for Geometric Biology has found that smaller algal cells had slower growth, lower storage of phosphorous and poorer recovery from phosphorous depletion but, interestingly, there was no effect of size when nitrogen was limiting.

Resource levels, such as food or nutrients, are rarely constant in nature but tend to fluctuate through time and across space. Such fluctuations in resources might have different impacts on organisms of different sizes but current ecological theories differ in their predictions of how the evolution of body size will be influenced by pulse inputs of food or nutrients.

While this is theoretically interesting, there is also a more pressing need for improving our understanding of such geometric biology. Phytoplankton cells are becoming smaller as a result of increased temperature and ocean acidification and we need to be able to better predict the consequences of this size shift under varying levels of resources.

Martino Malerba, Maria Palacios and Dustin Marshall have been able to test predictions from three different models of resource-use by using algae that have been genetically modified. They used 280 generations of artificial selection to create larger and smaller phytoplankton cells differing by as much as 1000% in mean body size.  

Cells were exposed to various resource levels by manipulating nitrogen (N) and phosphorous (P) in the growth media, to quantify how size can influence the ability of a species to cope with unpredictable nutrient conditions. 

Martino and his colleagues considered three different ecological theories that differ in their predictions on how size should mediate responses to fluctuating resources.  

  1. The ‘Fasting Endurance Hypothesis’ would predict that larger cells are more buffered against periods of nutrient limitation.
  2. The classic ‘r-K Selection Theory’ predicts that smaller cells with faster generation times will be better placed to take advantage of a nutrient pulse and so recover quickly from periods of nutrient limitation.  
  3. The ‘Metabolic Theory of Ecology’ would predict that tolerance to nutrient deprivation would decrease with increasing mass specific metabolic rate of an organism.

For the phytoplankton species used in this study (Dunaliella tertiolecta), the mass specific metabolic rate increases with size which means that larger cells should grow faster but be less tolerant to nutrient depletion than smaller cells. 

So which theory turned out to be correct?  The team found that periods of P depletion had a greater negative effect on smaller cells as predicted by the ‘Fasting Endurance Hypothesis’ but there was no effect of size on response to N depletion which was not predicted by any of the theories. 

Overall Martino, Maria and Dustin were able to determine that size interacts with stored resources in different ways. Increasing size can promote the ability to use stored P to supplement growth in D. tertiolecta, whereas the ability to store and utilise N does not change across sizes.

Transmission Electron Microscopy (TEM) photos with false coloring showing different densities of internal nutrient reserves between evolved algal cells from small-selected and large-selected lineages.
Mean population growth rate (with 95% confidence intervals) for each size-selected lineage of Dunaliella tertiolecta after experiencing nutrient-replete (red), nitrogen-deplete (green) or phosphorous-deplete conditions (blue) pre-trial conditions.

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