## Winton Charitable Foundation winners

**8 April 2013**

**Mathematical biology students have been awarded a number of internships and scholarships from the Winton Charitable Foundation. These students will use the power of mathematics to grapple with the complexity of the natural world.**

"The scholarships are an excellent opportunity to collaborate with academics from the School of Mathematics and Statistics," said biology student Joshua Christie. "Hopefully this holistic approach will generate more illuminating findings than could be obtained by either biological experiments or mathematical modelling alone."

The scholarships and internships were made possible by a generous grant from the Winton Charitable Trust. The grant was to support student projects that span both mathematics and biology.

A number of internships were made available to second and third year students, two of which were awarded to students in the School of Biological Sciences. Top-up scholarships for PhD students pursuing an interdisciplinary mathematical biology project were also funded and three of our graduate researchers received these. A number of internships and scholarships were also awarded to students in the School of Mathematics and Statistics and our congratulations go out to them also.

**Undergraduate internships**

**Robert Oppenheimer "Does size matter? Testing a mathematical model of decision-making in the slime mould Physarum polycephalum" (supervised by Dr Tanya Latty)**

Group decision making in 'lower order' animals takes place without discussion or voting or speeches in parliament. And, in slime mould, "without any fundamental change in the behaviour of individuals in the group," said Robbie. So how do they make a group decision? Robbie aims to test whether the size of the group, in this case the size of the slime fragments, affects their ability to make nutritional decisions.

"I'll present the slime mould with a choice between two options and see whether larger fragments of slime can discriminate between the options more frequently, rapidly or accurately. I'll also try to see whether there is an optimal fragment size for the number of options that the slime must discriminate between."

Robbie's project will test two different hypotheses from mathematical modelling papers to try and get a handle on this biological phenomenon. "Some things, especially in biology, are difficult to make hypotheses about because they involve so many interacting parts. Mathematical modelling is particularly helpful as it allows people to consider thousands or millions of interacting individuals at once and make hypotheses about them."

**Christopher Sharples "Modelling locust marching bands" (supervised by Dr Jerome Buhl)**

"I am trying to create a new mathematical model for locust marching bands," said Chris. These locust bands contain millions of locusts that eat the green vegetation in their path, and have been identified as a pest by the Australian Government. "I will be looking specifically at the Australian Plague Locust, which causes several million dollars of damage annually."

"By creating a new mathematical model, we can learn more about the way locusts interact with each other and with the environment. If you look at each locust individually, you can find a set of rules for their local interactions. But if you look at the group as a whole, you find trends which are not apparent at a small scale." Chris plans to look at the density and velocity of locusts to give new insights as to how bands evolve. "It is important to model these marching bands because it will allow us to predict their movement and determine suitable control methods."

"By studying the way locusts interact, I can learn how to use maths for complex situations, and potentially help solve a national problem."

**Postgraduate top-up scholarships**

**Joshua Christie "Does within-individual genomic conflict explain uniparental inheritance of mitochondria?" (supervised by Professor Madeleine Beekman)**

In sexually produced offspring genetic material in the nucleus is inherited from both parents, whereas mitochondrial DNA is inherited from the mother only. But why? Inheriting DNA from both parents ensures genetic diversity, so why is mitochondrial DNA inherited uniparentally? Josh is studying this conundrum in the slime mould*Physarum polycephalum*.

"Theory proposes that the presence of multiple mitochondrial types in a single cell should select for fast replicating strains," said Josh. "Even if these fast-replicating strains are otherwise deficient and lead to fitness costs to the cell. Uniparental inheritance of mitochondria is thought to be a nuclear-mediated mechanism to prevent the cell from self-destructing."

"Slime mould can inherit mitochondria from both parents in certain crosses, thus providing an ideal environment to examine intracellular competition between nuclear and mitochondrial genomes and whether there are fitness costs associated with biparental inheritance."

"Several existing mathematical models describe how uniparental inheritance of mitochondria could be explained by genomic conflict. While these models are important theoretical tools, the accuracy of the predictions is ultimately constrained by the assumptions and parameters fed into the system. My research proposes to bridge this gap between theoretical and experimental biology by developing aslime mould*-*specific mathematical model andparameterising relevant fitness metrics such as rate of mitochondrial respiration and replication between different strains."

**Martyna Molak "Developing a theoretical framework for studies of ancient DNA." (supervised by Associate Professor Simon Ho)**

DNA extracted from ancient specimens such as mummified tissues, preserved plants and permafrost cores is termed 'ancient DNA'. This ancient DNA is used to study evolution but its usefulness can be limited by damage due to time and exposure. "I am exploring the possibilities and limits of evolutionary inference using DNA extracted from ancient materials," explained Martyna. "My project elaborates theoretical framework for ancient DNA studies."

"I am investigating how different aspects of ancient DNA, such as post-mortem damage, uncertainty in estimating ages of samples and scarcity of ancient DNA sequences, can affect the reliability of evolutionary studies which incorporate such samples." Martyna is using statistical methods, mathematical models and computer simulations to quantify these effects and provide guidelines for designing future ancient DNA analyses.

"I feel so honoured by being awarded the Winton Charitable Trust top-up scholarship. It is very motivating receiving such recognition."

**Vuong Nguyen "A theoretical framework for understanding plant population dynamics in a variable environment using count data" (supervised by Associate Professor Glenda Wardle)**

Funding, weather, illness and equipment failure...trying to make observations in the field can be a fraught business. And the impact of these factors on the data set, especially when comparing season to season, needs to be accounted for. Vuong's project will analyse the usefulness of a mathematical framework for dealing with these experimental challenges. The framework is called the Multivariate Auto-Regressive(1) State-Space, blessedly abbreviated to MARSS.

"My project will evaluate the MARSS framework for use in plant population viability analysis," explained Vuong. "I am using toy datasets from the Simpson Desert to determine the appropriateness of the MARSS model in handling missing values, short time series lengths, stochastic extremities and environmental covariates. I will then apply the model to real data to estimate population trends."

The MARSS model has a long history in economics and physics, but its use in population viability analysis is relatively recent. "This modelling approach has great potential for plant population viability analysis and I think it will improve its use in conservation and management."