Wiki site of the practical exercise of the VII Southern-Summer School on Mathematical Biology.

Here you will find the exercise assignment and the group's products.

If you are a group member login to edit this page, create new pages from it, and upload files.

Sex determination is not always dependent solely on the genetics of individuals. For some species, sex is determined by environmental factors. Reptiles have well known examples of species presenting temperature-dependent sex determination, with low temperatures producing males in turtles and females in some lizards. A recent study by Johnson et al. (2017) found another factor capable of influencing sex determination in lampreys: the availability of resources. The authors experimentally manipulated environmental productivity (a proxy for the amount of resources available) in which larvae grew and found that it influenced adults’ sex ratio. Populations of individuals that grew in sites with lower productivity resulted in biased sex-ratio towards males.

There is wide evidence showing how the amount of resources influences life history traits. Individuals that grow with abundant resources can allocate them on both tissue growth and reproduction. However, when faced with restriction of resources, individuals tend to invest in somatic growth rather than reproduction. A similar trade-off exists in sex allocation, since female eggs cost more than male sperm to produce. The question then is how this trade-off determines sex bias.

Develop a model to understand the predicted sex-ratio of a population given differences in environmental productivity.

• Assuming a certain relationship between environment productivity and bias in sex ratio, what is the minimal amount of environmental productivity that allows a viable population?
• Along the same lines, what is the amount of resources that produces the greatest population size?
• Conversely, which sex ratio bias would be best for a given environment?
• How does the difference in the cost of reproduction between male and females affect your model? For instance, if female eggs were as costly as male sperm, does population size increases?

Many species are faced with environment unpredictability. How would you incorporate unpredictability of resources in your model and how does it affect population persistence?

Field study suggests that sex determination in sea lamprey is directly influenced by larval growth rate. Nicholas S. Johnson, William D. Swink, Travis O. Brenden. RSPB (2017). link.