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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, namely 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 availability of resources 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 in abundance of resources can allocate them both on tissue growth and reproduction. However, when faced with restriction of resources, individuals tend to invest in somatic growth rather than in reproduction. Considering that the production of female eggs is more costly than the production of male sperm, how the trade-off between the amount of resources invested in growth versus reproduction can influence a species of lamprey with environmental sex-determination?

Experiments have shown that environmental productivity influences sex-ratio in populations of lampreys. Develop a model to understand the predicted sex-ratio of a population given differences in environmental productivity. What is the minimal amount of environmental productivity that allows a viable population size? Along the same lines, what is the amount of resources that produces the greatest population size? 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? Does population persistence occurs for a poorer environments?

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