Investigating evolution and complexity with stochastic models

点击翻译按钮获取中文摘要

The motivation for this project is the current lack of consensus about the mechanisms behind the apparent development of ever more complex biological entities over time. Complexity is not a well-defined quantity in the context of animals: there is no single number that can compare the complexity of a wren to an octopus. There are however proxies for complexity which can be measured and compared between species. An example is repeating structures such as vertebral columns or segmented body parts as in a millipede. Measuring quantities such as the differences between repeating units, the number of units and calculating indices derived from these numbers allows comparison of different species and potentially the tracking of the quantities along lineages. This is an excellent starting point for studying the mechanism driving this evolution.The aim of this project is to use mathematical models involving stochastic processes to understand how systems evolve if they have features such as constraints (such as a minimum or maximum length of a limb), driving forces (such as environmental changes or mechanisms causing global directional change in certain features) and passive exploration of the space of all possible changes. The resulting understanding of these systems can be used to identify the processes causing changes to occur to species and by creating models which can be compared to data, it may be possible to determine how much of an effect each of the mechanisms driving change has. The mathematical models can be based on simulations of stochastic processes with the features described above, as well as analytic solutions to the equations describing systems with these features if they can be found. Using indices of complexity based on data such as the vast data available on the vertebral columns of mammals will allow for comparison of the results of such models. Producing models which effectively describe the evolution of measures along lineages will hopefully allow for more informed conclusions to be made about exactly how we have moved between single cells and the ecological diversity we enjoy today. A good enough model may also allow for the prediction of future adaptions which will be made in light of the changes facing the natural world today and could inform us about the relative risks to different species based on changes occurring in their habitat. For example, understanding the way that environmental factors constrain development in populations could provide a way to use boundary conditions to investigate the impact of a time dependent change in environment on different species. To do this, a greater investigation of the relationship between complexity and adaptability would need to be carried out. Understanding how different types of environmental change can be described by boundary conditions would also provide a theory to predict the way different environmental changes could affect populations. Thus, we may be able to envisage which types of species are most at risk of population decline, as well which environmental changes are likely to cause the most problems for species.