| Popis: |
We consider the application and analytical solution of a commonly-employed computational model to the phenomenon of evolutionary ageing. The Penna model is expressed in mathematical form and explicitly solved in the steady-state. It is demonstrated that incorporating non-genetic individuality into the Penna model can account for the onset of a mortality plateau, where the mortality rate no longer rises with age. The analytical approach we employ is used to solve the Penna model in a variety of dynamic states - steady growth, decline and fluctuations - broadening its applicability to real systems. Wherever possible, analytical solutions are confirmed by comparison with computational results. The effect of positive mutations is explicitly examined and is shown to have minimal effect on bulk properties of the population. The mathematical methods used in constructing the solution to the Penna model can be readily extended - through incorporating arbitrary birth rates, survival functions and mutation rates - to consider a class of tractable models of evolutionary ageing. This thesis presents a solid mathematical framework for further analytical study on evolutionary ageing, which need not be confined to the Penna model. |
