By Ola Bratteli

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The decrease in population is gradual, however, and over the 100-year time span shown here it decreases only from 3000 to 1148. 9830 times that of the previous year. 9830) ≈ 411 years. One could try to find the matrix element a32 that results in the largest magnitude eigenvalue of A being exactly 1, and while this is an interesting mathematical problem, from the point of view of population control, it would likely be an exercise in futility. Clearly, this model is highly simplified, and even if the assumptions about survival rates and fecundity rates held initially, they might well change over time.

4 ECOLOGICAL MODELS Computational biology is a growing field of application for numerical methods. In this section, we explore a simplified example from ecology. Suppose we wish to study the population of a certain species of bird. These birds are born in the spring and live at most 3 years. We will keep track of the population just before breeding, when there will be three classes of birds, based on age: Age 0 (born the previous spring), Age 1, and Age 2. Let , and represent the number of females in each age class in Year n.

Both deterministic methods and Monte Carlo methods are sometimes used in this case. The picture to the left is a finite element discretization used in a deterministic model for radiation transport problems. (Image reproduced with the kind permission of the Applied Modelling and Computational Group at Imperial College London and EDF Energy. 3 MODELING IN SPORTS In FIFA World Cup soccer matches, soccer balls curve and swerve through the air, in the players’ attempts to confuse goalkeepers and send the ball sailing to the back of the net.