Genetics and Genomics Commons^™

Approximation Methods For Singular Diffusions Arising In Genetics, Nacer E. Abrouk

Mathematical Sciences Technical Reports (MSTR)

Stochastic models in population genetics leading to diffusion equations are considered. When the drift and the square of the diffusion coefficients are polynomials, an infinite system of ordinary differential equations for the moments of the diffusion process can be derived using the Martingale property. An example is provided to show how the classical Fokker-Planck Equation approach may not be appropriate for this derivation. A Gauss-Galerkin method for approximating the laws of the diffusion, originally proposed by Dawson (1980), is examined. In the few special cases for which exact solutions are known, comparison shows that the method is accurate and the …

Sheep And Wool Industries Need To Improve Their Performance, Rob Kelly, Tim Marshall

Journal of the Department of Agriculture, Western Australia, Series 4

Today in Western Australia, sheep are run at slightly higher stocking rates, are achieving greater lambing percentages (up JO per cent) and higher wool cuts per animal ( up 0. 6 kg greasy) than in the 1960s. When all components of production are considered, the productivity of sheep fanns has increased by 2. 7 per cent per year over the past 35 years.

The challenge of the next decade is to achieve substantially greater rates of improvement than for past years if the sheep and wool industries are to maintain their significant place in Western Australian agriculture.