Estimation of Extinction Probabilities of Five German Cattle Breeds by Population Viability Analysis

The estimation of the expected loss of genetic diversity and marginal diversities in a set of breeds within a defined future time horizon requires initial estimates of breed extinction probabilities. In this study, the extinction probabilities of 5 German dual-purpose cattle breeds were estimated by population viability analysis. Regression was used to estimate the infinitesimal mean and variance of the population growth and this was based on the diffusion approximation of the density independent population growth (also known as the Dennis regression model). The annual number of milk-recorded cows in each breed was used as census data. Based on the regression results, the extinction probabilities and their confidence intervals were estimated for a wide variety of future time horizons using Monte Carlo time series simulations. The estimates of extinction probabilities were sensible, but in 2 cases they depended heavily on the time horizon considered. Additionally, the confidence intervals became very wide with an increased time horizon. We recommend the estimation of extinction probabilities for a set of future time horizons rather than for a single future time and the selection of an upper bound for this set that is not too large to be meaningful. The validity of the use of the number of milk-recorded cows as census data and of the model assumptions is discussed in detail.