MATRIX POPULATION-MODELS APPLIED TO VIABILITY ANALYSIS AND CONSERVATION - THEORY AND PRACTICE USING THE ULM SOFTWARE

We outline a general method to carry out population viability analyses (PVA) by making use of matrix population models. We consider a struct ured population (by age, sex, reproductive status, space, etc.) whose demographic parameters are known from field study. To assess the extin ction risk and define a management program, we advocate a three-step P VA: (1) Setting up a constant matrix model that includes the mean valu es of demographic rates. The sizes of each population class are linked from one year to the next by a transition matrix that contains all vi tal rates. When these parameters are taken to be constant (fixed to th eir mean), the matrix analysis yields the deterministic population gro wth rate, population structure, stage-specific reproductive values and the sensitivities of the growth rate to variations in demographic rat e. (2) Assessing the extinction risk due to stochastic factors: demogr aphic stochasticity, environmental stochasticity and catastrophes. We show how to compute the stochastic growth rate, extinction probabiliti es and the distribution of time to extinction, from computations based on the constant matrix model (step 1) together with Monte-Carlo simul ations. (3) Determining action on demographic parameters and ameliorat ion of monitoring programs. The extinction risk can be reduced by incr easing the population growth rate, decreasing its temporal variability or boosting current population size. Which parameters should be fine- tuned in order to cause the largest increase in population growth can be found out by computing the growth rate elasticities to demographic rates. Furthermore, variance in population growth can be decomposed in to that produced by mean parameter values, and that produced by fluctu ations in parameters. Finally, reproductive values and their sensitivi ties indicate which classes should be reinforced to obtain a long-last ing raise of population size. The ULM software allows one to apply thi s agenda automatically to any particular case study. The software can be conveniently used to model populations with any kind of life cycle. The user will enter the model by making use of a friendly, simplified programming language that leaves him or her entirely free to decide o f the matrix structure, parameter values and factors of parameter vari ations (stochastic factors, density-dependence...). All PVA-related pa rameters mentioned above (growth rate, sensitivities, elasticities, ex tinction probabilities, distribution of extinction time, etc.) are com puted by the software. Here this is illustrated with an overview of tw o case studies, that of a natural, declining population of snakes (Vip era ursinii ursinii) and that of a reintroduced, growing population of raptors (Gyps fulvus fulvus).