R. Ferriere et al., MATRIX POPULATION-MODELS APPLIED TO VIABILITY ANALYSIS AND CONSERVATION - THEORY AND PRACTICE USING THE ULM SOFTWARE, Acta oecologica, 17(6), 1996, pp. 629-656
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).