Abstract:
Transition matrix models are one of the most widely used tools for assessing
population viability. The technique allows inclusion of environmental variability,
thereby permitting estimation of probabilistic events, such as extinction. However, few
studies use the technique to compare the effects of management treatments on
population viability, and fewer still have evaluated the implications of using different
model assumptions. In this dissertation, I provide an example of the use of stochastic
matrix models to assess the effects of prescribed fire on Lomatium bradshawii
(Apiaceae), an endangered prairie plant. Using empirically derived data from 27
populations of five perennial plant species collected over a span of five to ten years, I
compare the effects of using different statistical distributions to model stochasticity, and
different methods of constraining stage-specific survival to [less than or equal to] 100% on population
viability estimates. Finally, the importance of correlation among transition elements is
tested, along with interactions between stochastic distributions and study species, on
population viability estimates.
Fire significantly increased population viability of L. bradshawii, regardless of
stochastic method (matrix selection or element selection). Different processes of
incorporating stochasticity (i.e., matrix selection vs. these statistical distributions for
element selection: beta, truncated normal, truncated gamma, triangular, uniform, and
bootstrap) and constraining survival (resampling vs. rescaling procedures) yielded
divergent estimates of stochastic growth rate, and there was a significant interaction
between these methods. These effects were largely explained by the degree of bias the
different methods caused in transition elements. Incorporating correlation among
elements caused a significant, but small, reduction in estimated stochastic growth rate
in two of five species examined, yet there was no interaction with stochastic method in
this effect. Much of the variation in average response to correlation structure among
species was due to the relative balance between positive and negative associations
among the vital rates. Although alternative techniques may lead to very strong
differences in estimates of population viability, conclusions about the relative ranking
of populations or treatments are robust to differences in stochastic methods.
