Stochastic demography and conservation of an endangered perennial plant (Lomatium bradshawii) in a dynamic fire regime

Lomatium bradshawii is an endangered herbaceous perennial plant found in grassland and prairie remnants in western Oregon and southwestern Washington. Fire was historically in important and highly dynamic component of the environment of L. Bradshawii. Evaluating the demographic consequences of a dynamic environment requires a model for the environment and a coupling between that model and the vital rates of the population. In this review, we analyze in detail the effects of fire schedules on demography of L. bradshawii. It has been suggested that L. bradshawii is adapted to frequent fire and that its populations would benefit from managed fires; our results support these suggestions.

We constructed size-structured population projection matrices for conditions corresponding to the year of a fire and to 1, 2, and 3 or more years post-fire, at each of two sites (Fisher Butte and Rse Prairie) in western Oregon. We used these matrices in two ways. First we treated the population growth rate lambda calculated from each matrix as a summary of the conditions in that environment. We found a significant decline in lambda with time since the last fire. Second, we developed models for L. bradshawii  in periodic and stochastic fire environments. The periodic models provide values of annual growth rate for any specified periodic burning schedule. The stochastic models describe the occurrence of fire as a two-state Markov chain specified in terms of the long-term frequency and auto-correlation of fires. The sequence of environments in terms of time since fire. From this model we calculated the stochastic growth rate log; it increased with increasing fire frequency and with negative auto-correlation.

The critical fire frequency, below which L. bradshawii cannot persist, is about 0.8 to 0.9 at Fisher Butter and about 0.4 to 0.5 at Rose Prairie. Extinction probability drops precipitously from 1 to near 0 as fire frequency increases through the critical value. We carried out a detailed perturbation analysis, calculating the sensitivity and elasticity of the stochastic growth rate to changes in the entries of the matrices. The sensitivity and elasticity of the stochastic growth rate are very highly correlated with the corresponding results from a deterministic model based on the mean projection matrix. Patterns of stochastic sensitivity and elasticity are also very insensitive to changes in the fire frequency. Taken together, these results show that estimates of sensitivity and elasticity are robust and not excessively sensitive to the details of the stochastic environment. Overall, our results show that L. bradshawii depends on frequent fire to persist in these habitats, and that controlled burning is an attractive management tool.