Modelling fire-return interval T: stochasticity and censoring in the two-parameter Weibull model

Abstract Biologists are heavily reliant on the characterisation and description of disturbance phenomena and disturbance regimes. This dependency is well illustrated within research on fire recurrence and models of fire-frequency. It is well understood that the process of fire-return is subject to stochastic variation. However, a deterministic paradigm underlies many contemporary studies of fire-frequency to the possible detriment of robust ecological description. It is also commonplace for data on historical fire processes to contain some degree of either partial or missing data. Yet the parameter estimators of the prevailing two-parameter Weibull model of fire-recurrence are rarely seen to account for incomplete data structuring. The consequences of ignoring the structure of incomplete data will likely lead to misrepresentation of predicted fire frequencies and trends. In this paper, we introduce methods for incorporating parameter stochasticity into the two-parameter Weibull model under different degrees of data censoring. Both the explicit handling of censored fire observations and the intrusion of variability about the average predicted patterns in inter-fire interval recurrence are obligatory to any modelling that admits an effective ecological and evolutionary interpretation. These points are well illustrated through a worked example on modelling the fire-return interval regime within the Cape of Good Hope Nature Reserve, South Africa. Here, the observed process of fire recurrence is seen to include a substantial stochastic component about the trends predicted from the two-parameter Weibull model. The implications of a stochastic fire-regime interpretation to both management practises and to the evolutionary understanding of fynbos vegetation are discussed.

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