Markov models in the study of post-fire succession in heathland communities

Abstract

Data on the presence of a number of vegetation 'states' (defined in terms of species dominance in areas of 10 X 10 cm) and transition probabilities were derived from permanent quadrats in a number of recently burned heath stands. Data were taken from a species-rich community, a' species-poor type and a high-level Calluna-Eriophorum bog. Simple M a r k o v i a n m o d e l s were constructed using these data, and the model predictions were compared with known or expected trends. Models for species-rich heath yielded poor simulations of expected trends since matrices derived from data for the first years after fire did not contain sufficient information on transitions to states important later in the developmental sequence. Model results for the simpler species-poor and bog communities were more satisfactory and simulated expected trends. In these types all species recovered quickly after fire and less rearrangement of species abundances took place. M a x i m u m likelihood statistics carried out on the transition matrices produced inconclusive results for the species-rich and species-poor types, but indicated that the data from the Calluna-Eriophorum bog approximated a first-order time-homogeneous M a r k o v chain. It was concluded that M a r k o v models lack predictive ability except in relatively simple systems, but that they may be useful in illustrating variations in short-term community dynamics.

Markov models and initial floristic composition in heathland vegetation dynamics

“…The model predicts only minor changes in the abundance of species and these can largely be accounted for by a delay in development of up to one unit of time in the older stands. Though the simulations of stand development are adequate to predict the consequences of fire in pioneer and building phase stands, the contrasts with mature and degenerate phase stands are not sufficiently great to follow the observed patterns of community development following fire in older vegetation (Hobbs, 1981;Hobbs & Gimingham, 1984). These patterns are followed much more closely by the 'Colonization' model.…”

“…The present paper illustrates the use of a Markov model to test the hypothesis studied elsewhere (Hobbs, 1981;Hobbs & Gimingham, 1984) that the post-fire development of heathland stands is greatly influenced by the nature of the stand present before fire. It has been proposed that the age of the stand when it is burned influences the availability of vegetative regrowth centres and stored seed, and the initial coIonization of bare ground determines which species will be able to return after fire, and hence the course of post-fire development.…”

“…Slightly different sets of states were used in the different studies, but the transition matrices were modified so that the data were compatible. This involved fusing some of the original states and inserting other states; transitions for these were obtained fro.rn data collected in other stands (Hobbs, 1981). The only possible problem associated with the fusion of the different types of data was the discrepancy in time scale involved.…”

“…In addition, sampling from a discontinuous series of stands of different ages may lead to many transitions being either missed or badly estimated. For this reason, Hobbs (1981 attempted to model the same system using actual transitions through time. Transition data were collected over a period of three years in recently burned stands (Gimingham, Hobbs & Mallik, 1981;.…”

Modelos Estocásticos Aplicados À Avaliação Dinâmica Da Paisagem Florestal De Remanescentes De Mata Atlântica No Município De Caxias Do Sul-Rs1

“…Além disso, é de fácil implementação em sistemas de informações geográficas e, ainda, não necessita de grande quantidade de dados do passado para prever o futuro (PEDROSA; CÂMARA, 2003). O processo básico de Markov, segundo Hobbs (1983), pode ser expresso pela notação matricial apresentada a seguir: em que é um vetor coluna, com n elementos, representando a condição do sistema em um tempo t particular; é um vetor de ocupação nos n Estados após o intervalo de tempo t+1 e é a matriz de probabilidade de transição.…”