On the dynamics of vegetation: Markov chains as models of succession

Hulst, Robert van

doi:10.1007/bf00052009

Cited by 115 publications

(67 citation statements)

References 12 publications

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“…decreased matrix complexity and rapid reappearance of all species taking part in the post-fire development. Van Hulst (1979) has pointed out that one of the attractions of using Markov models is that the assumptions on which they are based are testable; i.e. one can test whether the process being modelled as a first-order time-homogeneous Markov chain actually possesses the required characteristics.…”

Section: High-level Calluna-eriophorum Bogmentioning

confidence: 99%

“…Because the world is not that neat.' Nevertheless, much consideration has recently been given to the use of such models to study vegetation succession(e.g, van Hulst, 1979;Usher, 1979Usher, , 1981 ty types (e.g. Godron & Lepart, 1973;Henderson & Wilkins, 1975;Debussche et al, 1977;Enright & Ogden, 1979;Bellefleur, 1981;Acevedo, 1981;Gibson et al, 1983).…”

Section: Introductionmentioning

confidence: 99%

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

Hobbs

1984

Vegetatio

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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.

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Section: High-level Calluna-eriophorum Bogmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Hobbs

1984

Vegetatio

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“…Transition models have frequently been used to predict changes in vegetation (e.g., Debussche et al 1977, Van Hulst 1979, Usher 1981, Lippe et al 1985 or land use (e.g., Hett 1971, Burn-ham 1973, Johnson 1977) through time. However, these models have not been spatially explicit, and there is no standard approach to incorporate spatial dynamics into transition models.…”

Section: Introductionmentioning

confidence: 99%

Spatial simulation of landscape changes in Georgia: A comparison of 3 transition models

1987

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Spatial simulation models were developed to predict temporal changes in land use patterns in a piedmont county in Georgia (USA). Five land use categories were included: urban, cropland, abandoned cropland, pasture, and forest. Land use data were obtained from historical aerial photography and digitized into a matrix based on a 1 ha grid cell format. Three different types of spatial simulation were compared: (1) random simulations based solely on transition probabilities; (2) spatial simulations in which the four nearest neighbors (adjacent ceils only) influence transitions; and (3) spatial simulations in.which the eight nearest neighbors (adjacent and diagonal cells) influence transitions. Models and data were compared using the mean number and size of patches, fractal dimension of patches, and amount of edge between land uses. The random model simulated a highly fragmented landscape having numerous, small patches with relatively complex shapes. The two versions of the spatial model simulated.cropland well, but simulated patches of forest and abandoned cropland were fewer, larger, and more simple than those in the real landscape. Several possible modifications of model structure are proposed. The modefing approach presented here is a potentially general one for simulating human-influenced landscapes.

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“…The spatially explicit model can be applied in agricultural production, secondary forest succession (Wilkie et al, 1988), and coastal wet land change (Browder et al, 1985;Sklar et al, 1985), etc. Meanwhile, former FLMs were enhanced in spatial simulation, such as development and wide application of Markov chain and semi-Markov chain models (Collins et al, 1974;Collins, 1975;Hulst, 1979;Pickles, 1980;Henderson et al, 1975;Wilkins, 1977), further development of GAP model-FORET (Shugart, 1984), wildland fire behavior and fuel model-BEHAVE (Andrews, 1986;Andrews and Chase, 1989) and so on. At the same time, mathematical thoughts extracted from the cellular automata model (Wolfram, 1984) and neighborhood-based transition model (Turner, 1988) is adopted in building spatial landscape models.…”

Section: In the 1980s: Primary Development Of Spatial Landscape Modelmentioning

confidence: 99%

Progress and prospect of research on forest landscape model

Dai

Wang

et al. 2014

J. Geogr. Sci.

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Abstract:The Forest Landscape Model (FLM) is an efficiency tool of quantified expression of forest ecosystem's structure and function. This paper, on the basis of identifying FLM, according to the stage of development, summarizes the development characteristics of the model, which includes the theoretical foundation of mathematical model, FLM of stand-scale, primary development of spatial landscape model, rapid development of ecosystem process model as the priority, and developing period of structure and process driven by multi-factor. According to the characteristics of different FLMs, this paper classifies the existing FLM in terms of mechanism, property and application, and elaborates the identifications, advantages and disadvantages of different types of models. It summarizes and evaluates the main application fields of existing models from two aspects which are the changes of spatial pattern and ecological process. Eventually, this paper presents FLM's challenges and directions of development in the future, including: (1) more prominent service on the practical strategy of forest management's objectives; (2) construction of multi-modules and multi-plugin to satisfy landscape research demand in various conditions; (3) adoption of high resolution's spatial-temporal data; (4) structural construction of multi-version module; (5) improving the spatial suitability of model application.

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On the dynamics of vegetation: Markov chains as models of succession

Cited by 115 publications

References 12 publications

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

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

Spatial simulation of landscape changes in Georgia: A comparison of 3 transition models

Progress and prospect of research on forest landscape model

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