I have been interested in environmental modeling, especially models of ecological succession. However, whenever I see studies involving models of Markov chains type, there is no description of how the transition matrix of probabilities has been actually obtained. Would anyone guide me in this regard?
Henry Horn (Princeton U.) who originated Markov models of succession describes in his book, The Adaptive Geometry of Trees, and a Scientific American article authored about the same time (1970s) how he did this. He went out to a forest and identified the canopy trees growing above many mid-story saplings. He then assumed used these data to estimate the probabilities that each canopy individual of a given species would be succeeded by each species of understory trees (the saplings) - including by the same species (self-replacement). The sum of these probabilities should add to 1.0.
On coral reefs and rocky shores, researchers have looked at the species under fixed points on successive dates, either by relocating a quadrat each time census or by taking a photo and then matching locations.
e.g., See Tanner or Wootton papers
The Role of History in Community Dynamics: A Modelling Approach
Jason E. Tanner, Terence P. Hughes and Joseph H. Connell Ecology
Vol. 77, No. 1 (Jan., 1996), pp. 108-117
Wootton, J. T., 2001. Prediction in complex communities: analysis of empirically-derived Markov models. Ecology 82:580-598.
Olá Claus
A matrix de transição pode ser obtida cruzando dois mapas de uso do solo. A matrix pode ser global (todo o período) ou calculada por ano. Esta é uma das partes não tão complexas em modelagem ambiental ou modelagem dinâmica espacial. A obtenção dos pesos de evidência é um pouco mais. Posso te mostrar algum dia como se gera a matriz de transição no software dinâmica, desenvolvido pela UFMG, caso tenha interesse.
Rafael
Try to see here
http://link.springer.com/article/10.1007%2Fs10661-012-2951-z
Here's an approach using remote sensing data to determine the transition probabilities:
Hall, F.G., D.B. Botkin, D.E. Strebel, K.D. Woods, S.J. Goetz. Ecology, Vol. 72, No. 2, pp. 628-640, April 1991. Large-Scale Patterns of Forest Succession as Determined by Remote Sensing.
You may want to download "Markov chain: ..." from
https://www.researchgate.net/profile/Laszlo_Orloci/contributions
Good luck,
L. Orloci
I recommend paper by Dmitry Logofet and his colleagues:
Logofet, D.O.
Inhomogeneous Markov models for succession of plant communities: New perspectives on an old paradigm
(1997) Biology Bulletin, 24 (5), pp. 506-514.
Logofet, D.O.a , Lesnaya, E.V.b
The mathematics of Markov models: What Markov chains can really predict in forest successions
(2000) Ecological Modelling, 126 (2-3), pp. 285-298.
Korotkov, V.N.a , Logofet, D.O.b , Loreau, M.c
Succession in mixed boreal forest of Russia: Markov models and non-Markov effects
(2001) Ecological Modelling, 142 (1-2), pp. 25-38.
Logofet, D.O.a , Korotkov, V.N.b
'Hybrid' optimisation: A heuristic solution to the Markov-chain calibration problem
(2002) Ecological Modelling, 151 (1), pp. 51-61.
Benabdellah, B.a , Albrecht, K.-F.a , Pomaz, V.L.a b , Denisenko, E.A.c , Logofet, D.O.d
Markov chain models for forest successions in the Erzgebirge, Germany
(2003) Ecological Modelling, 159 (2-3), pp. 145-160.
Feldman, O.a c , Korotkov, V.N.b , Logofet, D.O.a
The monoculture vs. rotation strategies in forestry: Formalization and prediction by means of Markov-chain modelling
(2005) Journal of Environmental Management, 77 (2), pp. 111-121.
Logofet, D.O.
Convexity in projection matrices: Projection to a calibration problem
(2008) Ecological Modelling, 216 (2), pp. 217-228.
Logofet, D.O.a , Belova, I.N.b
Nonnegative matrices as a tool to model population dynamics: Classical models and contemporary expansions
(2008) Journal of Mathematical Sciences, 155 (6), pp. 894-907.
Dear prof. Donald!
Do you know where could I find that book? Thanks again, C.
Obrigado, Prof. Rafael!
Estou com agenda bem tranquila. Quando tiveres um tempo, me avisa que quero aprender no Dinamica, sim. Abraço, C.
Thank you very much prof. Lazlo. congratulations for you work. A hug, C.
In Brazil we have a software developed by Professor Fabio Giordano (USP ) in 2001. I used in one part of my thesis.
2 more papers if you need..
Eastman J.R., Toledano J. (2000), Markov Chain and Cellular Automata Approaches to Land Cover Change Modeling, Workshop presentation (invited), 4th International Conference on Integrating GIS and Environmental Modeling, Banff, Alberta, Sept. 2-8, 2000.
Eastman J.R. (2006), IDRISI Andes, Tutorial, MA, USA, Clark Labs, Clark University.
Hi Francesco, I have similar question as asked above, may you please send me the documents you sent to Haetinger please. My email address is [email protected]
thanks prof. Francesco, but I have not received the file: could you please send me it to [email protected]? A hug, c.
Dear Haetinger and DeNicola, I send you an email.
Regards
Francesco
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