Application du modele de distribution d'abondance de Mandelbrot a l'estimation des captures dans l'etang de Thau

Bach, Pascal; Amanieu, M.; Hoai, T. Lam; Lasserre, G

doi:10.1093/icesjms/44.3.235

Cited by 9 publications

(9 citation statements)

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“…These models were used for ecological applications (Wilson 1991, 1999, Naeem and Hawkins 1994, Watkins and Wilson 1994, Aoki 1995, Hill et al 1995, Wilson and Gitay 1995, Kevan et al 1997, Chiarucci et al 1999 but despite this, these models are often restrictive in their hypotheses and difficult to fit. Indeed, some authors have revealed that the distributions observed fit either all of the models or none at all (Hughes 1986, Bach et al 1988, Wilson 1991, Tokeshi 1993.…”

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confidence: 99%

The Fractal Model: a new model to describe the species accumulation process and relative abundance distribution (RAD)

Mouillot¹,

Leprêtre²,

Andreï-Ruiz³

et al. 2000

Oikos

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The FractalModel: a new model to describe the species accumulation process and relative abundance distribution (RAD). -Oikos 90: 333 -342.Quantifying a sampled collection of taxa is a widespread problem in ecology. A number of diversity indices have been proposed and used in numerous works in spite of a lack of statistical characteristics and tests of comparison. These Relative Abundance Distributions (RAD) can also be described using graphic representations exhibiting both the number of taxa and the quantitative distribution of the individuals which constitute these taxa. Fitting these RADs to deterministic or stochastic models remains problematic for different reasons like scale dependence or complexity of the numerical procedures. In our study, we introduce a new model to describe RAD and ecological succession. This model is a Fractal Model based on the assumption that during an ecological succession/accumulation process, at each step of the succession, K new species appear which are k times more abundant with K= k d (where d is a fractal dimension). We use a Monte-Carlo procedure with a Kolmogorov-Smirnov distance to fit this model and to estimate parameters. Through the study of entomological data from a Mediterranean Man And Biosphere reserve, we demonstrate the qualities of the new Fractal Model. Thus, the Fractal Model was rejected for none of the 13 RADs tested. In addition, the parameters (K, k and d) are independent of the Hill family diversity indices and of three evenness indices and are able to provide additional information concerning both the diversity of the sampled ecosystem and development of this biodiversity during the species accumulation process in this ecosystem.

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confidence: 99%

The Fractal Model: a new model to describe the species accumulation process and relative abundance distribution (RAD)

Mouillot¹,

Leprêtre²,

Andreï-Ruiz³

et al. 2000

Oikos

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“…Although the Zipf-Mandelbrot and Zipf models are commonly the best fit to rank abundance data, their parameters lack robustness [43,44]. Instead, we used Mouillot and Lepretre’s [45] p 1 and p 2 to obtain indices that behave similarly to the Zipf-Mandelbrot β and γ. β and γ showed highly erratic patterns and are non-independent, so p 1 and p 2 are recommended as alternatives [45].…”

Section: Methodsmentioning

confidence: 99%

Functional Roles Affect Diversity-Succession Relationships for Boreal Beetles

et al. 2013

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Species diversity commonly increases with succession and this relationship is an important justification for conserving large areas of old-growth habitats. However, species with different ecological roles respond differently to succession. We examined the relationship between a range of diversity measures and time since disturbance for boreal forest beetles collected over a 285 year forest chronosequence. We compared responses of “functional” groups related to threat status, dependence on dead wood habitats, diet and the type of trap in which they were collected (indicative of the breadth of ecologies of species). We examined fits of commonly used rank-abundance models for each age class and traditional and derived diversity indices. Rank abundance distributions were closest to the Zipf-Mandelbrot distribution, suggesting little role for competition in structuring most assemblages. Diversity measures for most functional groups increased with succession, but differences in slopes were common. Evenness declined with succession; more so for red-listed species than common species. Saproxylic species increased in diversity with succession while non-saproxylic species did not. Slopes for fungivores were steeper than other diet groups, while detritivores were not strongly affected by succession. Species trapped using emergence traps (log specialists) responded more weakly to succession than those trapped using flight intercept traps (representing a broader set of ecologies). Species associated with microhabitats that accumulate with succession (fungi and dead wood) thus showed the strongest diversity responses to succession. These clear differences between functional group responses to forest succession should be considered in planning landscapes for optimum conservation value, particularly functional resilience.

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“…A further distance measure, used in fitting studies on the ZM distribution, is the Hellinger distance, the discrete form of which is , 1985;BACH et al, 1988). Other measures of fit are, among others, Neyman's reduced chi-square measure (BERKSON, 1980;MOORE, 1986, Chap …”

Section: Aims and Methods Of Parameter Estimationmentioning

confidence: 99%

“…by MOUILLOT & LEPRETRE (2000). For example, the increase of the environmental maturity increases the value of b (BACH, 1988;FRONTIER, 1987;1994;BARANGÉ & CAMPOS, 1991;WILSON, 1991;WILSON et al, 1996). For example, the increase of the environmental maturity increases the value of b (BACH, 1988;FRONTIER, 1987;1994;BARANGÉ & CAMPOS, 1991;WILSON, 1991;WILSON et al, 1996).…”

Section: Link Between the Parametersmentioning

confidence: 98%

Some practical aspects of fitting and testing the Zipf-Mandelbrot model

Izsák¹

2006

Scientometrics

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The standardization of distribution fitting procedures is recommended also in informetrics. We examined the possibility of that standardization when fitting the Zipf-Mandelbrot (ZM) distribution. After propositions of possible steps of standardization, we stress the unique role of maximum likelihood estimates concerning the chi-square goodness-of-fit tests. We touch upon the possible correlation between the parameters of the ZM distribution. A numerical example demonstrates the method and the results.

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Application du modele de distribution d'abondance de Mandelbrot a l'estimation des captures dans l'etang de Thau

Cited by 9 publications

References 0 publications

The Fractal Model: a new model to describe the species accumulation process and relative abundance distribution (RAD)

The Fractal Model: a new model to describe the species accumulation process and relative abundance distribution (RAD)

Functional Roles Affect Diversity-Succession Relationships for Boreal Beetles

Some practical aspects of fitting and testing the Zipf-Mandelbrot model

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