Self-similarity and the species – area relation of Polish butterflies

Ulrich, Werner; Buszko, J.

doi:10.1078/1439-1791-00139

Cited by 54 publications

(51 citation statements)

References 37 publications

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“…They did not find the model parameters of their persistence model by SAR regression but on the basis of a persistence relationship; that is, area vs. the proportion of species remaining with the halved area. Ulrich & Buszko (2003, 2004 modified the P1 function and suggested a second persistence function (P2), also in response to data that did not follow the allometric relationship (power relationship). They did not explicitly discern between the two models and referred to the P2 model as the Plotkin (P1) model, which implies that they did not recognize the difference between the P1 and P2 models at the time.…”

Section: Extended Power Modelsmentioning

confidence: 95%

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Shapes and functions of species–area curves (II): a review of new models and parameterizations

Tjørve¹

2009

Journal of Biogeography

143

156

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This paper has extended and updated my earlier list and analysis of candidate models used in theoretical modelling and empirical examination of species–area relationships (SARs). I have also reviewed trivariate models that can be applied to include a second independent variable (in addition to area) and discussed extensively the justifications for fitting curves to SARs and the choice of model. There is also a summary of the characteristics of several new candidate models, especially extended power models, logarithmic models and parameterizations of the negative‐exponential family and the logistic family. I have, moreover, examined the characteristics and shapes of trivariate linear, logarithmic and power models, including combination variables and interaction terms. The choice of models according to best fit may conflict with problems of non‐normality or heteroscedasticity. The need to compare parameter estimates between data sets should also affect model choice. With few data points and large scatter, models with few parameters are often preferable. With narrow‐scale windows, even inflexible models such as the power model and the logarithmic model may produce good fits, whereas with wider‐scale windows where inflexible models do not fit well, more flexible models such as the second persistence (P2) model and the cumulative Weibull distribution may be preferable. When extrapolations and expected shapes are important, one should consider models with expected shapes, e.g. the power model for sample area curves and the P2 model for isolate curves. The choice of trivariate models poses special challenges, which one can more effectively evaluate by inspecting graphical plots.

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Section: Extended Power Modelsmentioning

confidence: 95%

“…Some studies have fitted species-area data to the second type of EPM, where a* is a function of x, (a*(x)) (Plotkin et al, 2000;Ulrich & Buszko, 2003, 2004. These models are referred to in the literature as persistence functions.…”

Section: Extended Power Modelsmentioning

confidence: 99%

Shapes and functions of species–area curves (II): a review of new models and parameterizations

Tjørve¹

2009

Journal of Biogeography

143

156

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“…Since C is the number of species per area unit, Ulrich and Buszko (2003a, 2003b, 2004) used the C value as an additional criterion to evaluate the adequacy of a model. In particular, Ulrich (personal communication) considers the C value of the linearized fit (about 9 species per km 2 ) a more realistic number of species than the C value of the curvilinear fit (about 23 species per km 2 ).…”

Section: Resultsmentioning

confidence: 99%

To Fit or Not to Fit? A Poorly Fitting Procedure Produces Inconsistent Results When the Species–Area Relationship is used to Locate Hotspots

Fattorini¹

2006

Biodivers Conserv

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Ulrich and Buszko (2005, Biodivers Conserv 14:1977-1988 have recently applied the species-area relationship (SAR) to find butterfly hotspots in Europe using the linearized power function. They found that, with this method, despite the fact that the larger southern European countries and the Asian part of Turkey belong to the group of ecological hotspots defined by Myers et al. (2000, Nature 403:853-858), the SAR was unable to separate these countries from others. However, this result was a consequence of a poor fit. When different fitting models are compared, there is no obvious reason to prefer the linearized power function model, while a curvilinear fit to the power function should be selected as a best fit for this data set. Using this fit, two large southern European countries (Italy and Greece) and the Asian part of Turkey are identified as hotspots by the SAR. This simple exercise illustrates how an inappropriate choice of the fitting equation for the SAR may lead to inconsistent results.

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“…This relationship is essential to understand the biological distribution of species diversity and it is determined by counting the number of distinct species in different sized areas. This studies, known as speciesarea relationship (SAR), are one of the most important tools to create biodiversity maps, to establish relationships between extinction and migration rates and to determinate minimum size areas for species preservation (Arrhenius, 1921;Ulrich et al, 2003). Generally, only one type of organism is observed; the fish diversity in a lagoon, for example.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Approach Using Latent Variable for Zero Truncated Poisson Distribution: Application for Species-Area Relationship

Arrabal¹,

Andrade²,

Silva³

2014

IJSP

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In ecology, understanding the species-area relationship (SARs) is extremely important to determine species diversity. SARs are fundamental to evaluate the impact in this diversity due to destruction of natural habitats, to create biodiversity maps and to determine the minimum area to preserve. In this study, the number of species is observed in different area sizes. These studies are referred in the literature through nonlinear models without assuming any distribution of the data. In this situation, it only makes sense to consider areas in which the number of species is greater than zero. As the dependent variable is a count data, we assume that this variable comes from a known distribution for discrete positive data. In this paper, we used the zero truncated poisson distribution (ZTP) to represent the probability distribution of the random variable "species diversity" and we considered some nonlinear models to describe the relationship between species diversity and habitat area. Among the proposed models in literature, we considered the Arrhenius power function, Persistence function (P1 e P2), Negative Exponential and Chapman-Richards to describe the abundance of species. In this paper, we take a Bayesian approach to fit models. With the purpose of obtaining conditional distributions, we propose the use of latent variables to implement the Gibbs Sampler. In order to progress using the best possible models for data, a comparison of performance between models referred in this paper will be verified through the criteria Extended Akaike Information Criterion (EAIC), Extended Bayesian Information Criterion (EBIC), Deviance Information Criterion (DIC) and Conditional Predictive Ordinate Criterion (CPO). In addition to selecting the best model, it will also assist to define the best selection criterion.

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Self-similarity and the species – area relation of Polish butterflies

Cited by 54 publications

References 37 publications

Shapes and functions of species–area curves (II): a review of new models and parameterizations

Shapes and functions of species–area curves (II): a review of new models and parameterizations

To Fit or Not to Fit? A Poorly Fitting Procedure Produces Inconsistent Results When the Species–Area Relationship is used to Locate Hotspots

Bayesian Approach Using Latent Variable for Zero Truncated Poisson Distribution: Application for Species-Area Relationship

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