The gambin model provides a superior fit to species abundance distributions with a single free parameter : evidence, implementation and interpretation

The species abundance distribution (SAD) has been a central focus of community ecology for over fifty years, and is currently the subject of widespread renewed interest. The gambin model has recently been proposed as a model that provides a superior fit to commonly preferred SAD models. It has also been argued that the model's single parameter (α) presents a potentially informative ecological diversity metric, because it summarises the shape of the SAD in a single number. Despite this potential, few empirical tests of the model have been undertaken, perhaps because the necessary methods and software for fitting the model have not existed. Here, we derive a maximum likelihood method to fit the model, and use it to undertake a comprehensive comparative analysis of the fit of the gambin model. The functions and computational code to fit the model are incorporated in a newly developed free-to-download R package (gambin). We test the gambin model using a variety of datasets and compare the fit of the gambin model to fits obtained using the Poisson lognormal, logseries and zero-sum multinomial distributions. We found that gambin almost universally provided a better fit to the data and that the fit was consistent for a variety of sample grain sizes. We demonstrate how α can be used to differentiate intelligibly between community structures of Azorean arthropods sampled in different land use types. We conclude that gambin presents a flexible model capable of fitting a wide variety of observed SAD data, while providing a useful index of SAD form in its single fitted parameter. As such, gambin has wide potential applicability in the study of SADs, and ecology more generally.

Harvesting dynamic aspects from a real rational map : the bulb of period 5

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Rhodolith forming coralline algae in the Upper Miocene of Santa Maria Island (Azores, NE Atlantic) : a critical evaluation

The Late Miocene Malbusca outcrop is located in the southeastern coast of Santa Maria Island (Azores, NE Atlantic), interspersed in volcanic formations. At ~20 meters above present sea level, a prominent discontinuous layer of rhodoliths seizes with an extension of ~250 meters. This paper presents the first taxonomic record of fossil rhodolith forming coralline algae for the Miocene of the Azores. The preserved taxonomic features used were the following: (1) arrangement of basal filaments, (2) epithallial cells (when observable), (3) presence of cell fusions, (4) conceptacle type, (5) number of cells layers which conceptacle chamber floors are situated below the surrounding thallus surface and (6) for the sporangial pores, the orientation of the filaments around the conceptacle pores. Based on these characters, six taxa were identified encompassing three Corallinaceae (Lithophyllum prototypum, Lithophyllum sp., Spongites sp., Hydrolithon sp.) and one Hapalidaceae (Phymatolithon calcareum and cf. Phymatolithon sp.). An unidentified coaxial thallus was also present, the coaxial construction ascribing the specimens to the genus Mesophyllum or Neogoniolithon. Taxonomic accounts for the identified taxa are described, illustrated and an identification key is provided. The report of L prototypum represents the first Miocene record and the preservation of the specimens is very good. Miocene coralline algae seem very consistent among deposits but some species are relevant for particular areas, like in the Azores.

Mapping stability : real rational maps of degree zero

In memory of our beloved Professor José Rodrigues Santos de Sousa Ramos (1948-2007), who João Cabral, one of the authors of this paper, had the honor of being his student between 2000 and 2006, we wrote this paper following the research by experimentation, using the new technologies to capture a new insight about a problem, as him so much love to do it. His passion was to create new relations between different fields of mathematics. He was a builder of bridges of knowledge, encouraging the birth of new ways to understand this science. One of the areas that Sousa Ramos researched was the iteration of maps and the description of its behavior, using the symbolic dynamics. So, in this issue of this journal, honoring his memory, we use experimental results to find some stable regions of a specific family of real rational maps, the ones that he worked with João Cabral. In this paper we describe a parameter space (a,b) to the real rational maps fa,b(x) = (x2 −a)/(x2 −b), using some tools of dynamical systems, as the study of the critical point orbit and Lyapunov exponents. We give some results regarding the stability of these family of maps when we iterate it, specially the ones connected to the order 3 of iteration. We hope that our results would help to understand better the behavior of these maps, preparing the ground to a more efficient use of the Kneading Theory on these family of maps, using symbolic dynamics.