On the limitations of standard statistical modeling in biological systems: A full Bayesian approach for biology

One of the most important scientific challenges today is the quantitative and predictive understanding of biological function. Classical mathematical and computational approaches have been enormously successful in modeling inert matter, but they may be inadequate to address inherent features of biological systems. We address the conceptual and methodological obstacles that lie in the inverse problem in biological systems modeling. We introduce a full Bayesian approach (FBA), a theoretical framework to study biological function, in which probability distributions are conditional on biophysical information that physically resides in the biological system that is studied by the scientist.     

Long‐term non‐equilibrium dynamics of insular floras: a 17‐year record

Aim To document long‐term rates of immigration, extinction and turnover in insular floras and evaluate the relative impacts of recent hurricane activity and climate change. Location Three archipelagos of small islands, in the Exuma Cays, Andros and Abacos, Bahamas. Methods I surveyed the floras of 194 vegetated islands in three archipelagos over several multi‐year periods, spanning up to 17 years. Changes in abundance (foliar cover) of persistent populations were measured on a subset of 14 islands in the Exuma Cays over a 9‐year period. Results Rates of plant turnover were generally low compared with other organisms, but varied among archipelagos and time periods. Turnover rates were usually higher in the second decade of this study, and extinction rates were often dramatically higher than immigration rates in the second decade, resulting in overall decreases in species richness. Turnover did not differ significantly among island types based on generalized location and surrounding water depths, and extinctions were not more likely to occur on more exposed islands. The abundance (foliar cover) of populations that did not go extinct decreased steadily over the second decade of this study, indicating, along with higher extinction rates, a generalized decline in these insular floras. Main conclusions Although some islands may have been at or near a state of dynamic equilibrium in the first decade of this study, average species richness declined in all three archipelagos during the second decade, when extinctions greatly outnumbered immigrations. Four major hurricanes affected the study archipelagos in the second decade of this study, although the available evidence suggests that the hurricanes were not directly responsible for the declines. Indirect effects of hurricanes such as increased herbivory and possible decreased nutrient availability, along with a long‐term (25 years) increase in temperature and decline in rainfall are likely contributing factors.     

Growth and derived life-history characteristics of the Brazilian electric ray Narcine brasiliensis

The majority of batoids are listed as Threatened (20.4%) or Data Deficient (41%) by the IUCN Red List. A key challenge to assessing Data-Deficient species is obtaining estimates of key life-history characteristics. Here, a Bayesian approach was used to estimate derived life-history characteristics from a growth model applied to the Data-Deficient Brazilian electric ray Narcine brasiliensis. The age of 170 specimens (107 females, 63 males) was estimated from vertebral centra, and total length, disc width, total weight and birth size were used in a joint estimation of sex-specific length-weight models and two-dimensional von Bertalanffy growth models. Estimates of age at length zero, age at maturity, longevity and mortality at age were derived simultaneously. The Bayesian joint modelling approach was robust to small sample sizes by adding a likelihood to constrain L₀ and sharing parameters, such as Brody growth coefficient between length measurements. The median growth parameter estimates were a shared L₀ = 38.8 mm, female L_∞ = 515 mm, 𝑘 = 0.125 and male L_∞ = 387 mm, 𝑘 = 0.194. Age at maturity was estimated to be 7.40–7.49 years for females and 4.45–4.47 years for males, whereas longevity was 22.5–22.6 years for females and 14.2 years for males depending on length measurement. Age-1 natural mortality was estimated to be 0.199–0.207 for females and 0.211–0.213 for males. The derived life-history characteristics indicate N. brasiliensis is earlier maturing, but slower growing relative to other Torpediniformes. These characteristics along with the species’ endemism to southern Brazil and high by-catch rates indicate that one of the IUCN Red List threatened categories may be more appropriate for the currently Data-Deficient status. The Bayesian approach used for N. brasiliensis can prove useful for utilizing limited age-growth data in other Data-Deficient batoid species to inform necessary life characteristics for conservation and management.     

Molecular evidence for glacial refugia of mountain plants in the European Alps

Many mountain ranges have been strongly glaciated during the Quaternary ice ages, and the locations of glacial refugia of mountain plants have been debated for a long time. A series of detailed molecular studies, investigating intraspecific genetic variation of mountain plants in the European Alps, now allows for a first synopsis. A comparison of the phylogeographic patterns with geological and palaeoenvironmental data demonstrates that glacial refugia were located along the southwestern, southern, eastern and northern border of the Alps. Additional glacial refugia were present in central Alpine areas, where high-elevation plants survived the last glaciation on ice-free mountain tops. The observed intraspecific phylogeographies suggest general patterns of glacial survival, which conform to well-known centres of Alpine species diversity and endemism. This implies that evolutionary or biogeographic processes induced by climatic fluctuations act on gene and species diversity in a similar way.     

Inference of Gene Flow between Species under Misspecified Models

Genomic sequence data provide a rich source of information about the history of species divergence and interspecific hybridization or introgression. Despite recent advances in genomics and statistical methods, it remains challenging to infer gene flow, and as a result, one may have to estimate introgression rates and times under misspecified models. Here we use mathematical analysis and computer simulation to examine estimation bias and issues of interpretation when the model of gene flow is misspecified in analysis of genomic datasets, for example, if introgression is assigned to the wrong lineages. In the case of two species, we establish a correspondence between the migration rate in the continuous migration model and the introgression probability in the introgression model. When gene flow occurs continuously through time but in the analysis is assumed to occur at a fixed time point, common evolutionary parameters such as species divergence times are surprisingly well estimated. However, the time of introgression tends to be estimated towards the recent end of the period of continuous gene flow. When introgression events are assigned incorrectly to the parental or daughter lineages, introgression times tend to collapse onto species divergence times, with introgression probabilities underestimated. Overall, our analyses suggest that the simple introgression model is useful for extracting information concerning between-specific gene flow and divergence even when the model may be misspecified. However, for reliable inference of gene flow it is important to include multiple samples per species, in particular, from hybridizing species.     

Climatic stability in the Brazilian Cerrado: implications for biogeographical connections of South American savannas,species richness and conservation in a biodiversity hotspot

Aim To investigate the historical distribution of the Cerrado across Quaternary climatic fluctuations and to generate historical stability maps to test: (1) whether the ‘historical climate’ stability hypothesis explains squamate reptile richness in the Cerrado; and (2) the hypothesis of Pleistocene connections between savannas located north and south of Amazonia. Location The Cerrado, a savanna biome and a global biodiversity hotspot distributed mainly in central Brazil. Methods We generated occurrence datasets from 1000 presence points randomly selected from the entire distribution of the Cerrado, as determined by two spatial definitions. We modelled the potential Cerrado distribution by implementing a maximum‐entropy machine‐learning algorithm across four time projections: current, mid‐Holocene (6 ka), Last Glacial Maximum (LGM, 21 ka) and Last Interglacial (LIG, 120 ka). We generated historical stability maps (refugial areas) by overlapping presence/absence projections of all scenarios, and checked consistencies with qualitative comparisons with available fossil pollen records. We built a spatially explicit simultaneous autoregressive model to explore the relationship between current climate, climatic stability, and squamate species richness. Results Models predicted the LGM and LIG as the periods of narrowest and widest Cerrado distributions, respectively, and were largely corroborated by palynological evidence. We found evidence for two savanna corridors (eastern coastal during the LIG, and Andean during the LGM) and predicted a large refugial area in the north‐eastern Cerrado (Serra Geral de Goiás refugium). Variables related to climatic stability predicted squamate richness better than present climatic variables did. Main conclusions Our results indicate that Bolivian savannas should be included within the Cerrado range and that the Cerrado’s biogeographical counterparts are not Chaco and Caatinga but rather the disjunct savannas of the Guyana shield plateaus. Climatic stability is a good predictor of Cerrado squamate richness, and our stability maps could be used in future studies to test diversity patterns and genetic signatures of different taxonomic groups and as a higher‐order landscape biodiversity surrogate for conservation planning.     

Phylogeography of the chestnut‐tailed antbird (Myrmeciza hemimelaena) clarifies the role of rivers in Amazonian biogeography

Aim We examined patterns of spatial and temporal diversification of the Amazonian endemic chestnut‐tailed antbird, Mymeciza hemimelaena (Thamnophilidae), to evaluate the diversification of a widespread avian taxon across rivers that potentially represent major natural barriers. Location Lowland Amazonia. Methods Sequences of the mitochondrial ND2 and cytochrome b genes were investigated from 65 individuals distributed throughout the entire range of M. hemimelaena, and including the two currently valid subspecies M. h. hemimelaena and M. h. pallens. Based on a combination of phylogeographic tools, molecular dating, and population genetic methods, we reconstructed a spatio‐temporal scenario of diversification of M. hemimelaena in the Amazon. Results The data revealed three genetically divergent and monophyletic groups in M. hemimelaena, which can also be distinguished by a combination of morphological and vocal characters. Two of these clades correspond to the previously described taxa M. h. hemimelaena and M. h. pallens, which are separated by the upper Madeira River, a main Amazonian tributary. The third clade is distributed between the middle reaches of the Madeira River and the much smaller tributaries Jiparaná and Aripuanã, and, although currently treated as M. h. pallens, clearly constitutes an independent evolutionary lineage probably deserving separate species status. Molecular clock and population genetic analyses indicate that diversification in this group occurred throughout the Pleistocene, with demographic fluctuations assumed for M. h. hemimelaena and M. h. pallens. Main conclusions The findings implicate rivers as barriers driving diversification in the M. hemimelaena complex. Levels of mitochondrial DNA divergence and associated morphological and vocal traits support its division into at least three separate species with comparatively small ranges. The existence of a previously unrecognized lineage in the M. hemimelaena complex, and the high degree of population structuring found in M. h. hemimelaena underscore the pervasiveness of cryptic endemism throughout Amazonia and the importance of DNA‐based taxonomic and phylogeographic studies in providing the accurate estimates of diversity that are essential for conservation planning.     

The latitudinal position of peak marine diversity in living and fossil biotas

Aim Peak marine taxonomic diversity has only rarely occurred at or near the equator during the Phanerozoic Eon, in contrast to the present‐day pattern. This fundamental difference is difficult to reconcile because the latitude at which peak diversity occurs for living marine taxa has not yet been explicitly determined at a broad taxonomic and spatial scale. Here, we attempt to determine this value in order to compare the contemporary and fossil patterns directly. Location Our data are global in coverage. Methods We used a literature compilation of 149 present‐day marine latitudinal diversity gradients. We summed the number of marine taxa that exhibited peak diversity within 10° latitudinal bins. In addition, we recorded locality data, general habitat (benthic/pelagic), and the taxonomic level of the study organisms. Results We found that peak diversity for most sampled marine taxa currently occurs between 10° and 20° N, even after correcting for a Northern Hemisphere sampling bias. Moreover, this peak position is a global phenomenon: it is found across habitats and higher taxa, within all sampled ocean basins, and on both sides of the Atlantic and Pacific oceans. Benthic taxa, which dominate our data, exhibit one peak at 10°–20° N, while pelagic taxa exhibit a peak at 10°–20° N and an additional peak at 10°–20° S, producing a distinct trough at the equator. Main conclusions Our data indicate that peak marine diversity for many taxa is currently within 10°–20° N rather than at the equator, and that this is not likely to result from either undersampling at lower latitudes or the pattern being dominated by a particular taxon. Possible explanations may include a coincidence with the intertropical convergence zone, a mid‐domain effect, abundant shallow marine habitat, or high ocean temperatures at latitudes nearest the equator. Regardless of its exact cause, the position of peak diversity should be considered a fundamental feature of the latitudinal diversity gradient that must be accounted for within attempts to explain the latter’s existence.