Estimating biophysical variable dependences with kernels

This paper introduces a nonlinear measure of dependence between random variables in the context of remote sensing data analysis. The Hilbert-Schmidt Independence Criterion (HSIC) is a kernel method for evaluating statistical dependence. HSIC is based on computing the Hilbert-Schmidt norm of the cross-covariance operator of mapped samples in the corresponding Hilbert spaces. The HSIC empirical estimator is very easy to compute and has good theoretical and practical properties. We exploit the capabilities of HSIC to explain nonlinear dependences in two remote sensing problems: temperature estimation and chlorophyll concentration prediction from spectra. Results show that, when the relationship between random variables is nonlinear or when few data are available, the HSIC criterion outperforms other standard methods, such as the linear correlation or mutual information.

Effects of a fire response trait on diversification in replicated radiations.

Fire has been proposed as a factor explaining the exceptional plant species richness found in Mediterranean regions. A fire response trait that allows plants to cope with frequent fire by either reseeding or resprouting could differentially affect rates of species diversification. However, little is known about the generality of the effects of differing fire response on species evolution. We study this question in the Restionaceae, a family that radiated in Southern Africa and Australia. These radiations occurred independently and represent evolutionary replicates. We apply Bayesian approaches to estimate trait-specific diversification rates and patterns of climatic niche evolution. We also compare the climatic heterogeneity of South Africa and Australia. Reseeders diversify faster than resprouters in South Africa, but not in Australia. We show that climatic preferences evolve more rapidly in reseeder lineages than in resprouters and that the optima of these climatic preferences differ between the two strategies. We find that South Africa is more climatically heterogeneous than Australia, independent of the spatial scale we consider. We propose that rapid shifts between states of the fire response trait promote speciation by separating species ecologically, but this only happens when the landscape is sufficiently heterogeneous.

A probabilistic approach to niche-based community models for spatial forecasts of assemblage properties and their uncertainties

Aim Conservation strategies are in need of predictions that capture spatial community composition and structure. Currently, the methods used to generate these predictions generally focus on deterministic processes and omit important stochastic processes and other unexplained variation in model outputs. Here we test a novel approach of community models that accounts for this variation and determine how well it reproduces observed properties of alpine butterfly communities. Location The western Swiss Alps. Methods We propose a new approach to process probabilistic predictions derived from stacked species distribution models (S-SDMs) in order to predict and assess the uncertainty in the predictions of community properties. We test the utility of our novel approach against a traditional threshold-based approach. We used mountain butterfly communities spanning a large elevation gradient as a case study and evaluated the ability of our approach to model species richness and phylogenetic diversity of communities. Results S-SDMs reproduced the observed decrease in phylogenetic diversity and species richness with elevation, syndromes of environmental filtering. The prediction accuracy of community properties vary along environmental gradient: variability in predictions of species richness was higher at low elevation, while it was lower for phylogenetic diversity. Our approach allowed mapping the variability in species richness and phylogenetic diversity projections. Main conclusion Using our probabilistic approach to process species distribution models outputs to reconstruct communities furnishes an improved picture of the range of possible assemblage realisations under similar environmental conditions given stochastic processes and help inform manager of the uncertainty in the modelling results

Mixed mating in androdioecious Mercurialis annua inferred using progeny arrays and diploid-acting microsatellite loci in a hexaploid background.

Background and Aims The frequency at which males can be maintained with hermaphrodites in androdioecious populations is predicted to depend on the selfing rate, because self-fertilization by hermaphrodites reduces prospective siring opportunities for males. In particular, high selfing rates by hermaphrodites are expected to exclude males from a population. Here, the first estimates are provided of the mating system from two wild hexaploid populations of the androdioecious European wind-pollinated plant M. annua with contrasting male frequencies.Methods Four diploid microsatellite loci were used to genotype 19-20 progeny arrays from two populations of M. annua, one with males and one without. Mating-system parameters were estimated using the program MLTR.Key Results Both populations had similar, intermediate outcrossing rates (t(m) = 0.64 and 0.52 for the population with and without males, respectively). The population without males showed a lower level of correlated paternity and biparental inbreeding and higher allelic richness and gene diversity than the population with males.Conclusions The results demonstrate the utility of new diploid microsatellite loci for mating system analysis in a hexaploid plant. It would appear that androdioecious M. annua has a mixed-mating system in the wild, an uncommon finding for wind-pollinated species. This study sets a foundation for future research to assess the relative importance of the sexual system, plant-density variation and stochastic processes for the regulation of male frequencies in M. annua over space and time.

Reservoir compensation releases : impact on the macroinvertebrate community of the Derwent River, Northumberland, UK-A longitudinal

River regulation for the purposes of public water supply causes the flow regime downstream of a dam to change. Traditionally, in the UK, such regulation was accompanied by requirements for reservoir releases to compensate downstream water users (e.g. industry) for the loss of natural flow (compensation flows). In this article, we compare a unique pre-impoundment macroinvertebrate data set for a regulated upland river with survey data post-impoundment. This allows a longitudinal assessment of the response of the system to regulation. The Derwent River, Northumberland, was impounded in 1966. Impacts on the hydrological regime were quantified by comparing long-term hydrographs, flow duration curves, flow ranges and flashiness indices for the pre-impoundment and post-impoundment periods. The comparison of changes in macroinvertebrate richness and diversity post-impoundment showed that the change in flow regime has had limited effect on the ecological community structure. The flow regime of the Derwent River has become less flashy with fewer extreme events, and the richness and the diversity of macroinvertebrates have, in some cases, increased and at worst have not deteriorated. We suggest that this reflects the strict compensation regime, which has guaranteed minimum flows at all times. Copyright (c) 2012 John Wiley & Sons, Ltd.

Performance anxiety : cardiorespiratory activity in high- and low-anxious professional music students in a performance situation

Questionnaire studies indicate that high-anxious musicians may suffer from hyperventilation symptoms before and/or during performance. Reported symptoms include amongst others shortness of breath, fast or deep breathing, dizziness and thumping heart. A self-report study by Widmer, Conway, Cohen and Davies (1997) shows that up to seventy percent of the tested highly anxious musicians are hyperventilators during performance. However, no study has yet tested if these self-reported symptoms reflect actual cardiorespiratory changes just before and during performance. Disturbances in breathing patterns and hyperventilation may negatively affect the performance quality in stressful performance situations. The main goal of this study is to determine if music performance anxiety is manifest physiologically in specific correlates of cardiorespiratory activity. We studied 74 professional music students of Swiss Music Universities divided into two groups (high- and lowanxious) based on their self-reported performance anxiety (State-Trait Anxiety Inventory by Spielberger). The students were tested in three distinct situations: baseline, performance without audience, performance with audience. We measured a) breathing patterns, end-tidal carbon dioxide, which is a good non-invasive estimator for hyperventilation, and cardiac activation and b) self-perceived emotions and self-perceived physiological activation. Analyses of heart rate, respiratory rate, self-perceived palpitations, self-perceived shortness of breath and self-perceived anxiety for the 15 most and the 15 least anxious musicians show that high-anxious and low-anxious music students have a comparable physiological activation during the different measurement periods. However, highanxious music students feel significantly more anxious and perceive significantly stronger palpitations and significantly stronger shortness of breath just before and during a public performance. The results indicate that low- and high-anxious music students a) do not differ in the considered physiological responses and b) differ in the considered self-perceived physiological symptoms and the selfreported anxiety before and/or during a public performance.

Accuracy of plant assemblage predictions from species distribution models varies along environmental gradients

Aim: Climatic niche modelling of species and community distributions implicitly assumes strong and constant climatic determinism across geographic space. This assumption had however never been tested so far. We tested it by assessing how stacked-species distribution models (S-SDMs) perform for predicting plant species assemblages along elevation. Location: Western Swiss Alps. Methods: Using robust presence-absence data, we first assessed the ability of topo-climatic S-SDMs to predict plant assemblages in a study area encompassing a 2800 m wide elevation gradient. We then assessed the relationships among several evaluation metrics and trait-based tests of community assembly rules. Results: The standard errors of individual SDMs decreased significantly towards higher elevations. Overall, the S-SDM overpredicted far more than they underpredicted richness and could not reproduce the humpback curve along elevation. Overprediction was greater at low and mid-range elevations in absolute values but greater at high elevations when standardised by the actual richness. Looking at species composition, the evaluation metrics accounting for both the presence and absence of species (overall prediction success and kappa) or focusing on correctly predicted absences (specificity) increased with increasing elevation, while the metrics focusing on correctly predicted presences (Jaccard index and sensitivity) decreased. The best overall evaluation - as driven by specificity - occurred at high elevation where species assemblages were shown to be under significant environmental filtering of small plants. In contrast, the decreased overall accuracy in the lowlands was associated with functional patterns representing any type of assembly rule (environmental filtering, limiting similarity or null assembly). Main Conclusions: Our study reveals interesting patterns of change in S-SDM errors with changes in assembly rules along elevation. Yet, significant levels of assemblage prediction errors occurred throughout the gradient, calling for further improvement of SDMs, e.g., by adding key environmental filters that act at fine scales and developing approaches to account for variations in the influence of predictors along environmental gradients.

Niche, distribution and global change : modeling insights into biogeography and conservation biology Olivier Broennimann

RESUME Les évidences montrant que les changements globaux affectent la biodiversité s'accumulent. Les facteurs les plus influant dans ce processus sont les changements et destructions d'habitat, l'expansion des espèces envahissantes et l'impact des changements climatiques. Une évaluation pertinente de la réponse des espèces face à ces changements est essentielle pour proposer des mesures permettant de réduire le déclin actuel de la biodiversité. La modélisation de la répartition d'espèces basée sur la niche (NBM) est l'un des rares outils permettant cette évaluation. Néanmoins, leur application dans le contexte des changements globaux repose sur des hypothèses restrictives et demande une interprétation critique. Ce travail présente une série d'études de cas investiguant les possibilités et limitations de cette approche pour prédire l'impact des changements globaux. Deux études traitant des menaces sur les espèces rares et en danger d'extinction sont présentées. Les caractéristiques éco-géographiques de 118 plantes avec un haut degré de priorité de conservation sont revues. La prévalence des types de rareté sont analysées en relation avec leur risque d'extinction UICN. La revue souligne l'importance de la conservation à l'échelle régionale. Une évaluation de la rareté à échelle globale peut être trompeuse pour certaine espèces car elle ne tient pas en compte des différents degrés de rareté que présente une espèce à différentes échelles spatiales. La deuxième étude test une approche pour améliorer l'échantillonnage d'espèces rares en incluant des phases itératives de modélisation et d'échantillonnage sur le terrain. L'application de l'approche en biologie de la conservation (illustrée ici par le cas du chardon bleu, Eryngium alpinum), permettrait de réduire le temps et les coûts d'échantillonnage. Deux études sur l'impact des changements climatiques sur la faune et la flore africaine sont présentées. La première étude évalue la sensibilité de 227 mammifères africains face aux climatiques d'ici 2050. Elle montre qu'un nombre important d'espèces pourrait être bientôt en danger d'extinction et que les parcs nationaux africains (principalement ceux situé en milieux xériques) pourraient ne pas remplir leur mandat de protection de la biodiversité dans le futur. La seconde étude modélise l'aire de répartition en 2050 de 975 espèces de plantes endémiques du sud de l'Afrique. L'étude propose l'inclusion de méthodes améliorant la prédiction des risques liés aux changements climatiques. Elle propose également une méthode pour estimer a priori la sensibilité d'une espèce aux changements climatiques à partir de ses propriétés écologiques et des caractéristiques de son aire de répartition. Trois études illustrent l'utilisation des modèles dans l'étude des invasions biologiques. Une première étude relate l'expansion de la laitue sáuvage (Lactuca serriola) vers le nord de l'Europe en lien avec les changements du climat depuis 250 ans. La deuxième étude analyse le potentiel d'invasion de la centaurée tachetée (Centaures maculosa), une mauvaise herbe importée en Amérique du nord vers 1890. L'étude apporte la preuve qu'une espèce envahissante peut occuper une niche climatique différente après introduction sur un autre continent. Les modèles basés sur l'aire native prédisent de manière incorrecte l'entier de l'aire envahie mais permettent de prévoir les aires d'introductions potentielles. Une méthode alternative, incluant la calibration du modèle à partir des deux aires où l'espèce est présente, est proposée pour améliorer les prédictions de l'invasion en Amérique du nord. Je présente finalement une revue de la littérature sur la dynamique de la niche écologique dans le temps et l'espace. Elle synthétise les récents développements théoriques concernant le conservatisme de la niche et propose des solutions pour améliorer la pertinence des prédictions d'impact des changements climatiques et des invasions biologiques. SUMMARY Evidences are accumulating that biodiversity is facing the effects of global change. The most influential drivers of change in ecosystems are land-use change, alien species invasions and climate change impacts. Accurate projections of species' responses to these changes are needed to propose mitigation measures to slow down the on-going erosion of biodiversity. Niche-based models (NBM) currently represent one of the only tools for such projections. However, their application in the context of global changes relies on restrictive assumptions, calling for cautious interpretations. In this thesis I aim to assess the effectiveness and shortcomings of niche-based models for the study of global change impacts on biodiversity through the investigation of specific, unsolved limitations and suggestion of new approaches. Two studies investigating threats to rare and endangered plants are presented. I review the ecogeographic characteristic of 118 endangered plants with high conservation priority in Switzerland. The prevalence of rarity types among plant species is analyzed in relation to IUCN extinction risks. The review underlines the importance of regional vs. global conservation and shows that a global assessment of rarity might be misleading for some species because it can fail to account for different degrees of rarity at a variety of spatial scales. The second study tests a modeling framework including iterative steps of modeling and field surveys to improve the sampling of rare species. The approach is illustrated with a rare alpine plant, Eryngium alpinum and shows promise for complementing conservation practices and reducing sampling costs. Two studies illustrate the impacts of climate change on African taxa. The first one assesses the sensitivity of 277 mammals at African scale to climate change by 2050 in terms of species richness and turnover. It shows that a substantial number of species could be critically endangered in the future. National parks situated in xeric ecosystems are not expected to meet their mandate of protecting current species diversity in the future. The second study model the distribution in 2050 of 975 endemic plant species in southern Africa. The study proposes the inclusion of new methodological insights improving the accuracy and ecological realism of predictions of global changes studies. It also investigates the possibility to estimate a priori the sensitivity of a species to climate change from the geographical distribution and ecological proprieties of the species. Three studies illustrate the application of NBM in the study of biological invasions. The first one investigates the Northwards expansion of Lactuca serriola L. in Europe during the last 250 years in relation with climate changes. In the last two decades, the species could not track climate change due to non climatic influences. A second study analyses the potential invasion extent of spotted knapweed, a European weed first introduced into North America in the 1890s. The study provides one of the first empirical evidence that an invasive species can occupy climatically distinct niche spaces following its introduction into a new area. Models fail to predict the current full extent of the invasion, but correctly predict areas of introduction. An alternative approach, involving the calibration of models with pooled data from both ranges, is proposed to improve predictions of the extent of invasion on models based solely on the native range. I finally present a review on the dynamic nature of ecological niches in space and time. It synthesizes the recent theoretical developments to the niche conservatism issues and proposes solutions to improve confidence in NBM predictions of the impacts of climate change and species invasions on species distributions.

Effects of total fishing prohibition on the rocky fish assemblages of Medes Islands marine reserve (NW Mediterranean)

Visual scuba diving censuses were used to assess the effects of fishing prohibition on abundance and size structure of littoral fish populations by comparing the same benthic communities inside and outside the protected area of Medes Islands (NE Catalonia, Spain). The total number of species found was 43 in the reserve and 44 outside, but the mean value of species richness per sampling station was significantly higher in the protected area. However, diversity, heavily affected by the presence or absence of large schools of pelagic species, showed no significant differences between sites. The prohibition of fishing for 6 years is the first factor affecting the qualitative and quantitative structure of fish populations ('reserve effect'), and depth is the second factor. Thus, except in the cases of Serranus cabrilla and Mullus surmuletus, all other vulnerable species are highly sensitive to the protection measures. The size structure of all vulnerable species was found to be absolutely different at the reserve sites than in the unprotected zones, and the modal size classes of size frequency distributions were always higher in the reserve than outside. The reserve effect was significantly responsible of the differences observed in this change on size structure. Some highly vulnerable species, such as Epinephelus guaza and Sciaena umbra, have only been found in the protected area. Others, such as Sparus aurata, Diplodus cervinus and Dicentrarchus labrax, were much more frequent inside the reserve.

Can we disentangle predator-prey interactions from species distributions at a macro-scale? A case study with a raptor species.

There is a debate on whether an influence of biotic interactions on species distributions can be reflected at macro-scale levels. Whereas the influence of biotic interactions on spatial arrangements is beginning to be studied at local scales, similar studies at macro-scale levels are scarce. There is no example disentangling, from other similarities with related species, the influence of predator-prey interactions on species distributions at macro-scale levels. In this study we aimed to disentangle predator-prey interactions from species distribution data following an experimental approach including a factorial design. As a case of study we selected the short-toed eagle because of its known specialization on certain prey reptiles. We used presence-absence data at a 100 Km2 spatial resolution to extract the explanatory capacity of different environmental predictors (five abiotic and two biotic predictors) on the short-toed eagle species distribution in Peninsular Spain. Abiotic predictors were relevant climatic and topographic variables, and relevant biotic predictors were prey richness and forest density. In addition to the short-toed eagle, we also obtained the predictor's explanatory capacities for i) species of the same family Accipitridae (as a reference), ii) for other birds of different families (as controls) and iii) species with randomly selected presences (as null models). We run 650 models to test for similarities of the short-toed eagle, controls and null models with reference species, assessed by regressions of explanatory capacities. We found higher similarities between the short-toed eagle and other species of the family Accipitridae than for the other two groups. Once corrected by the family effect, our analyses revealed a signal of predator-prey interaction embedded in species distribution data. This result was corroborated with additional analyses testing for differences in the concordance between the distributions of different bird categories and the distributions of either prey or non-prey species of the short-toed eagle. Our analyses were useful to disentangle a signal of predator-prey interactions from species distribution data at a macro-scale. This study highlights the importance of disentangling specific features from the variation shared with a given taxonomic level.

Robust accelerated failure time regression

Robust estimators for accelerated failure time models with asymmetric (or symmetric) error distribution and censored observations are proposed. It is assumed that the error model belongs to a log-location-scale family of distributions and that the mean response is the parameter of interest. Since scale is a main component of mean, scale is not treated as a nuisance parameter. A three steps procedure is proposed. In the first step, an initial high breakdown point S estimate is computed. In the second step, observations that are unlikely under the estimated model are rejected or down weighted. Finally, a weighted maximum likelihood estimate is computed. To define the estimates, functions of censored residuals are replaced by their estimated conditional expectation given that the response is larger than the observed censored value. The rejection rule in the second step is based on an adaptive cut-off that, asymptotically, does not reject any observation when the data are generat ed according to the model. Therefore, the final estimate attains full efficiency at the model, with respect to the maximum likelihood estimate, while maintaining the breakdown point of the initial estimator. Asymptotic results are provided. The new procedure is evaluated with the help of Monte Carlo simulations. Two examples with real data are discussed.

High altitude Chironomidae (Diptera) of Serra da Estrela (Portugal): Additions to the Portuguese and Iberian Peninsula fauna

A Chironomidae (Diptera) fauna list for headwater streams of high altitude areas in Serra da Estrela (Portugal) is presented, doubling the previously established species richness for the region. The findings include 17 new records for Portugal, which represent an increase to 219 species for the Continental Portugal Chironomidae fauna. Two new records were detected for the Iberian Peninsula: one species (Tvetenia duodenaria), and one subgenusPsectrocladius (Mesopsectrocladius); and the presence of the genus Natarsia is confirmed. The last two occurrences correspond to monoespecific taxa of the Palearctic region. However, as taxonomic identification has been based on larval material, instead of pupae, pupal exuviae or imagoes, species level assignment is still uncertain. Key words: Diptera, Chironomidae, high mountain streams, Serra da Estrela, Portugal, Iberian Peninsula. RESUMEN Quironómidos (Diptera, Chironomidae) de alta montaña de la Sierra de Estrela (Portugal) y adiciones a la fauna de Portugal y la Península Ibérica Se presenta una lista de especies de Chironomidae (Diptera) recolectados en los ríos de cabecera de zonas de alta montaña en la Serra da Estrela (Portugal). Con esta aportación se duplica la riqueza de especies regional conocida hasta el momento y se eleva la fauna de quironómidos del Portugal continental a 219 especies. Se incluyen dos nuevas citas para la Península Ibérica, una especie (Tvetenia duodenaria) y un subgéneroPsectrocladius (Mesopsectrocladius), y se confirma la presencia del género Natarsia. En los dos últimos casos se trata de larvas de taxones hasta el momento monoespecíficos en la región paleárctica, pero al no haberse recolectado pupas o adultos no se puede asegurar la identificación específica. Palabras clave: Diptera, Chironomidae, ríos de alta montaña, Serra da Estrela, Portugal,

Benthic macroinvertebrates assemblages and macrohabitat connectivity in Mediterranean-climate streams of northern California

Abstract. Drought leads to a loss of longitudinal and lateral hydrologic connectivity, which causes direct or indirect changes in stream ecosystem properties. Changes in macrohabitat availability from a rifflepool sequence to isolated pools are among the most conspicuous consequences of connectivity loss. Macroinvertebrate assemblages were compared among 3 distinct stream macrohabitats (riffles [R], pools connected to riffles [Pc], disconnected pools [Pd]) of 19 Mediterranean-climate sites in northern California to examine the influence of loss of habitat resulting from drought disturbance. At the time of sampling, 10 sites were perennial and included R and Pc macrohabitats, whereas 9 sites were intermittent and included only Pd macrohabitats. Taxa richness was more variable in Pd, and taxa richness was significantly lower in Pd than in Pc but not R. These results suggested a decline in richness between Pc and Pd that might be associated with loss of connectivity. Lower Ephemeroptera, Plecoptera, and Trichoptera (EPT) richness relative to Odonata, Coleoptera, and Heteroptera (OCH) richness was observed for Pd than R and Pc macrohabitats. Family composition was more similar between R and Pc than between R or Pc and Pd macrohabitats. This similarity may be associated with greater connectivity between R and Pc macrohabitats. Correspondence analysis indicated that macroinvertebrate composition changed along a gradient from R to Pc and Pd that was related to a perennialintermittent gradient across sites. High variability among macroinvertebrate assemblages in Pd could have been related to variability in the duration of intermittency. In cluster analysis, macroinvertebrate assemblages were grouped by macrohabitat first and then by site, suggesting that the macrohabitat filter had a greater influence on macroinvertebrate assemblages than did local site characteristics. Few taxa were found exclusively in Pc, and this macrohabitat shared numerous taxa with R and Pd, indicating that Pc may act as a bridge between R and Pd during drought. Drought is regarded as a ramp disturbance, but our results suggest that the response of macroinvertebrate assemblages to the loss of hydrological connectivity among macrohabitats is gradual, at least in Mediterranean-climate streams where drying is gradual. However, the changes may be more dramatic in arid and semiarid streams or in Mediterranean-climate streams if drying is rapid.

Integrative analyses of speciation and divergence in Psammodromus hispanicus (Squamata: Lacertidae).

BackgroundGenetic, phenotypic and ecological divergence within a lineage is the result of past and ongoing evolutionary processes, which lead ultimately to diversification and speciation. Integrative analyses allow linking diversification to geological, climatic, and ecological events, and thus disentangling the relative importance of different evolutionary drivers in generating and maintaining current species richness.ResultsHere, we use phylogenetic, phenotypic, geographic, and environmental data to investigate diversification in the Spanish sand racer (Psammodromus hispanicus). Phylogenetic, molecular clock dating, and phenotypic analyses show that P. hispanicus consists of three lineages. One lineage from Western Spain diverged 8.3 (2.9-14.7) Mya from the ancestor of Psammodromus hispanicus edwardsianus and P. hispanicus hispanicus Central lineage. The latter diverged 4.8 (1.5-8.7) Mya. Molecular clock dating, together with population genetic analyses, indicate that the three lineages experienced northward range expansions from southern Iberian refugia during Pleistocene glacial periods. Ecological niche modelling shows that suitable habitat of the Western lineage and P. h. edwardsianus overlap over vast areas, but that a barrier may hinder dispersal and genetic mixing of populations of both lineages. P. h. hispanicus Central lineage inhabits an ecological niche that overlaps marginally with the other two lineages.ConclusionsOur results provide evidence for divergence in allopatry and niche conservatism between the Western lineage and the ancestor of P. h. edwardsianus and P. h. hispanicus Central lineage, whereas they suggest that niche divergence is involved in the origin of the latter two lineages. Both processes were temporally separated and may be responsible for the here documented genetic and phenotypic diversity of P. hispanicus. The temporal pattern is in line with those proposed for other animal lineages. It suggests that geographic isolation and vicariance played an important role in the early diversification of the group, and that lineage diversification was further amplified through ecological divergence.

On the relationship between connections and the asymptotic properties of predictive distributions

In a recent paper, Komaki studied the second-order asymptotic properties of predictive distributions, using the Kullback-Leibler divergence as a loss function. He showed that estimative distributions with asymptotically efficient estimators can be improved by predictive distributions that do not belong to the model. The model is assumed to be a multidimensional curved exponential family. In this paper we generalize the result assuming as a loss function any f divergence. A relationship arises between alpha connections and optimal predictive distributions. In particular, using an alpha divergence to measure the goodness of a predictive distribution, the optimal shift of the estimate distribution is related to alpha-covariant derivatives. The expression that we obtain for the asymptotic risk is also useful to study the higher-order asymptotic properties of an estimator, in the mentioned class of loss functions.