Strategy and model building in the fourth dimension: a null model for genotype × age interaction as a Gaussian stationary stochastic process

Abstract Background Using univariate and multivariate variance components linkage analysis methods, we studied possible genotype × age interaction in cardiovascular phenotypes related to the aging process from the Framingham Heart Study. Results We found evidence for genotype × age interaction for fasting glucose and systolic blood pressure. Conclusions There is polygenic genotype × age interaction for fasting glucose and systolic blood pressure and quantitative trait locus × age interaction for a linkage signal for systolic blood pressure phenotypes located on chromosome 17 at 67 cM.

A landscape-scale test of the predictive ability of a spatially explicit model for population viability analysis

1. Although population viability analysis (PVA) is widely employed, forecasts from PVA models are rarely tested. This study in a fragmented forest in southern Australia contrasted field data on patch occupancy and abundance for the arboreal marsupial greater glider Petauroides volans with predictions from a generic spatially explicit PVA model. This work represents one of the first landscape-scale tests of its type. 2. Initially we contrasted field data from a set of eucalypt forest patches totalling 437 ha with a naive null model in which forecasts of patch occupancy were made, assuming no fragmentation effects and based simply on remnant area and measured densities derived from nearby unfragmented forest. The naive null model predicted an average total of approximately 170 greater gliders, considerably greater than the true count (n = 81). 3. Congruence was examined between field data and predictions from PVA under several metapopulation modelling scenarios. The metapopulation models performed better than the naive null model. Logistic regression showed highly significant positive relationships between predicted and actual patch occupancy for the four scenarios (P = 0.001-0.006). When the model-derived probability of patch occupancy was high (0.50-0.75, 0.75-1.00), there was greater congruence between actual patch occupancy and the predicted probability of occupancy. 4. For many patches, probability distribution functions indicated that model predictions for animal abundance in a given patch were not outside those expected by chance. However, for some patches the model either substantially over-predicted or under-predicted actual abundance. Some important processes, such as inter-patch dispersal, that influence the distribution and abundance of the greater glider may not have been adequately modelled. 5. Additional landscape-scale tests of PVA models, on a wider range of species, are required to assess further predictions made using these tools. This will help determine those taxa for which predictions are and are not accurate and give insights for improving models for applied conservation management.

An Integrated Framework To Improve The Concept Of Resource Specialisation.

Resource specialisation, although a fundamental component of ecological theory, is employed in disparate ways. Most definitions derive from simple counts of resource species. We build on recent advances in ecophylogenetics and null model analysis to propose a concept of specialisation that comprises affinities among resources as well as their co-occurrence with consumers. In the distance-based specialisation index (DSI), specialisation is measured as relatedness (phylogenetic or otherwise) of resources, scaled by the null expectation of random use of locally available resources. Thus, specialists use significantly clustered sets of resources, whereas generalists use over-dispersed resources. Intermediate species are classed as indiscriminate consumers. The effectiveness of this approach was assessed with differentially restricted null models, applied to a data set of 168 herbivorous insect species and their hosts. Incorporation of plant relatedness and relative abundance greatly improved specialisation measures compared to taxon counts or simpler null models, which overestimate the fraction of specialists, a problem compounded by insufficient sampling effort. This framework disambiguates the concept of specialisation with an explicit measure applicable to any mode of affinity among resource classes, and is also linked to ecological and evolutionary processes. This will enable a more rigorous deployment of ecological specialisation in empirical and theoretical studies.

Individual-level diet variation in four species of Brazilian frogs

Many natural populations exploiting a wide range of resources are actually composed of relatively specialized individuals. This interindividual variation is thought to be a consequence of the invasion of `empty` niches in depauperate communities, generally in temperate regions. If individual niches are constrained by functional trade-offs, the expansion of the population niche is only achieved by an increase in interindividual variation, consistent with the `niche variation hypothesis`. According to this hypothesis, we should not expect interindividual variation in species belonging to highly diverse, packed communities. In the present study, we measured the degree of interindividual diet variation in four species of frogs of the highly diverse Brazilian Cerrado, using both gut contents and delta(13)C stable isotopes. We found evidence of significant diet variation in the four species, indicating that this phenomenon is not restricted to depauperate communities in temperate regions. The lack of correlations between the frogs` morphology and diet indicate that trade-offs do not depend on the morphological characters measured here and are probably not biomechanical. The nature of the trade-offs remains unknown, but are likely to be cognitive or physiological. Finally, we found a positive correlation between the population niche width and the degree of diet variation, but a null model showed that this correlation can be generated by individuals sampling randomly from a common set of resources. Therefore, albeit consistent with, our results cannot be taken as evidence in favour of the niche variation hypothesis.

Biological determinants of extinction risk: why are smaller species less vulnerable?

It is becoming increasingly clear that species of smaller body size tend to be less vulnerable to contemporary extinction threats than larger species, but few studies have examined the mechanisms underlying this pattern. In this paper, data for the Australian terrestrial mammal fauna are used to ask whether higher reproductive output or smaller home ranges can explain the reduced extinction risk of smaller species. Extinct and endangered species do indeed have smaller litters and larger home ranges for their body size than expected under a null model. In multiple regressions, however, only litter size is a significant predictor of extinction risk once body size and phylogeny are controlled for. Larger litters contribute to fast population growth, and are probably part of the reason that smaller species are less extinction-prone. The effect of litter size varies between the mesic coastal regions and the and interior of Australia, indicating that the environment a species inhabits mediates the effect of biology on extinction risk. These results suggest that predicting extinction risk from biological traits is likely to be a complex task which must consider explicitly interactions between biology and environment.

Oligocene CO2 decline promoted C4 photosynthesis in grasses.

C4 photosynthesis is an adaptation derived from the more common C3 photosynthetic pathway that confers a higher productivity under warm temperature and low atmospheric CO2 concentration [1, 2]. C4 evolution has been seen as a consequence of past atmospheric CO2 decline, such as the abrupt CO2 fall 32-25 million years ago (Mya) [3-6]. This relationship has never been tested rigorously, mainly because of a lack of accurate estimates of divergence times for the different C4 lineages [3]. In this study, we inferred a large phylogenetic tree for the grass family and estimated, through Bayesian molecular dating, the ages of the 17 to 18 independent grass C4 lineages. The first transition from C3 to C4 photosynthesis occurred in the Chloridoideae subfamily, 32.0-25.0 Mya. The link between CO2 decrease and transition to C4 photosynthesis was tested by a novel maximum likelihood approach. We showed that the model incorporating the atmospheric CO2 levels was significantly better than the null model, supporting the importance of CO2 decline on C4 photosynthesis evolvability. This finding is relevant for understanding the origin of C4 photosynthesis in grasses, which is one of the most successful ecological and evolutionary innovations in plant history.

Random mating with a finite number of matings.

Random mating is the null model central to population genetics. One assumption behind random mating is that individuals mate an infinite number of times. This is obviously unrealistic. Here we show that when each female mates a finite number of times, the effective size of the population is substantially decreased.

Intrinsic test of independence in contingency tables

A condition needed for testing nested hypotheses from a Bayesianviewpoint is that the prior for the alternative model concentratesmass around the small, or null, model. For testing independencein contingency tables, the intrinsic priors satisfy this requirement.Further, the degree of concentration of the priors is controlled bya discrete parameter m, the training sample size, which plays animportant role in the resulting answer regardless of the samplesize.In this paper we study robustness of the tests of independencein contingency tables with respect to the intrinsic priors withdifferent degree of concentration around the null, and comparewith other “robust” results by Good and Crook. Consistency ofthe intrinsic Bayesian tests is established.We also discuss conditioning issues and sampling schemes,and argue that conditioning should be on either one margin orthe table total, but not on both margins.Examples using real are simulated data are given

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Using analytical tools from game theory, we investigate the relevance of a series of hypotheses concerning natal dispersal, focusing in particular on the interaction between inbreeding and kin competition, as well as on the components of mating and social systems that are likely to interfere with these phenomena. A null model of pure kin competition avoidance predicts a balanced equilibrium in wich both sexes disperse equally. Inbreeding costs have the potential to destabilize the equilibrium, resulting in strongly sex-biased dispersal. This effect is mostly evident when the peculiarities of the mating system induce asymmetries in dispersal and/or inbreeding costs, or when kin cooperation counteracts kin competition. Inbreeding depression, however, is not the only possible cause for sex biases. The relevance of our results to empirical findings is dicussed and suggestions are made for further empirical or modelling work.

Distribuição de abundância e tamanho do corpo de invertebrados do folhiço em uma floresta de terra firme na Amazônia Central, Brasil

Abundace and body size distribution of invertebrates of leaf litter in Amazonian forest, Brazil. Based on 605 invertebrates sampled of the litter in an Amazonian Forest, some basic macroecological patterns for this assemblage were described. The relationship between abundance and body size, at logarithmic scale, was triangular, and the distribution of species was constrained in an asymmetric triangular envelope, that was tested using null model procedures in ECOSIM (P= 0,0002). The most abundant species were at an intermediated body size. The relationship between maximum abundance with different mean body size classes confirmed the Energetic Equivalent Rule (b = -1,069; t-0,75 = -2,13; P = 0.079). This way, species tend to consume energy from the community independent of their body size, since requirements are compensated by local population density.

A scaled difference chi-square test statistic for moment structure analysis

A family of scaling corrections aimed to improve the chi-square approximation of goodness-of-fit test statistics in small samples, large models, and nonnormal data was proposed in Satorra and Bentler (1994). For structural equations models, Satorra-Bentler's (SB) scaling corrections are available in standard computer software. Often, however, the interest is not on the overall fit of a model, but on a test of the restrictions that a null model say ${\cal M}_0$ implies on a less restricted one ${\cal M}_1$. If $T_0$ and $T_1$ denote the goodness-of-fit test statistics associated to ${\cal M}_0$ and ${\cal M}_1$, respectively, then typically the difference $T_d = T_0 - T_1$ is used as a chi-square test statistic with degrees of freedom equal to the difference on the number of independent parameters estimated under the models ${\cal M}_0$ and ${\cal M}_1$. As in the case of the goodness-of-fit test, it is of interest to scale the statistic $T_d$ in order to improve its chi-square approximation in realistic, i.e., nonasymptotic and nonnormal, applications. In a recent paper, Satorra (1999) shows that the difference between two Satorra-Bentler scaled test statistics for overall model fit does not yield the correct SB scaled difference test statistic. Satorra developed an expression that permits scaling the difference test statistic, but his formula has some practical limitations, since it requires heavy computations that are notavailable in standard computer software. The purpose of the present paper is to provide an easy way to compute the scaled difference chi-square statistic from the scaled goodness-of-fit test statistics of models ${\cal M}_0$ and ${\cal M}_1$. A Monte Carlo study is provided to illustrate the performance of the competing statistics.

Ecological assembly rules in plant communities--approaches, patterns and prospects.

Understanding how communities of living organisms assemble has been a central question in ecology since the early days of the discipline. Disentangling the different processes involved in community assembly is not only interesting in itself but also crucial for an understanding of how communities will behave under future environmental scenarios. The traditional concept of assembly rules reflects the notion that species do not co-occur randomly but are restricted in their co-occurrence by interspecific competition. This concept can be redefined in a more general framework where the co-occurrence of species is a product of chance, historical patterns of speciation and migration, dispersal, abiotic environmental factors, and biotic interactions, with none of these processes being mutually exclusive. Here we present a survey and meta-analyses of 59 papers that compare observed patterns in plant communities with null models simulating random patterns of species assembly. According to the type of data under study and the different methods that are applied to detect community assembly, we distinguish four main types of approach in the published literature: species co-occurrence, niche limitation, guild proportionality and limiting similarity. Results from our meta-analyses suggest that non-random co-occurrence of plant species is not a widespread phenomenon. However, whether this finding reflects the individualistic nature of plant communities or is caused by methodological shortcomings associated with the studies considered cannot be discerned from the available metadata. We advocate that more thorough surveys be conducted using a set of standardized methods to test for the existence of assembly rules in data sets spanning larger biological and geographical scales than have been considered until now. We underpin this general advice with guidelines that should be considered in future assembly rules research. This will enable us to draw more accurate and general conclusions about the non-random aspect of assembly in plant communities.

Inferring epidemic contact structure from phylogenetic trees.

Contact structure is believed to have a large impact on epidemic spreading and consequently using networks to model such contact structure continues to gain interest in epidemiology. However, detailed knowledge of the exact contact structure underlying real epidemics is limited. Here we address the question whether the structure of the contact network leaves a detectable genetic fingerprint in the pathogen population. To this end we compare phylogenies generated by disease outbreaks in simulated populations with different types of contact networks. We find that the shape of these phylogenies strongly depends on contact structure. In particular, measures of tree imbalance allow us to quantify to what extent the contact structure underlying an epidemic deviates from a null model contact network and illustrate this in the case of random mixing. Using a phylogeny from the Swiss HIV epidemic, we show that this epidemic has a significantly more unbalanced tree than would be expected from random mixing.

Do stacked species distribution models reflect altitudinal diversity patterns?

The objective of this study was to evaluate the performance of stacked species distribution models in predicting the alpha and gamma species diversity patterns of two important plant clades along elevation in the Andes. We modelled the distribution of the species in the Anthurium genus (53 species) and the Bromeliaceae family (89 species) using six modelling techniques. We combined all of the predictions for the same species in ensemble models based on two different criteria: the average of the rescaled predictions by all techniques and the average of the best techniques. The rescaled predictions were then reclassified into binary predictions (presence/absence). By stacking either the original predictions or binary predictions for both ensemble procedures, we obtained four different species richness models per taxa. The gamma and alpha diversity per elevation band (500 m) was also computed. To evaluate the prediction abilities for the four predictions of species richness and gamma diversity, the models were compared with the real data along an elevation gradient that was independently compiled by specialists. Finally, we also tested whether our richness models performed better than a null model of altitudinal changes of diversity based on the literature. Stacking of the ensemble prediction of the individual species models generated richness models that proved to be well correlated with the observed alpha diversity richness patterns along elevation and with the gamma diversity derived from the literature. Overall, these models tend to overpredict species richness. The use of the ensemble predictions from the species models built with different techniques seems very promising for modelling of species assemblages. Stacking of the binary models reduced the over-prediction, although more research is needed. The randomisation test proved to be a promising method for testing the performance of the stacked models, but other implementations may still be developed.

Intrinsic test of independence in contingency tables

A condition needed for testing nested hypotheses from a Bayesian viewpoint is that the prior for the alternative model concentrates mass around the small, or null, model. For testing independence in contingency tables, the intrinsic priors satisfy this requirement. Further, the degree of concentration of the priors is controlled by a discrete parameter m, the training sample size, which plays an important role in the resulting answer regardless of the sample size. In this paper we study robustness of the tests of independence in contingency tables with respect to the intrinsic priors with different degree of concentration around the null, and compare with other “robust” results by Good and Crook. Consistency of the intrinsic Bayesian tests is established. We also discuss conditioning issues and sampling schemes, and argue that conditioning should be on either one margin or the table total, but not on both margins. Examples using real are simulated data are given