Bayesian inference of causal effects from observational data in Gaussian graphical models

We assume that multivariate observational data are generated from a distribution whose conditional independencies are encoded in a Directed Acyclic Graph (DAG). For any given DAG, the causal effect of a variable onto another one can be evaluated through intervention calculus. A DAG is typically not identifiable from observational data alone. However, its Markov equivalence class (a collection of DAGs) can be estimated from the data. As a consequence, for the same intervention a set of causal effects, one for each DAG in the equivalence class, can be evaluated. In this paper, we propose a fully Bayesian methodology to make inference on the causal effects of any intervention in the system. Main features of our method are: (a) both uncertainty on the equivalence class and the causal effects are jointly modeled; (b) priors on the parameters of the modified Cholesky decomposition of the precision matrices across all DAG models are constructively assigned starting from a unique prior on the complete (unrestricted) DAG; (c) an efficient algorithm to sample from the posterior distribution on graph space is adopted; (d) an objective Bayes approach, requiring virtually no user specification, is used throughout. We demonstrate the merits of our methodology in simulation studies, wherein comparisons with current state‐of‐the‐art procedures turn out to be highly satisfactory. Finally we examine a real data set of gene expressions for Arabidopsis thaliana.     

Evaluating the accuracy and calibration of expert predictions under uncertainty: predicting the outcomes of ecological research

Aim Expert knowledge routinely informs ecological research and decision‐making. Its reliability is often questioned, but is rarely subject to empirical testing and validation. We investigate the ability of experts to make quantitative predictions of variables for which the answers are known. Location Global. Methods Experts in four ecological subfields were asked to make predictions about the outcomes of scientific studies, in the form of unpublished (in press) journal articles, based on information in the article introduction and methods sections. Estimates from students were elicited for one case study for comparison. For each variable, participants assessed a lower and upper bound, best guess and level of confidence that the observed value will lie within their ascribed interval. Responses were assessed for (1) accuracy: the degree to which predictions corresponded with observed experimental results, (2) informativeness: precision of the uncertainty bounds, and (3) calibration: degree to which the uncertainty bounds contained the truth as often as specified. Results Expert responses were found to be overconfident, specifying 80% confidence intervals that captured the truth only 49–65% of the time. In contrast, student 80% intervals captured the truth 76% of the time, displaying close to perfect calibration. Best estimates from experts were on average more accurate than those from students. The best students outperformed the worst experts. No consistent relationships were observed between performance and years of experience, publication record or self‐assessment of expertise. Main conclusions Experts possess valuable knowledge but may require training to communicate this knowledge accurately. Expert status is a poor guide to good performance. In the absence of training and information on past performance, simple averages of expert responses provide a robust counter to individual variation in performance.     

Testing causal structure in the biogeography of avian extinctions on oceanic islands

In their recent comment in this journal, T. M. Blackburn and colleagues called into question the use of standardized partial regression modelling (also called path analysis and structural equation modelling) when null expectations for regression coefficients are not zero. Here, we answer their critique by showing how randomization can be used to illuminate and interpret causal modelling in analyses that have non-zero expectations. Causal modelling is a powerful tool that can yield novel insights in biogeography when properly interpreted.     

Influence of environmental heterogeneity on genetic diversity and structure in an endemic southern Californian oak

Understanding how specific environmental factors shape gene flow while disentangling their importance relative to the effects of geographical isolation is a major question in evolutionary biology and a specific goal of landscape genetics. Here, we combine information from nuclear microsatellite markers and ecological niche modelling to study the association between climate and spatial genetic structure and variability in Engelmann oak (Quercus engelmannii), a wind-pollinated species with high potential for gene flow. We first test whether genetic diversity is associated with climatic niche suitability and stability since the Last Glacial Maximum (LGM). Second, we use causal modelling to analyse the potential influence of climatic factors (current and LGM niche suitability) and altitude in the observed patterns of genetic structure. We found that genetic diversity is negatively associated with local climatic stability since the LGM, which may be due to higher immigration rates in unstable patches during favourable climatic periods and/or temporally varying selection. Analyses of spatial genetic structure revealed the presence of three main genetic clusters, a pattern that is mainly driven by two highly differentiated populations located in the northern edge of the species distribution range. After controlling for geographic distance, causal modelling analyses showed that genetic relatedness decreases with the environmental divergence among sampling sites estimated as altitude and current and LGM niche suitability. Natural selection against nonlocal genotypes and/or asynchrony in reproductive phenology may explain this pattern. Overall, this study suggests that local environmental conditions can shape patterns of genetic structure and variability even in species with high potential for gene flow and relatively small distribution ranges.     

Quantifying and mathematical modelling of the influence of soluble adenylate cyclase on cell cycle in human endothelial cells with Bayesian inference

Adenosine‐3′, 5′‐cyclic monophosphate (cAMP) produced by adenylate cyclases (ADCYs) is an established key regulator of cell homoeostasis. However, its role in cell cycle control is still controversially discussed. This study focussed on the impact of soluble HCO₃ ⁻ ‐activated ADCY10 on cell cycle progression. Effects are quantified with Bayesian inference integrating a mathematical model and experimental data. The activity of ADCY10 in human umbilical vein endothelial cells (HUVECs) was either pharmacologically inhibited by KH7 or endogenously activated by HCO₃ ⁻. Cell numbers of individual cell cycle phases were assessed over time using flow cytometry. Based on these numbers, cell cycle dynamics were analysed using a mathematical model. This allowed precise quantification of cell cycle dynamics with model parameters that describe the durations of individual cell cycle phases. Endogenous inactivation of ADCY10 resulted in prolongation of mean cell cycle times (38.7 ± 8.3 h at 0 mM HCO₃ ⁻ vs 30.3 ± 2.7 h at 24 mM HCO₃ ⁻), while pharmacological inhibition resulted in functional arrest of cell cycle by increasing mean cell cycle time after G₀/G₁ synchronization to 221.0 ± 96.3 h. All cell cycle phases progressed slower due to ADCY10 inactivation. In particular, the G₁‐S transition was quantitatively the most influenced by ADCY10. In conclusion, the data of the present study show that ADCY10 is a key regulator in cell cycle progression linked specifically to the G₁‐S transition.     

Evolutionary and demographic history of the Californian scrub white oak species complex: an integrative approach

Understanding the factors promoting species formation is a major task in evolutionary research. Here, we employ an integrative approach to study the evolutionary history of the Californian scrub white oak species complex (genus Quercus). To infer the relative importance of geographical isolation and ecological divergence in driving the speciation process, we (i) analysed inter‐ and intraspecific patterns of genetic differentiation and employed an approximate Bayesian computation (ABC) framework to evaluate different plausible scenarios of species divergence. In a second step, we (ii) linked the inferred divergence pathways with current and past species distribution models (SDMs) and (iii) tested for niche differentiation and phylogenetic niche conservatism across taxa. ABC analyses showed that the most plausible scenario is the one considering the divergence of two main lineages followed by a more recent pulse of speciation. Genotypic data in conjunction with SDMs and niche differentiation analyses support that different factors (geography vs. environment) and modes of speciation (parapatry, allopatry and maybe sympatry) have played a role in the divergence process within this complex. We found no significant relationship between genetic differentiation and niche overlap, which probably reflects niche lability and/or that multiple factors, have contributed to speciation. Our study shows that different mechanisms can drive divergence even among closely related taxa representing early stages of species formation and exemplifies the importance of adopting integrative approaches to get a better understanding of the speciation process.     

Contrasting responses of native and alien plant species to soil properties shed new light on the invasion of dune systems

在陆地生态系统中,沿海沙丘特别容易受到外来植物的入侵。许多研究将沙丘生境的入侵归因于人为因素,但对土壤性质和植物性状在植物 入侵中的作用却知之甚少。本研究考察了沙丘系统土壤特征与外来植物入侵的关系,重点研究了土壤养分、土壤盐分和植物功能特征之间的相互作 用。研究地点是马拉诺和格拉多泻湖(北亚得里亚海)的沙质堰洲岛。根据沙丘系统生态梯度上的主要生境(前沙丘、后沙丘和盐沼),在10 个区域内选择100个地块(4 m × 4 m)。在每个地块中记录所有植物物种的发生和丰度,并收集一个土壤核。对每个土壤样品进行土壤质地、电导率(代表土壤盐 分)、有机碳和氮含量分析,并与本地和外来植物的种类数和覆盖度相关联。分析外来和本地物种主要的生殖功能和营养功能性状在生境中的变化。研究结果表明,土壤性质对外来物种库和本地物种库的影响不同,与植物整体多样性密切相关。在后沙丘(最易入侵)的生境中,高的土壤导电性限制了外来物种的数量,但土壤有机碳含量随着外来植物丰度的增加而增加,这也表明植物入侵与土壤之间存在潜在的反馈过程。只有在后沙丘生境中,随着环境条件的改善和植物竞争的加剧,本地植物和外来植物的功能性状谱有显著的趋同。本研究结果表明,在恶劣条件下,只有本地特有植物才能茁壮成长,而在中等条件下,土壤特性梯度与植物特性协同作用,抑制/促进外来植物丰富度。     

The effect of sample size on the accuracy of species distribution models: considering both presences and pseudo‐absences or background sites

Most high‐performing species distribution modelling techniques require both presences, and either absences or pseudo‐absences or background points. In this paper, we explore the effect of sample size, towards developing improved strategies for modelling. We generated 1800 virtual species with three levels of prevalence using ten modelling techniques, while varying the number of training presences (NTP) and the number of random points (NRP representing pseudo‐absences or background sites). For five of the ten modelling techniques we built two versions of models: one with an equal total weight (ETW) setting where the total weight for pseudo‐absence is equivalent to the total weight for presence, and another with an unequal total weight (UTW) setting where the total weight for pseudo‐absence is not required to be equal to the total weight for presence. We compared two strategies for NRP: a small multiplier strategy (i.e. setting NRP at a few times as large as NTP), and a large number strategy (i.e. using numerous random points). We produced ensemble models (by averaging the predictions from 30 models built with the same set of training presences and different sets of random points in equivalent numbers) for three NTP magnitudes and two NRP strategies. We found that model accuracy altered as NRP increased with four distinct patterns of performance: increasing, decreasing, arch‐shaped and horizontal. In most cases ETW improved model performance. Ensemble models had higher accuracy than the corresponding single models, and this improvement was pronounced when NTP was low. We conclude that a large NRP is not always an appropriate strategy. The best choice for NRP will depend on the modelling techniques used, species prevalence and NTP. We recommend building ensemble models instead of single models, using the small multiplier strategy for NRP with ETW, especially when only a small number of species presence records are available.     

An attack on two fronts: predicting how changes in land use and climate affect the distribution of stream macroinvertebrates

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Direct and indirect effects of area,energy and habitat heterogeneity on breeding bird communities

Aim To compare the ability of island biogeography theory, niche theory and species–energy theory to explain patterns of species richness and density for breeding bird communities across islands with contrasting characteristics. Location Thirty forested islands in two freshwater lakes in the boreal forest zone of northern Sweden (65°55′ N to 66°09′ N; 17°43′ E to 17°55′ E). Methods We performed bird censuses on 30 lake islands that have each previously been well characterized in terms of size, isolation, habitat heterogeneity (plant diversity and forest age), net primary productivity (NPP), and invertebrate prey abundance. To test the relative abilities of island biogeography theory, niche theory and species–energy theory to describe bird community patterns, we used both traditional statistical approaches (linear and multiple regressions) and structural equation modelling (SEM; in which both direct and indirect influences can be quantified). Results Using regression‐based approaches, area and bird abundance were the two most important predictors of bird species richness. However, when the data were analysed by SEM, area was not found to exert a direct effect on bird species richness. Instead, terrestrial prey abundance was the strongest predictor of bird abundance, and bird abundance in combination with NPP was the best predictor of bird species richness. Area was only of indirect importance through its positive effect on terrestrial prey abundance, but habitat heterogeneity and spatial subsidies (emerging aquatic insects) also showed important indirect influences. Thus, our results provided the strongest support for species–energy theory. Main conclusions Our results suggest that, by using statistical approaches that allow for analyses of both direct and indirect influences, a seemingly direct influence of area on species richness can be explained by greater energy availability on larger islands. As such, animal community patterns that seem to be in line with island biogeography theory may be primarily driven by energy availability. Our results also point to the need to consider several aspects of habitat quality (e.g. heterogeneity, NPP, prey availability and spatial subsidies) for successful management of breeding bird diversity at local spatial scales and in fragmented or insular habitats.     

Phylogeography in continuous space: coupling species distribution models and circuit theory to assess the effect of contiguous migration at different climatic periods on genetic differentiation in Busseola fusca (Lepidoptera: Noctuidae)

Current population genetic models fail to cope with genetic differentiation for species with large, contiguous and heterogeneous distribution. We show that in such a case, genetic differentiation can be predicted at equilibrium by circuit theory, where conductance corresponds to abundance in species distribution models (SDMs). Circuit‐SDM approach was used for the phylogeographic study of the lepidopteran cereal stemborer Busseola fuscaFüller (Noctuidae) across sub‐Saharan Africa. Species abundance was surveyed across its distribution range. SDMs were optimized and selected by cross‐validation. Relationship between observed matrices of genetic differentiation between individuals, and between matrices of resistance distance was assessed through Mantel tests and redundancy discriminant analyses (RDAs). A total of 628 individuals from 130 localities in 17 countries were genotyped at seven microsatellite loci. Six population clusters were found based on a Bayesian analysis. The eastern margin of Dahomey gap between East and West Africa was the main factor of genetic differentiation. The SDM projections at present, last interglacial and last glacial maximum periods were used for the estimation of circuit resistance between locations of genotyped individuals. For all periods of time, when using either all individuals or only East African individuals, partial Mantel r and RDA conditioning on geographic distance were found significant. Under future projections (year 2080), partial r and RDA significance were different. From this study, it is concluded that analytical solutions provided by circuit theory are useful for the evolutionary management of populations and for phylogeographic analysis when coalescence times are not accessible by approximate Bayesian simulations.     

Spatio-temporal modelling of the effect of selected environmental and land-use factors on acid grassland vegetation

特定环境和土地利用因素对酸性草原植被影响的时空建模酸性草原受到了农业集约化作业(伴随着养分添加)、牲畜密度增加以及土地撂荒等多种因素的威胁。为了认识和量化所选环境和土地利用因子对酸性草地植被观测变化的影响,本研究采用结构方程模型拟合了大尺度时空精度植被覆盖监测数据。通过分层模型结构将测量和采样不确定性的重要来源纳入其中。此外,本研究也将测量和采样的不确定性与过程的不确定性分离,这在生成可能反馈给当地保护管理决策的生态预测时有着重要的意义。研究结果表明,一般而言,大气氮沉降的增加会导致非禾本草本植物的盖度,取而代之的会是更多的以禾草植物为主的酸性草原生境。沙质土壤的酸性相对较强,而土壤类型既会对植被构成直接的影响,也会通过影响土壤pH值的方式对植被产生间接影响。土壤的类型和土壤的pH值都会对酸性草原上的植被造成影响。对于植被覆盖情况在时间上的变化,尽管该模型仅解释了其中相对较小的一部分,但在使用该模型对局部生态状况进行预测并制定具有自适应性的管理计划时,对不确定性的量化仍然是有价值的。     

Assessing the impact of deforestation and climate change on the range size and environmental niche of bird species in the Atlantic forests,Brazil

Aim Habitat loss and climate change are two major drivers of biological diversity. Here we quantify how deforestation has already changed, and how future climate scenarios may change, environmental conditions within the highly disturbed Atlantic forests of Brazil. We also examine how environmental conditions have been altered within the range of selected bird species. Location Atlantic forests of south‐eastern Brazil. Methods The historical distribution of 21 bird species was estimated using Maxent . After superimposing the present‐day forest cover, we examined the environmental niches hypothesized to be occupied by these birds pre‐ and post‐deforestation using environmental niche factor analysis (ENFA). ENFA was also used to compare conditions in the entire Atlantic forest ecosystem pre‐ and post‐deforestation. The relative influence of land use and climate change on environmental conditions was examined using analysis of similarity and principal components analysis. Results Deforestation in the region has resulted in a decrease in suitable habitat of between 78% and 93% for the Atlantic forest birds included here. Further, Atlantic forest birds today experience generally wetter and less seasonal forest environments than they did historically. Models of future environmental conditions within forest remnants suggest generally warmer conditions and lower annual variation in rainfall due to greater precipitation in the driest quarter of the year. We found that deforestation resulted in a greater divergence of environmental conditions within Atlantic forests than that predicted by climate change. Main conclusions The changes in environmental conditions that have occurred with large‐scale deforestation suggest that selective regimes may have shifted and, as a consequence, spatial patterns of intra‐specific variation in morphology, behaviour and genes have probably been altered. Although the observed shifts in available environmental conditions resulting from deforestation are greater than those predicted by climate change, the latter will result in novel environments that exceed temperatures in any present‐day climates and may lead to biotic attrition unless organisms can adapt to these warmer conditions. Conserving intra‐specific diversity over the long term will require considering both how changes in the recent past have influenced contemporary populations and the impact of future environmental change.     

The interactive effects of livestock exclusion and mammalian pest control on the restoration of invertebrate communities in small forest remnants

Abstract

In many agricultural landscapes, significant biodiversity gains can be made by improving the ecological condition of degraded remnants of semi‐natural habitat. Recent emphasis has been on the level of management intervention required to initiate vegetation recovery in small forest remnants, but no comparable emphasis has been placed on benefits for invertebrate communities. In the Waikato region, New Zealand, we tested the effects of livestock exclusion, mammalian pest control, and their interaction, on leaf‐litter invertebrate communities in 30 forest remnants, using a space‐for‐time substitution approach. A total of 87 376 invertebrates were extracted from 964 leaf‐litter samples. Invertebrate density was an order of magnitude lower in remnants than in nearby large forest reserves. For key taxa, such as Diplopoda, Isopoda, Coleoptera and Mollusca, 10‐ to 100‐fold lower densities were recorded in remnants with no pest control, particularly where livestock were not excluded. By contrast, other taxa such as Thysanoptera and For‐micidae (Hymenoptera) had up to 100‐fold greater densities in remnants with recent stock exclusion and pest control. These changes led to a significant livestock exclusion x pest control interaction effect on the degree of invertebrate community dissimilarity between forest remnants and forest reserves. Using structural equation modelling, we found that treatment effects were largely mediated by a cascading series of indirect causal paths involving altered soil chemistry, vegetation composition, and litter mass relative to large forest reserves, although the livestock exclusion × pest control interaction was inadvertently confounded with differing slopes and areas of remnants in different treatments. Livestock exclusion and mammalian pest control have significant, but contrasting, effects on invertebrates in the first 10–20 years following livestock exclusion from forest remnants, with mammalian pest control having limited benefit for the leaf‐litter invertebrate fauna without livestock exclusion.