Causal modeling in a multi-omic setting: insights from GAW20

Background

Increasingly available multilayered omics data on large populations has opened exciting analytic opportunities and posed unique challenges to robust estimation of causal effects in the setting of complex disease phenotypes. The GAW20 Causal Modeling Working Group has applied complementary approaches (eg, Mendelian randomization, structural equations modeling, Bayesian networks) to discover novel causal effects of genomic and epigenomic variation on lipid phenotypes, as well as to validate prior findings from observational studies.

Results

Two Mendelian randomization studies have applied novel approaches to instrumental variable selection in methylation data, identifying bidirectional causal effects of CPT1A and triglycerides, as well as of RNMT and C6orf42, on high-density lipoprotein cholesterol response to fenofibrate. The CPT1A finding also emerged in a Bayesian network study. The Mendelian randomization studies have implemented both existing and novel steps to account for pleiotropic effects, which were independently detected in the GAW20 data via a structural equation modeling approach. Two studies estimated indirect effects of genomic variation (via DNA methylation and/or correlated phenotypes) on lipid outcomes of interest. Finally, a novel weighted R² measure was proposed to complement other causal inference efforts by controlling for the influence of outlying observations.

Conclusions

The GAW20 contributions illustrate the diversity of possible approaches to causal inference in the multi-omic context, highlighting the promises and assumptions of each method and the benefits of integrating both across methods and across omics layers for the most robust and comprehensive insights into disease processes.

     

Bayesian lasso for semiparametric structural equation models

There has been great interest in developing nonlinear structural equation models and associated statistical inference procedures, including estimation and model selection methods. In this paper a general semiparametric structural equation model (SSEM) is developed in which the structural equation is composed of nonparametric functions of exogenous latent variables and fixed covariates on a set of latent endogenous variables. A basis representation is used to approximate these nonparametric functions in the structural equation and the Bayesian Lasso method coupled with a Markov Chain Monte Carlo (MCMC) algorithm is used for simultaneous estimation and model selection. The proposed method is illustrated using a simulation study and data from the Affective Dynamics and Individual Differences (ADID) study. Results demonstrate that our method can accurately estimate the unknown parameters and correctly identify the true underlying model.     

Local average treatment effects estimation via substantive model compatible multiple imputation

Nonadherence to assigned treatment is common in randomized controlled trials (RCTs). Recently, there has been increased interest in estimating causal effects of treatment received, for example, the so‐called local average treatment effect (LATE). Instrumental variables (IV) methods can be used for identification, with estimation proceeding either via fully parametric mixture models or two‐stage least squares (TSLS). TSLS is popular but can be problematic for binary outcomes where the estimand of interest is a causal odds ratio. Mixture models are rarely used in practice, perhaps because of their perceived complexity and need for specialist software. Here, we propose using multiple imputation (MI) to impute the latent compliance class appearing in the mixture models. Since such models include an interaction term between the latent compliance class and randomized treatment, we use “substantive model compatible” MI (SMC MIC), which can additionally handle missing data in outcomes and other variables in the model, before fitting the mixture models via maximum likelihood to the MI data sets and combining results via Rubin's rules. We use simulations to compare the performance of SMC MIC to existing approaches and also illustrate the methods by reanalyzing an RCT in UK primary health. We show that SMC MIC can be more efficient than full Bayesian estimation when auxiliary variables are incorporated, and is superior to two‐stage methods, especially for binary outcomes.     

Analysis of ionization and recombination processes under the coronal equilibrium conditions by using a statistical atomic model

Ionization and recombination processes accompanying collisions of free electrons with plasma ions are considered using a statistical atomic model in which ionization and recombination are regarded as the processes of pair electron collisions in the electron gas of an atom. An expression for the ionization rate as a function of the ionization energy I and temperature T is derived. According to this expression, the ionization rate at I ? T is proportional to exp(?I/T). The statistical atomic model provides an estimate of the recombination rate for an ion with an arbitrary nuclear charge number Z, whereas more exact calculations of the recombination rate can be performed only for large Z. The model explains relatively low values of I/T (as compared to those given by the Saha equation) under the coronal equilibrium conditions and predicts a reduction in I/T with increasing Z. The values of I/T and the average ion charge number obtained from the balance equation for multielectron ions with the use of one fitting coefficient agree with the tabulated data calculated in the multilevel coronal model.     

A framework for structural equation models in general pedigrees

Background/Aims: Structural Equation Modeling (SEM) is an analysis approach that accounts for both the causal relationships between variables and the errors associated with the measurement of these variables. In this paper, a framework for implementing structural equation models (SEMs) in family data is proposed. Methods: This framework includes both a latent measurement model and a structural model with covariates. It allows for a wide variety of models, including latent growth curve models. Environmental, polygenic and other genetic variance components can be included in the SEM. Kronecker notation makes it easy to separate the SEM process from a familial correlation model. A limited information method of model fitting is discussed. We show how missing data and ascertainment may be handled. We give several examples of how the framework may be used. Results: A simulation study shows that our method is computationally feasible, and has good statistical properties. Conclusion: Our framework may be used to build and compare causal models using family data without any genetic marker data. It also allows for a nearly endless array of genetic association and/or linkage tests. A preliminary Matlab program is available, and we are currently implementing a more complete and user-friendly R package.     

Influences of size and sex on invasive species aggression and native species vulnerability: a case for modern regression techniques

Animal behaviour is of fundamental importance but is often overlooked in biological invasion research. A problem with such studies is that they may add pressure to already threatened species and subject vulnerable individuals to increased risk. One solution is to obtain the maximum possible information from the generated data using a variety of statistical techniques, instead of solely using simple versions of linear regression or generalized linear models as is customary. Here, we exemplify and compare the use of modern regression techniques which have very different conceptual backgrounds and aims (negative binomial models, zero-inflated regression, and expectile regression), and which have rarely been applied to behavioural data in biological invasion studies. We show that our data display overdispersion, which is frequent in ecological and behavioural data, and that conventional statistical methods such as Poisson generalized linear models are inadequate in this case. Expectile regression is similar to quantile regression and allows the estimation of functional relationships between variables for all portions of a probability distribution and is thus well suited for modelling boundaries in polygonal relationships or cases with heterogeneous variances which are frequent in behavioural data. We applied various statistical techniques to aggression in invasive mosquitofish, Gambusia holbrooki, and the concomitant vulnerability of native toothcarp, Aphanius iberus, in relation to individual size and sex. We found that medium sized male G. holbrooki carry out the majority of aggressive acts and that smaller and medium size A. iberus are most vulnerable. Of the regression techniques used, only negative binomial models and zero-inflated and expectile Poisson regressions revealed these relationships.     

Plant traits shape the effects of tidal flooding on soil and plant communities in saltmarshes

Saltmarshes are recognised worldwide to be among the most complex ecosystems, where several environmental factors concur to sustain their fragile functioning. Among them, soil–plant interactions are pivotal but often overlooked. The aim of this work was to use a structural equation modelling (SEM) approach to get new insight into soil–plant interactions, focusing on the effect of plant traits and abundance on soil, and test the effect of soil and/or plants on the entire community, monitoring changes in plant richness. The target halophytes Limonium narbonense and Sarcocornia fruticosa were sampled in the Marano and Grado lagoon (northern Adriatic Sea). Basal leaves of L. narbonense and green shoots of S. fruticosa were used to estimate plant growth, while the abundance of both species was used as a proxy of species competition. SEM was applied to test relationships between predictors and response variables in a single causal network. The flooding period (hydroperiod) negatively affected plant growth and soil properties, whereas plants decreased the intensity of soil reduction. Flooding did not directly affect species abundance or diversity, whose changes were instead driven by plant traits. The direct relationships between plant traits and species richness highlighted that species competition could be even more important than environmental stresses in defining plant diversity and zonation.     

A Two-Stage System for the Large-Scale Cultivation of Biomass: a Design and Operation Analysis Based on a Simple Steady-State Model Tuned on Laboratory Measurements

The optimal design and operation at large scale of a continuous fermentation process including a biological reactor/photobioreactor and a gravity settler with partial recycle and purge of the biomass are addressed. The proposed method is developed with reference to microalgae (Scenedesmus obliquus) cultivation, but it can be applied to any fermentation process as well as to activated sludge wastewater treatment. A procedure is developed to predict the effect of process variables, mainly the recycle ratio (R), the solid retention time (θ _c ), the reactor residence time (θ), and the ratio between feed and purge flow rates (F _I /F _W ). It includes a simple steady-state model of the two units coupled in the process and the experimental measurement of basic kinetic data, in both the bioreactor and the settler, for the tuning of model parameters. The bioreactor is assumed as perfectly mixed, and a rigorous gravity-flux approach is used for the settler. The process model is solved in terms of dimensionless variables, and plots are given to allow sensitivity analyses and optimization of operating conditions. A discussion about washout is presented, and a simple method is outlined for the calculation of the minimum values of residence time (θ _min ) and recycle ratio (R _min ) and of the maximum allowed recycle ratio (R _{max,operating} ) and biomass purge rate (F _Wmax ). In particular, it is shown that the system is sensitive to the concentration of biomass lost from the top of the settler (C _X ^S ). The proposed method can be useful for the design and analysis of large-scale processes of this type.     

Perceived Risk of Avian Influenza and Urbanization in Northern Vietnam

Decision-analytic models provide forecasts of how systems of interest will respond to management. These models can be parameterized using empirical data, but sometimes require information elicited from experts. When evaluating the effects of disease in species translocation programs, expert judgment is likely to play a role because complete empirical information will rarely be available. We illustrate development of a decision-analytic model built to inform decision-making regarding translocations and other management actions for the boreal toad (Anaxyrus boreas boreas), a species with declines linked to chytridiomycosis caused by Batrachochytrium dendrobatidis (Bd). Using the model, we explored the management implications of major uncertainties in this system, including whether there is a genetic basis for resistance to pathogenic infection by Bd, how translocation can best be implemented, and the effectiveness of efforts to reduce the spread of Bd. Our modeling exercise suggested that while selection for resistance to pathogenic infection by Bd could increase numbers of sites occupied by toads, and translocations could increase the rate of toad recovery, efforts to reduce the spread of Bd may have little effect. We emphasize the need to continue developing and parameterizing models necessary to assess management actions for combating chytridiomycosis-associated declines.     

Root strength and density decay after felling in a Silver Fir-Norway Spruce stand in the Italian Alps

Aims

Forests induce a mechanical reinforcement of soil, generally quantified in terms of additional root cohesion (c _r ), which decreases due to root decay after felling. The aim of this work is providing new field data on soil reinforcement by roots after trees cutting.

Methods

The present work investigated c _r decay in a mixed Silver Fir-Norway Spruce (Abies alba Mill. Picea abies (L.) Karst.) stand in the Italian Alps over a period of 3 years after felling by monitoring the two c _r driving variables: root tensile resistance and root density.

Results

Results showed that a significant difference in root resistance occurred only 3 years after felling, whereas the decrease in the number of roots was significant in the second year. The degradation process was more rapid in shallower layers and for thinner roots, as a consequence of the pattern of biological activity rate. The reduction of c _r after felling was, for a reference profile depth of 70 cm, 55 % in the first 2 years and another 16 % in the third year.

Conclusions

The findings of this study, providing new data on the decrease of c _r after felling, can be introduced into geotechnical models allowing a better estimation of the stability of forest hillslopes.

     

Comparison of model selection technique performance in predicting the spread of newly invasive species: a case study with <Emphasis Type="Italic">Batrachochytrium salamandrivorans</Emphasis>

Species distribution models (SDMs) increasingly have been used to anticipate the spread of invasive species. However, these models are powerful conservation tools only if they are biologically relevant, and thus validation of these models is essential. Here, we evaluate four model selection frameworks for their ability to identify a best fit model of spread under low data conditions early in an invasion, specifically testing the efficacy of methods that utilize absence data in addition to presence data in evaluating models. We test this question using a simulation where we generated data with varying confidence in the accuracy of the absence data, as absences in early invasions may become presences in the future, and increasing quantity of observation data to test the models. We create these simulations based on a real-world example of a newly emergent, invasive fungal pathogen, Batrachochytrium salamandrivorans (Bsal). The simulation demonstrated that AIC and Likelihood consistently outperform both Kappa and AUC in selecting the true model as the best model when data are limited and absence data are low quality, with AIC providing the most conservative results due to penalties for overparameterization. With these results, we then used these techniques to compare five candidate models for predicting the spread of Bsal. Consistent with the simulation, the best fit model of the candidate models for Bsal was inconsistent across the four metrics. However, AIC, which performed best in the simulation study, suggested that the spread of Bsal into Western Europe was best predicted by a combination of bioclimatic suitability, salamander richness, and number of salamander imports. Our results highlight the difficulty in evaluating predictive models when data are limited and of low quality, as with a newly invasive species, but show that these challenges can be partially addressed with the appropriate model selection approach. Use of this approach is critical as SDMs of invasive species are often used to inform conservation policy and efforts before the invasion spreads, when limited data are available.     

Bayesian estimation and use of high-throughput remote sensing indices for quantitative genetic analyses of leaf growth

Key message

We develop Bayesian function-valued trait models that mathematically isolate genetic mechanisms underlying leaf growth trajectories by factoring out genotype-specific differences in photosynthesis. Remote sensing data can be used instead of leaf-level physiological measurements.

Abstract

Characterizing the genetic basis of traits that vary during ontogeny and affect plant performance is a major goal in evolutionary biology and agronomy. Describing genetic programs that specifically regulate morphological traits can be complicated by genotypic differences in physiological traits. We describe the growth trajectories of leaves using novel Bayesian function-valued trait (FVT) modeling approaches in Brassica rapa recombinant inbred lines raised in heterogeneous field settings. While frequentist approaches estimate parameter values by treating each experimental replicate discretely, Bayesian models can utilize information in the global dataset, potentially leading to more robust trait estimation. We illustrate this principle by estimating growth asymptotes in the face of missing data and comparing heritabilities of growth trajectory parameters estimated by Bayesian and frequentist approaches. Using pseudo-Bayes factors, we compare the performance of an initial Bayesian logistic growth model and a model that incorporates carbon assimilation (A _max) as a cofactor, thus statistically accounting for genotypic differences in carbon resources. We further evaluate two remotely sensed spectroradiometric indices, photochemical reflectance (pri2) and MERIS Terrestrial Chlorophyll Index (mtci) as covariates in lieu of A _max, because these two indices were genetically correlated with A _max across years and treatments yet allow much higher throughput compared to direct leaf-level gas-exchange measurements. For leaf lengths in uncrowded settings, including A _max improves model fit over the initial model. The mtci and pri2 indices also outperform direct A _max measurements. Of particular importance for evolutionary biologists and plant breeders, hierarchical Bayesian models estimating FVT parameters improve heritabilities compared to frequentist approaches.

     

Secondary structure prediction of ITS rRNA region and molecular phylogeny: an integrated approach for the precise speciation of <Emphasis Type="Italic">Muscodor</Emphasis> species

Muscodor is a non-sporulating, volatile organic compounds producing endophytic fungi that has been extensively explored as a bio-fumigant and bio-preservative. Novel species of this genus have been mainly identified using ITS sequences. However, the ITS hyper-variability hinders the creation of reproducible alignments and stable phylogenetic trees. Conserved structural data of the ITS region represents as a vital auxiliary information for accurate speciation of fungi. In the present study, secondary structural data of ITS1, 5.8S, and ITS2 region of all Muscodor species were generated using LocaRNA web server. The predicted secondary structural data displayed greater variability in ITS1 region in comparison to ITS2. The structural data of all sequences exhibited characteristic conserved features of eukaryotic rRNA. Evolutionary conserved motifs were found among all 5.8S and ITS2 sequences. Profile neighbor joining (PNJ) tree based on combined sequence-structural information of ITS region was generated in ProfDists. The PNJ tree resolved into four major groups whereby M. fengyangenesis and M. albus species formed monophyletic clades. However, three M. albus species along with other Muscodor species emerged as sister branches to the existing clades, thereby, improving the precision of phylogenetic analysis for identification of novel species of Muscodor genus. Hence, the results indicated that structural analysis along with primary sequence information can provide new insights for precise identification of Muscodor species.     

Mathematical models for cellular systems the von Foerster equation. Part I

P. B. M. Walker (1954) and H. C. Longuet-Higgins (quoted by Walker), as well as O. Scherbaum and G. Rasch (1957), made the first attempts towards a mathematical study of the age distribution in a cellular population. It was H. Von Foerster (1959), however, who derived the complete differential equation for the age density function,n(t, a). His equation is obtained from an analysis of the infinitesimal changes occurring during a time elementdt in a group of cells with ages betweena anda+da. The behavior of the population is determined by a quantity λ which we call the loss function. In this paper a rigorous discussion of the Von Foerster equation is presented, and a solution is given for the special case when λ depends, ont (time) anda (age) but not on other variables (such asn itself). It is also shown that the age density,n(t, a), is completely known only if the birth rate,α(t), and the initial age distribution, β(a), are given as boundary conditions. In Section II the steady state solution and some plausible forms of intrinsic loss functions (depending ona only) are discussed in view of later applications.     

Anthropogenic and Climatic Effects on the Distribution of <Emphasis Type="Italic">Eulemur</Emphasis> Species: An Ecological Niche Modeling Approach

Several factors can influence primate distributions, including evolutionary history, interspecific competition, climate, and anthropogenic impacts. In Madagascar, several small spatial scale studies have shown that anthropogenic habitat modification affects the density and distribution of many lemur species. Ecological niche models can be used to examine broad-scale influences of anthropogenic impacts on primate distributions. In this study, we examine how climate and anthropogenic factors influence the distribution of 11 Eulemur species using ecological niche models. Specifically, we created one set of models only using rainfall and temperature variables. We then created a second set of models that combined these climate variables with three anthropogenic factors: distance to dense settlements, villages, and croplands. We used MaxEnt to generate all the models. We found that the addition of anthropogenic variables improved the climate models. Also, most Eulemur species exhibited reduced predicted geographic distributions once anthropogenic factors were added to the model. Distance to dense settlements was the most important anthropogenic factor in most cases. We suggest that including anthropogenic variables in ecological niche models is important for understanding primate distributions, especially in regions with significant human impacts. In addition, we identify several Eulemur species that were most affected by anthropogenic factors and should be the focus of increased conservation efforts.     

Climate Change Could Increase the Geographic Extent of Hendra Virus Spillover Risk

Disease risk mapping is important for predicting and mitigating impacts of bat-borne viruses, including Hendra virus (Paramyxoviridae:Henipavirus), that can spillover to domestic animals and thence to humans. We produced two models to estimate areas at potential risk of HeV spillover explained by the climatic suitability for its flying fox reservoir hosts, Pteropus alecto and P. conspicillatus. We included additional climatic variables that might affect spillover risk through other biological processes (such as bat or horse behaviour, plant phenology and bat foraging habitat). Models were fit with a Poisson point process model and a log-Gaussian Cox process. In response to climate change, risk expanded southwards due to an expansion of P. alecto suitable habitat, which increased the number of horses at risk by 175–260% (110,000–165,000). In the northern limits of the current distribution, spillover risk was highly uncertain because of model extrapolation to novel climatic conditions. The extent of areas at risk of spillover from P. conspicillatus was predicted shrink. Due to a likely expansion of P. alecto into these areas, it could replace P. conspicillatus as the main HeV reservoir. We recommend: (1) HeV monitoring in bats, (2) enhancing HeV prevention in horses in areas predicted to be at risk, (3) investigate and develop mitigation strategies for areas that could experience reservoir host replacements.     

Precise feeding of probiotics in the treatment of edwardsiellosis by accurate estimation of <Emphasis Type="Italic">Edwardsiella tarda</Emphasis>

Edwardsiella tarda is one of the leading fish pathogens for the aquaculture industry. To realize efficient disease control of edwardsiellosis, a predictive model for E. tarda in seawater was developed. The modified logistic model was used to regress the growth curves of E. tarda JN at five different temperatures (range from 10 to 30 °C) and four organic nutrient concentrations (range from 5 to 40 mg l^?1 measured by chemical oxygen demand (COD)). The modeling effects of temperature and COD on the specific growth rate (μ) were developed by square-root model and saturation-growth rate model, respectively. The growth model was validated in turbot aquaculture tanks by estimating the dynamics of inoculated E. tarda. The accurate feeding of probiotic Bacillus pumilus strain H2 was calculated based on the estimation of E. tarda. Results showed that the logistic model produced a good fit to the growth curves of E. tarda JN (average R²?=?0.962). The overall predictions based on above models agreed well with the growth curve of E. tarda JN observed by plate counting in the validation tests (average Af?=?1.16; average Bf?=?1.32). The use of predicted amount of B. pumilus (5.66 log CFU ml^?1) successfully prevent the deterioration of disease for turbot with 13.3% mortality rate in a recirculating aquaculture system (RAS), while the feeding of 0 and 3.0 log CFU ml^?1 of B. pumilus resulted in 53.7 and 75.3% of turbot mortality rate, respectively. In conclusion, accurate estimation of E. tarda realized the precise feeding of probiotics, which successfully prevent the rapid progression of the edwardsiellosis.