Analyses of gene frequencies of mates

A genic analysis of variance of data on mate pairs for a codominant gene is developed. This analysis provides estimators of the correlation, F, of genes within individuals, of the correlation, Θ, of genes between mates, and of various variances—all relative to the correlation or variation among genes of nonmates. The data are manipulated into marginal distributions to produce another method of obtaining the same estimators. Several examples are given of how assumptions about the model and parameters modify the estimators and which were utilized in constructing χ² tests of hypotheses concerning F and Θ.—A recessive gene is also considered. Only the frequency of recessive genotypes and the correlation of recessive mates are estimable in this case unless one makes very demanding assumptions about the model.—Numerical examples of the analysis of variance and estimators are given for both a codominant and recessive gene.     

Socioeconomic and Sociodemographic Factors Associated with Asthma Related Outcomes in Early Childhood: The Generation R Study

Rationale

Few studies have analyzed the association of socioeconomic and sociodemographic factors with asthma related outcomes in early childhood, including Fraction of exhaled Nitric Oxide (FeNO) and airway resistance (Rint). We examined the association of socioeconomic and sociodemographic factors with wheezing, asthma, FeNO and Rint at age 6 years. Additionally, the role of potential mediating factors was studied.

Methods

The study included 6717 children participating in The Generation R Study, a prospective population-based cohort study. Data on socioeconomic and sociodemographic factors, wheezing and asthma were obtained by questionnaires. FeNO and Rint were measured at the research center. Statistical analyses were performed using logistic and linear regression models.

Results

At age 6 years, 9% (456/5084) of the children had wheezing symptoms and 7% (328/4953) had asthma. Children from parents with financial difficulties had an increased risk of wheezing (adjusted Odds Ratio (aOR) = 1.63, 95% Confidence Interval (CI):1.18–2.24). Parental low education, paternal unemployment and child''s male sex were associated with asthma, independent of other socioeconomic or sociodemographic factors (aOR = 1.63, 95% CI:1.24–2.15, aOR = 1.85, 95% CI:1.11–3.09, aOR = 1.58, 95% CI:1.24–2.01, respectively). No socioeconomic or gender differences in FeNO were found. The risks of wheezing, asthma, FeNO and Rint measurements differed between ethnic groups (p<0.05). Associations between paternal unemployment, child''s sex, ethnicity and asthma related outcomes remained largely unexplained.

Conclusions

This study showed differences between the socioeconomic and sociodemographic correlates of wheezing and asthma compared to the correlates of FeNO and Rint at age 6 years. Several socioeconomic and sociodemographic factors were independently associated with wheezing and asthma. Child''s ethnicity was the only factor independently associated with FeNO. We encourage further studies on underlying pathways and public health intervention programs, focusing on reducing socioeconomic or sociodemographic inequalities in asthma.     

Inducible Nitric Oxide Synthase Promoter Haplotypes and Residential Traffic-Related Air Pollution Jointly Influence Exhaled Nitric Oxide Level in Children

BackgroundExhaled nitric oxide (FeNO), a biomarker of airway inflammation, predicts asthma risk in children. We previously found that the promoter haplotypes in inducible nitric oxide synthase (NOS2) and exposure to residential traffic independently influence FeNO level. Because NOS2 is inducible by environmental exposures such as traffic-related exposure, we tested the hypothesis that common NOS2 promoter haplotypes modulate the relationship between residential traffic-related exposure and FeNO level in children.MethodsIn a cross-sectional population-based study, subjects (N = 2,457; 7–11 year-old) were Hispanic and non-Hispanic white children who participated in the Southern California Children’s Health Study and had FeNO measurements. For residential traffic, lengths of local roads within circular buffers (50m, 100m and 200m radii around homes) around the subjects’ homes were estimated using geographic information system (GIS) methods. We interrogated the two most common NOS2 promoter haplotypes that were found to affect FeNO level.ResultsThe relationship between local road lengths within 100m and 200m circular buffers and FeNO level varied significantly by one of the NOS2 promoter haplotypes (P-values for interaction between road length and NOS2 promoter haplotype = 0.02 and 0.03, respectively). In children who had ≤250m of local road lengths within 100m buffer around their homes, those with two copies of the haplotype had significantly lower FeNO (adjusted geometric mean = 11.74ppb; 95% confidence intervals (CI): 9.99 to 13.80) than those with no copies (adjusted geometric mean = 15.28ppb; 95% CI: 14.04 to 16.63) with statistically significant trend of lower FeNO level with increasing number of haplotype copy (P-value for trend = 0.002). In contrast, among children who had >250m of local road lengths within 100m buffer, FeNO level did not significantly differ by the haplotype copy-number (P-value for trend = 0.34). Similar interactive effects of this haplotype and local road lengths within 200m buffer on FeNO were also observed.ConclusionsHigher exposure from residential traffic nullifies the protective effect of one common NOS2 promoter haplotype on FeNO level. Regulation of traffic-related pollution may protect children’s respiratory health.     

A brief history and popularity of methods and tools used to estimate micro‐evolutionary forces

Population genetics is a field of research that predates the current generations of sequencing technology. Those approaches, that were established before massively parallel sequencing methods, have been adapted to these new marker systems (in some cases involving the development of new methods) that allow genome‐wide estimates of the four major micro‐evolutionary forces—mutation, gene flow, genetic drift, and selection. Nevertheless, classic population genetic markers are still commonly used and a plethora of analysis methods and programs is available for these and high‐throughput sequencing (HTS) data. These methods employ various and diverse theoretical and statistical frameworks, to varying degrees of success, to estimate similar evolutionary parameters making it difficult to get a concise overview across the available approaches. Presently, reviews on this topic generally focus on a particular class of methods to estimate one or two evolutionary parameters. Here, we provide a brief history of methods and a comprehensive list of available programs for estimating micro‐evolutionary forces. We furthermore analyzed their usage within the research community based on popularity (citation bias) and discuss the implications of this bias for the software community. We found that a few programs received the majority of citations, with program success being independent of both the parameters estimated and the computing platform. The only deviation from a model of exponential growth in the number of citations was found for the presence of a graphical user interface (GUI). Interestingly, no relationship was found for the impact factor of the journals, when the tools were published, suggesting accessibility might be more important than visibility.     

Exhaled nitric oxide in a population-based study of Southern California Schoolchildren

Background

Determinants of exhaled nitric oxide (FeNO) need to be understood better to maximize the value of FeNO measurement in clinical practice and research. Our aim was to identify significant predictors of FeNO in an initial cross-sectional survey of southern California schoolchildren, part of a larger longitudinal study of asthma incidence.

Methods

During one school year, we measured FeNO at 100 ml/sec flow, using a validated offline technique, in 2568 children of age 7–10 yr. We estimated online (50 ml/sec flow) FeNO using a prediction equation from a separate smaller study with adjustment for offline measurement artifacts, and analyzed its relationship to clinical and demographic characteristics.

Results

FeNO was lognormally distributed with geometric means ranging from 11 ppb in children without atopy or asthma to 16 ppb in children with allergic asthma. Although effects of atopy and asthma were highly significant, ranges of FeNO for children with and without those conditions overlapped substantially. FeNO was significantly higher in subjects aged > 9, compared to younger subjects. Asian-American boys showed significantly higher FeNO than children of all other sex/ethnic groups; Hispanics and African-Americans of both sexes averaged slightly higher than non-Hispanic whites. Increasing height-for-age had no significant effect, but increasing weight-for-height was associated with decreasing FeNO.

Conclusion

FeNO measured offline is a useful biomarker for airway inflammation in large population-based studies. Further investigation of age, ethnicity, body-size, and genetic influences is needed, since they may contribute to substantial variation in FeNO.     

The Effect of Framing and Normative Messages in Building Support for Climate Policies

Deep cuts in greenhouse gas emissions are required to mitigate climate change. However, there is low willingness amongst the public to prioritise climate policies for reducing emissions. Here we show that the extent to which Australians are prepared to reduce their country''s CO₂ emissions is greater when the costs to future national income are framed as a “foregone-gain”—incomes rise in the future but not by as much as in the absence of emission cuts—rather than as a “loss”—incomes decrease relative to the baseline expected future levels (Studies 1 & 2). The provision of a normative message identifying Australia as one of the world''s largest CO₂ emitters did not increase the amount by which individuals were prepared to reduce emissions (Study 1), whereas a normative message revealing the emission policy preferences of other Australians did (Study 2). The results suggest that framing the costs of reducing emissions as a smaller increase in future income and communicating normative information about others'' emission policy preferences are effective methods for leveraging public support for emission cuts.     

A bottom-up characterization of transfer functions for synthetic biology designs: lessons from enzymology

Within the field of synthetic biology, a rational design of genetic parts should include a causal understanding of their input-output responses—the so-called transfer function—and how to tune them. However, a commonly adopted strategy is to fit data to Hill-shaped curves without considering the underlying molecular mechanisms. Here we provide a novel mathematical formalization that allows prediction of the global behavior of a synthetic device by considering the actual information from the involved biological parts. This is achieved by adopting an enzymology-like framework, where transfer functions are described in terms of their input affinity constant and maximal response. As a proof of concept, we characterize a set of Lux homoserine-lactone-inducible genetic devices with different levels of Lux receptor and signal molecule. Our model fits the experimental results and predicts the impact of the receptor''s ribosome-binding site strength, as a tunable parameter that affects gene expression. The evolutionary implications are outlined.     

Modelling to infer the role of animals in gambiense human African trypanosomiasis transmission and elimination in the DRC

Gambiense human African trypanosomiasis (gHAT) has been targeted for elimination of transmission (EoT) to humans by 2030. Whilst this ambitious goal is rapidly approaching, there remain fundamental questions about the presence of non-human animal transmission cycles and their potential role in slowing progress towards, or even preventing, EoT. In this study we focus on the country with the most gHAT disease burden, the Democratic Republic of Congo (DRC), and use mathematical modelling to assess whether animals may contribute to transmission in specific regions, and if so, how their presence could impact the likelihood and timing of EoT.By fitting two model variants—one with, and one without animal transmission—to the human case data from 2000–2016 we estimate model parameters for 158 endemic health zones of the DRC. We evaluate the statistical support for each model variant in each health zone and infer the contribution of animals to overall transmission and how this could impact predicted time to EoT.We conclude that there are 24/158 health zones where there is substantial to decisive statistical support for some animal transmission. However—even in these regions—we estimate that animals would be extremely unlikely to maintain transmission on their own. Animal transmission could hamper progress towards EoT in some settings, with projections under continuing interventions indicating that the number of health zones expected to achieve EoT by 2030 reduces from 68/158 to 61/158 if animal transmission is included in the model. With supplementary vector control (at a modest 60% tsetse reduction) added to medical screening and treatment interventions, the predicted number of health zones meeting the goal increases to 147/158 for the model including animal transmission. This is due to the impact of vector reduction on transmission to and from all hosts.     

No Longer Confidential: Estimating the Confidence of Individual Regression Predictions

Quantitative predictions in computational life sciences are often based on regression models. The advent of machine learning has led to highly accurate regression models that have gained widespread acceptance. While there are statistical methods available to estimate the global performance of regression models on a test or training dataset, it is often not clear how well this performance transfers to other datasets or how reliable an individual prediction is–a fact that often reduces a user’s trust into a computational method. In analogy to the concept of an experimental error, we sketch how estimators for individual prediction errors can be used to provide confidence intervals for individual predictions. Two novel statistical methods, named CONFINE and CONFIVE, can estimate the reliability of an individual prediction based on the local properties of nearby training data. The methods can be applied equally to linear and non-linear regression methods with very little computational overhead. We compare our confidence estimators with other existing confidence and applicability domain estimators on two biologically relevant problems (MHC–peptide binding prediction and quantitative structure-activity relationship (QSAR)). Our results suggest that the proposed confidence estimators perform comparable to or better than previously proposed estimation methods. Given a sufficient amount of training data, the estimators exhibit error estimates of high quality. In addition, we observed that the quality of estimated confidence intervals is predictable. We discuss how confidence estimation is influenced by noise, the number of features, and the dataset size. Estimating the confidence in individual prediction in terms of error intervals represents an important step from plain, non-informative predictions towards transparent and interpretable predictions that will help to improve the acceptance of computational methods in the biological community.     

Surveying Capsid Assembly Pathways through Simulation-Based Data Fitting

Virus capsid assembly has attracted considerable interest from the biophysical modeling community as a model system for complicated self-assembly processes. Simulation methods have proven valuable for characterizing the space of possible kinetics and mechanisms of capsid assembly, but they have so far been able to say little about the assembly kinetics or pathways of any specific virus. It is not possible to directly measure the detailed interaction rates needed to parameterize a model, and there is only a limited amount of experimental evidence available to constrain possible pathways, with almost all of it gathered from in vitro studies of purified coat proteins. In prior work, we developed methods to address this problem by using simulation-based data-fitting to learn rate parameters consistent with both structure-based rule sets and experimental light-scattering data on bulk assembly progress in vitro. We have since improved these methods and extended them to fit simulation parameters to one or more experimental light-scattering curves. Here, we apply the improved data-fitting approach to three capsid systems—human papillomavirus (HPV), hepatitis B virus (HBV), and cowpea chlorotic mottle virus (CCMV)—to assess both the range of pathway types the methods can learn and the diversity of assembly strategies in use between these viruses. The resulting fits suggest three different in vitro assembly mechanisms for the three systems, with HPV capsids fitting a model of assembly via a nonnucleation-limited pathway of accumulation of individual capsomers while HBV and CCMV capsids fit similar but subtly different models of nucleation-limited assembly through ensembles of pathways involving trimer-of-dimer intermediates. The results demonstrate the ability of such data fitting to learn very different pathway types and show some of the versatility of pathways that may exist across real viruses.     

Some Formal Approaches to the Analysis of Kinetic Data in Terms of Linear Compartmental Systems

A formal approach to the routine analysis of kinetic data in terms of linear compartmental systems is presented. The methods of analysis are general in that they include much of the theory in common use, such as direct solution of differential equations, integral equations, transfer functions, fitting of data to sums of exponentials, matrix solutions, etc. The key to the formalism presented lies in the fact that a basic operational unit—called “compartment”—has been defined, in terms of which physical and mathematical models as well as input and output functions can be expressed. Additional features for calculating linear combinations of functions and for setting linear dependence relations between parameters add to the versatility of this method. The actual computations for the values of model parameters to yield a least squares fit of the data are performed on a digital computer. A general computer program was developed that permits the routine fitting of data and the evolution of models.     

Estimating Relatedness in the Presence of Null Alleles

Studies of genetics and ecology often require estimates of relatedness coefficients based on genetic marker data. However, with the presence of null alleles, an observed genotype can represent one of several possible true genotypes. This results in biased estimates of relatedness. As the numbers of marker loci are often limited, loci with null alleles cannot be abandoned without substantial loss of statistical power. Here, we show how loci with null alleles can be incorporated into six estimators of relatedness (two novel). We evaluate the performance of various estimators before and after correction for null alleles. If the frequency of a null allele is <0.1, some estimators can be used directly without adjustment; if it is >0.5, the potency of estimation is too low and such a locus should be excluded. We make available a software package entitled PolyRelatedness v1.6, which enables researchers to optimize these estimators to best fit a particular data set.     

Correcting the Bias of Empirical Frequency Parameter Estimators in Codon Models

Markov models of codon substitution are powerful inferential tools for studying biological processes such as natural selection and preferences in amino acid substitution. The equilibrium character distributions of these models are almost always estimated using nucleotide frequencies observed in a sequence alignment, primarily as a matter of historical convention. In this note, we demonstrate that a popular class of such estimators are biased, and that this bias has an adverse effect on goodness of fit and estimates of substitution rates. We propose a “corrected” empirical estimator that begins with observed nucleotide counts, but accounts for the nucleotide composition of stop codons. We show via simulation that the corrected estimates outperform the de facto standard estimates not just by providing better estimates of the frequencies themselves, but also by leading to improved estimation of other parameters in the evolutionary models. On a curated collection of sequence alignments, our estimators show a significant improvement in goodness of fit compared to the approach. Maximum likelihood estimation of the frequency parameters appears to be warranted in many cases, albeit at a greater computational cost. Our results demonstrate that there is little justification, either statistical or computational, for continued use of the -style estimators.     

Long-Branch Attraction Bias and Inconsistency in Bayesian Phylogenetics

Bayesian inference (BI) of phylogenetic relationships uses the same probabilistic models of evolution as its precursor maximum likelihood (ML), so BI has generally been assumed to share ML''s desirable statistical properties, such as largely unbiased inference of topology given an accurate model and increasingly reliable inferences as the amount of data increases. Here we show that BI, unlike ML, is biased in favor of topologies that group long branches together, even when the true model and prior distributions of evolutionary parameters over a group of phylogenies are known. Using experimental simulation studies and numerical and mathematical analyses, we show that this bias becomes more severe as more data are analyzed, causing BI to infer an incorrect tree as the maximum a posteriori phylogeny with asymptotically high support as sequence length approaches infinity. BI''s long branch attraction bias is relatively weak when the true model is simple but becomes pronounced when sequence sites evolve heterogeneously, even when this complexity is incorporated in the model. This bias—which is apparent under both controlled simulation conditions and in analyses of empirical sequence data—also makes BI less efficient and less robust to the use of an incorrect evolutionary model than ML. Surprisingly, BI''s bias is caused by one of the method''s stated advantages—that it incorporates uncertainty about branch lengths by integrating over a distribution of possible values instead of estimating them from the data, as ML does. Our findings suggest that trees inferred using BI should be interpreted with caution and that ML may be a more reliable framework for modern phylogenetic analysis.     

Modeling the Pre-Industrial Roots of Modern Super-Exponential Population Growth

To Malthus, rapid human population growth—so evident in 18th Century Europe—was obviously unsustainable. In his Essay on the Principle of Population, Malthus cogently argued that environmental and socioeconomic constraints on population rise were inevitable. Yet, he penned his essay on the eve of the global census size reaching one billion, as nearly two centuries of super-exponential increase were taking off. Introducing a novel extension of J. E. Cohen''s hallmark coupled difference equation model of human population dynamics and carrying capacity, this article examines just how elastic population growth limits may be in response to demographic change. The revised model involves a simple formalization of how consumption costs influence carrying capacity elasticity over time. Recognizing that complex social resource-extraction networks support ongoing consumption-based investment in family formation and intergenerational resource transfers, it is important to consider how consumption has impacted the human environment and demography—especially as global population has become very large. Sensitivity analysis of the consumption-cost model''s fit to historical population estimates, modern census data, and 21^st Century demographic projections supports a critical conclusion. The recent population explosion was systemically determined by long-term, distinctly pre-industrial cultural evolution. It is suggested that modern globalizing transitions in technology, susceptibility to infectious disease, information flows and accumulation, and economic complexity were endogenous products of much earlier biocultural evolution of family formation''s embeddedness in larger, hierarchically self-organizing cultural systems, which could potentially support high population elasticity of carrying capacity. Modern super-exponential population growth cannot be considered separately from long-term change in the multi-scalar political economy that connects family formation and intergenerational resource transfers to wider institutions and social networks.     

Comparison of Filtering Methods for the Modeling and Retrospective Forecasting of Influenza Epidemics

A variety of filtering methods enable the recursive estimation of system state variables and inference of model parameters. These methods have found application in a range of disciplines and settings, including engineering design and forecasting, and, over the last two decades, have been applied to infectious disease epidemiology. For any system of interest, the ideal filter depends on the nonlinearity and complexity of the model to which it is applied, the quality and abundance of observations being entrained, and the ultimate application (e.g. forecast, parameter estimation, etc.). Here, we compare the performance of six state-of-the-art filter methods when used to model and forecast influenza activity. Three particle filters—a basic particle filter (PF) with resampling and regularization, maximum likelihood estimation via iterated filtering (MIF), and particle Markov chain Monte Carlo (pMCMC)—and three ensemble filters—the ensemble Kalman filter (EnKF), the ensemble adjustment Kalman filter (EAKF), and the rank histogram filter (RHF)—were used in conjunction with a humidity-forced susceptible-infectious-recovered-susceptible (SIRS) model and weekly estimates of influenza incidence. The modeling frameworks, first validated with synthetic influenza epidemic data, were then applied to fit and retrospectively forecast the historical incidence time series of seven influenza epidemics during 2003–2012, for 115 cities in the United States. Results suggest that when using the SIRS model the ensemble filters and the basic PF are more capable of faithfully recreating historical influenza incidence time series, while the MIF and pMCMC do not perform as well for multimodal outbreaks. For forecast of the week with the highest influenza activity, the accuracies of the six model-filter frameworks are comparable; the three particle filters perform slightly better predicting peaks 1–5 weeks in the future; the ensemble filters are more accurate predicting peaks in the past.     

Use of artificial genomes in assessing methods for atypical gene detection

Parametric methods for identifying laterally transferred genes exploit the directional mutational biases unique to each genome. Yet the development of new, more robust methods—as well as the evaluation and proper implementation of existing methods—relies on an arbitrary assessment of performance using real genomes, where the evolutionary histories of genes are not known. We have used the framework of a generalized hidden Markov model to create artificial genomes modeled after genuine genomes. To model a genome, “core” genes—those displaying patterns of mutational biases shared among large numbers of genes—are identified by a novel gene clustering approach based on the Akaike information criterion. Gene models derived from multiple “core” gene clusters are used to generate an artificial genome that models the properties of a genuine genome. Chimeric artificial genomes—representing those having experienced lateral gene transfer—were created by combining genes from multiple artificial genomes, and the performance of the parametric methods for identifying “atypical” genes was assessed directly. We found that a hidden Markov model that included multiple gene models, each trained on sets of genes representing the range of genotypic variability within a genome, could produce artificial genomes that mimicked the properties of genuine genomes. Moreover, different methods for detecting foreign genes performed differently—i.e., they had different sets of strengths and weaknesses—when identifying atypical genes within chimeric artificial genomes.     

Children's Separation Anxiety Scale (CSAS): Psychometric Properties

This study describes the psychometric properties of the Children''s Separation Anxiety Scale (CSAS), which assesses separation anxiety symptoms in childhood. Participants in Study 1 were 1,908 schoolchildren aged between 8 and 11. Exploratory factor analysis identified four factors: worry about separation, distress from separation, opposition to separation, and calm at separation, which explained 46.91% of the variance. In Study 2, 6,016 children aged 8–11 participated. The factor model in Study 1 was validated by confirmatory factor analysis. The internal consistency (α = 0.82) and temporal stability (r = 0.83) of the instrument were good. The convergent and discriminant validity were evaluated by means of correlations with other measures of separation anxiety, childhood anxiety, depression and anger. Sensitivity of the scale was 85% and its specificity, 95%. The results support the reliability and validity of the CSAS.     

Evaluating the Predictive Value of Biomarkers with Stratified Case‐Cohort Design

Summary Identification of novel biomarkers for risk assessment is important for both effective disease prevention and optimal treatment recommendation. Discovery relies on the precious yet limited resource of stored biological samples from large prospective cohort studies. Case‐cohort sampling design provides a cost‐effective tool in the context of biomarker evaluation, especially when the clinical condition of interest is rare. Existing statistical methods focus on making efficient inference on relative hazard parameters from the Cox regression model. Drawing on recent theoretical development on the weighted likelihood for semiparametric models under two‐phase studies ( Breslow and Wellner, 2007 ), we propose statistical methods to evaluate accuracy and predictiveness of a risk prediction biomarker, with censored time‐to‐event outcome under stratified case‐cohort sampling. We consider nonparametric methods and a semiparametric method. We derive large sample properties of proposed estimators and evaluate their finite sample performance using numerical studies. We illustrate new procedures using data from Framingham Offspring Study to evaluate the accuracy of a recently developed risk score incorporating biomarker information for predicting cardiovascular disease.     

gauseR: Simple methods for fitting Lotka‐Volterra models describing Gause’s “Struggle for Existence”

Point 1: The ecological models of Alfred J. Lotka and Vito Volterra have had an enormous impact on ecology over the past century. Some of the earliest—and clearest—experimental tests of these models were famously conducted by Georgy Gause in the 1930s. Although well known, the data from these experiments are not widely available and are often difficult to analyze using standard statistical and computational tools.Point 2: Here, we introduce the gauseR package, a collection of tools for fitting Lotka‐Volterra models to time series data of one or more species. The package includes several methods for parameter estimation and optimization, and includes 42 datasets from Gause''s species interaction experiments and related work. Additionally, we include with this paper a short blog post discussing the historical importance of these data and models, and an R vignette with a walk‐through introducing the package methods. The package is available for download at github.com/adamtclark/gauseR.Point 3: To demonstrate the package, we apply it to several classic experimental studies from Gause, as well as two other well‐known datasets on multi‐trophic dynamics on Isle Royale, and in spatially structured mite populations. In almost all cases, models fit observations closely and fitted parameter values make ecological sense.Point 4: Taken together, we hope that the methods, data, and analyses that we present here provide a simple and user‐friendly way to interact with complex ecological data. We are optimistic that these methods will be especially useful to students and educators who are studying ecological dynamics, as well as researchers who would like a fast tool for basic analyses.