Comparison of different neuron models to conductance-based post-stimulus time histograms obtained in cortical pyramidal cells using dynamic-clamp in vitro

A wide diversity of models have been proposed to account for the spiking response of central neurons, from the integrate-and-fire (IF) model and its quadratic and exponential variants, to multiple-variable models such as the Izhikevich (IZ) model and the well-known Hodgkin–Huxley (HH) type models. Such models can capture different aspects of the spiking response of neurons, but there is few objective comparison of their performance. In this article, we provide such a comparison in the context of well-defined stimulation protocols, including, for each cell, DC stimulation, and a series of excitatory conductance injections, arising in the presence of synaptic background activity. We use the dynamic-clamp technique to characterize the response of regular-spiking neurons from guinea-pig visual cortex by computing families of post-stimulus time histograms (PSTH), for different stimulus intensities, and for two different background activities (low- and high-conductance states). The data obtained are then used to fit different classes of models such as the IF, IZ, or HH types, which are constrained by the whole data set. This analysis shows that HH models are generally more accurate to fit the series of experimental PSTH, but their performance is almost equaled by much simpler models, such as the exponential or pulse-based IF models. Similar conclusions were also reached by performing partial fitting of the data, and examining the ability of different models to predict responses that were not used for the fitting. Although such results must be qualified by using more sophisticated stimulation protocols, they suggest that nonlinear IF models can capture surprisingly well the response of cortical regular-spiking neurons and appear as useful candidates for network simulations with conductance-based synaptic interactions.     

Non-negative matrix factorization for learning alignment-specific models of protein evolution

Models of protein evolution currently come in two flavors: generalist and specialist. Generalist models (e.g. PAM, JTT, WAG) adopt a one-size-fits-all approach, where a single model is estimated from a number of different protein alignments. Specialist models (e.g. mtREV, rtREV, HIVbetween) can be estimated when a large quantity of data are available for a single organism or gene, and are intended for use on that organism or gene only. Unsurprisingly, specialist models outperform generalist models, but in most instances there simply are not enough data available to estimate them. We propose a method for estimating alignment-specific models of protein evolution in which the complexity of the model is adapted to suit the richness of the data. Our method uses non-negative matrix factorization (NNMF) to learn a set of basis matrices from a general dataset containing a large number of alignments of different proteins, thus capturing the dimensions of important variation. It then learns a set of weights that are specific to the organism or gene of interest and for which only a smaller dataset is available. Thus the alignment-specific model is obtained as a weighted sum of the basis matrices. Having been constrained to vary along only as many dimensions as the data justify, the model has far fewer parameters than would be required to estimate a specialist model. We show that our NNMF procedure produces models that outperform existing methods on all but one of 50 test alignments. The basis matrices we obtain confirm the expectation that amino acid properties tend to be conserved, and allow us to quantify, on specific alignments, how the strength of conservation varies across different properties. We also apply our new models to phylogeny inference and show that the resulting phylogenies are different from, and have improved likelihood over, those inferred under standard models.     

Equivalence of aggregated Markov models of ion-channel gating

One cannot always distinguish different Markov models of ion-channel kinetics solely on the basis of steady-state kinetic data. If two generator (or transition) matrices are related by a similarity transformation that does not combine states with different conductances, then the models described by these generator matrices have the same observable steady-state statistics. This result suggests a procedure for expressing the model in a unique form, and sometimes reducing the number of parameters in a model. I apply the similarity transformation procedure to a number of simple models. When a model specifies the dependence of the rates of transition on an experimentally variable parameter such as the concentration of a ligand or the membrane potential, the class of equivalent models may be further restricted, but a model is not always uniquely determined even under these conditions. Voltage-step experiments produce non-stationary data that can also be used to distinguish models.     

Complexity is costly: a meta‐analysis of parametric and non‐parametric methods for short‐term population forecasting

Short‐term forecasts based on time series of counts or survey data are widely used in population biology to provide advice concerning the management, harvest and conservation of natural populations. A common approach to produce these forecasts uses time‐series models, of different types, fit to time series of counts. Similar time‐series models are used in many other disciplines, however relative to the data available in these other disciplines, population data are often unusually short and noisy and models that perform well for data from other disciplines may not be appropriate for population data. In order to study the performance of time‐series forecasting models for natural animal population data, we assembled 2379 time series of vertebrate population indices from actual surveys. Our data were comprised of three vastly different types: highly variable (marine fish productivity), strongly cyclic (adult salmon counts), and small variance but long‐memory (bird and mammal counts). We tested the predictive performance of 49 different forecasting models grouped into three broad classes: autoregressive time‐series models, non‐linear regression‐type models and non‐parametric time‐series models. Low‐dimensional parametric autoregressive models gave the most accurate forecasts across a wide range of taxa; the most accurate model was one that simply treated the most recent observation as the forecast. More complex parametric and non‐parametric models performed worse, except when applied to highly cyclic species. Across taxa, certain life history characteristics were correlated with lower forecast error; specifically, we found that better forecasts were correlated with attributes of slow growing species: large maximum age and size for fishes and high trophic level for birds. Synthesis Evaluating the data support for multiple plausible models has been an integral focus of many ecological analyses. However, the most commonly used tools to quantify support have weighted models’ hindcasting and forecasting abilities. For many applications, predicting the past may be of little interest. Concentrating only on the future predictive performance of time series models, we performed a forecasting competition among many different kinds of statistical models, applying each to many different kinds of vertebrate time series of population abundance. Low‐dimensional (simple) models performed well overall, but more complex models did slightly better when applied to time series of cyclic species (e.g. salmon).     

Integral projection models perform better for small demographic data sets than matrix population models: a case study of two perennial herbs

1. Matrix population models are widely used to describe population dynamics, conduct population viability analyses and derive management recommendations for plant populations. For endangered or invasive species, management decisions are often based on small demographic data sets. Hence, there is a need for population models which accurately assess population performance from such small data sets.
2. We used demographic data on two perennial herbs with different life histories to compare the accuracy and precision of the traditional matrix population model and the recently developed integral projection model (IPM) in relation to the amount of data.
3. For large data sets both matrix models and IPMs produced identical estimates of population growth rate (λ). However, for small data sets containing fewer than 300 individuals, IPMs often produced smaller bias and variance for λ than matrix models despite different matrix structures and sampling techniques used to construct the matrix population models.
4. Synthesis and applications . Our results suggest that the smaller bias and variance of λ estimates make IPMs preferable to matrix population models for small demographic data sets with a few hundred individuals. These results are likely to be applicable to a wide range of herbaceous, perennial plant species where demographic fate can be modelled as a function of a continuous state variable such as size. We recommend the use of IPMs to assess population performance and management strategies particularly for endangered or invasive perennial herbs where little demographic data are available.     

Effect of inventory method on niche models: Random versus systematic error

Data from large-scale biological inventories are essential for understanding and managing Earth's ecosystems. The Forest Inventory and Analysis Program (FIA) of the U.S. Forest Service is the largest biological inventory in North America; however, the FIA inventory recently changed from an amalgam of different approaches to a nationally-standardized approach in 2000. Full use of both data sets is clearly warranted to target many pressing research questions including those related to climate change and forest resources. However, full use requires lumping FIA data from different regionally-based designs (pre-2000) and/or lumping the data across the temporal changeover. Combining data from different inventory types must be approached with caution as inventory types represent different probabilities of detecting trees per sample unit, which can ultimately confound temporal and spatial patterns found in the data. Consequently, the main goal of this study is to evaluate the effect of inventory on a common analysis in ecology, modeling of climatic niches (or species-climate relations). We use non-parametric multiplicative regression (NPMR) to build and compare niche models for 41 tree species from the old and new FIA design in the Pacific coastal United States. We discover two likely effects of inventory on niche models and their predictions. First, there is an increase from 4 to 6% in random error for modeled predictions from the different inventories when compared to modeled predictions from two samples of the same inventory. Second, systematic error (or directional disagreement among modeled predictions) is detectable for 4 out of 41 species among the different inventories: Calocedrus decurrens, Pseudotsuga menziesii, and Pinus ponderosa, and Abies concolor. Hence, at least 90% of niche models and predictions of probability of occurrence demonstrate no obvious effect from the change in inventory design. Further, niche models built from sub-samples of the same data set can yield systematic error that rivals systematic error in predictions for models built from two separate data sets. This work corroborates the pervasive and pressing need to quantify different types of error in niche modeling to address issues associated with data quality and large-scale data integration.     

The conservation value of elevation data accuracy and model sophistication in reserve design under sea‐level rise

Many studies have explored the value of using more sophisticated coastal impact models and higher resolution elevation data in sea‐level rise (SLR) adaptation planning. However, we know little about to what extent the improved models and data could actually lead to better conservation outcomes under SLR. This is important to know because high‐resolution data are likely to not be available in some data‐poor coastal areas in the world and running more complicated coastal impact models is relatively time‐consuming, expensive, and requires assistance by qualified experts and technicians. We address this research question in the context of identifying conservation priorities in response to SLR. Specifically, we investigated the conservation value of using more accurate light detection and ranging (Lidar)‐based digital elevation data and process‐based coastal land‐cover change models (Sea Level Affecting Marshes Model, SLAMM) to identify conservation priorities versus simple “bathtub” models based on the relatively coarse National Elevation Dataset (NED) in a coastal region of northeast Florida. We compared conservation outcomes identified by reserve design software (Zonation) using three different model dataset combinations (Bathtub–NED, Bathtub–Lidar, and SLAMM–Lidar). The comparisons show that the conservation priorities are significantly different with different combinations of coastal impact models and elevation dataset inputs. The research suggests that it is valuable to invest in more accurate coastal impact models and elevation datasets in SLR adaptive conservation planning because this model–dataset combination could improve conservation outcomes under SLR. Less accurate coastal impact models, including ones created using coarser Digital Elevation Model (DEM) data can still be useful when better data and models are not available or feasible, but results need to be appropriately assessed and communicated. A future research priority is to investigate how conservation priorities may vary among different SLR scenarios when different combinations of model‐data inputs are used.     

Is more data always better? A simulation study of benefits and limitations of integrated distribution models

Species distribution models are popular and widely applied ecological tools. Recent increases in data availability have led to opportunities and challenges for species distribution modelling. Each data source has different qualities, determined by how it was collected. As several data sources can inform on a single species, ecologists have often analysed just one of the data sources, but this loses information, as some data sources are discarded. Integrated distribution models (IDMs) were developed to enable inclusion of multiple datasets in a single model, whilst accounting for different data collection protocols. This is advantageous because it allows efficient use of all data available, can improve estimation and account for biases in data collection. What is not yet known is when integrating different data sources does not bring advantages. Here, for the first time, we explore the potential limits of IDMs using a simulation study integrating a spatially biased, opportunistic, presence-only dataset with a structured, presence–absence dataset. We explore four scenarios based on real ecological problems; small sample sizes, low levels of detection probability, correlations between covariates and a lack of knowledge of the drivers of bias in data collection. For each scenario we ask; do we see improvements in parameter estimation or the accuracy of spatial pattern prediction in the IDM versus modelling either data source alone? We found integration alone was unable to correct for spatial bias in presence-only data. Including a covariate to explain bias or adding a flexible spatial term improved IDM performance beyond single dataset models, with the models including a flexible spatial term producing the most accurate and robust estimates. Increasing the sample size of presence–absence data and having no correlated covariates also improved estimation. These results demonstrate under which conditions integrated models provide benefits over modelling single data sources.     

A general modeling framework for open wildlife populations based on the Polya tree prior

Wildlife monitoring for open populations can be performed using a number of different survey methods. Each survey method gives rise to a type of data and, in the last five decades, a large number of associated statistical models have been developed for analyzing these data. Although these models have been parameterized and fitted using different approaches, they have all been designed to either model the pattern with which individuals enter and/or exit the population, or to estimate the population size by accounting for the corresponding observation process, or both. However, existing approaches rely on a predefined model structure and complexity, either by assuming that parameters linked to the entry and exit pattern (EEP) are specific to sampling occasions, or by employing parametric curves to describe the EEP. Instead, we propose a novel Bayesian nonparametric framework for modeling EEPs based on the Polya tree (PT) prior for densities. Our Bayesian nonparametric approach avoids overfitting when inferring EEPs, while simultaneously allowing more flexibility than is possible using parametric curves. Finally, we introduce the replicate PT prior for defining classes of models for these data allowing us to impose constraints on the EEPs, when required. We demonstrate our new approach using capture–recapture, count, and ring-recovery data for two different case studies.     

Conceptual data modelling for bioinformatics

Current research in the biosciences depends heavily on the effective exploitation of huge amounts of data. These are in disparate formats, remotely dispersed, and based on the different vocabularies of various disciplines. Furthermore, data are often stored or distributed using formats that leave implicit many important features relating to the structure and semantics of the data. Conceptual data modelling involves the development of implementation-independent models that capture and make explicit the principal structural properties of data. Entities such as a biopolymer or a reaction, and their relations, eg catalyses, can be formalised using a conceptual data model. Conceptual models are implementation-independent and can be transformed in systematic ways for implementation using different platforms, eg traditional database management systems. This paper describes the basics of the most widely used conceptual modelling notations, the ER (entity-relationship) model and the class diagrams of the UML (unified modelling language), and illustrates their use through several examples from bioinformatics. In particular, models are presented for protein structures and motifs, and for genomic sequences.     

Anthropological Models of Incest Laws in the United States

The incest laws of the fifty states are esoteric folk models or norms. The fifty state laws seem haphazard in their prohibitions and do not scale. However, using two different approaches, anthropological models may be constructed to explain the data.     

Additive and multiplicative models for the joint effect of two risk factors

Simple tests are given for consistency of the data with additive and with multiplicative effects of two risk factors on a binary outcome. A combination of the procedures will show whether data are consistent with neither, one or both of the models of no additive or no multiplicative interaction. Implications for the size of the study needed to detect differences between the models are also addressed. Because of the simple form of the test statistics, combination of evidence from different studies or strata is straightforward. Illustration of how the method could be extended to data from a 2xRxC table is also given.     

Influence of Feature Encoding and Choice of Classifier on Disease Risk Prediction in Genome-Wide Association Studies

Various attempts have been made to predict the individual disease risk based on genotype data from genome-wide association studies (GWAS). However, most studies only investigated one or two classification algorithms and feature encoding schemes. In this study, we applied seven different classification algorithms on GWAS case-control data sets for seven different diseases to create models for disease risk prediction. Further, we used three different encoding schemes for the genotypes of single nucleotide polymorphisms (SNPs) and investigated their influence on the predictive performance of these models. Our study suggests that an additive encoding of the SNP data should be the preferred encoding scheme, as it proved to yield the best predictive performances for all algorithms and data sets. Furthermore, our results showed that the differences between most state-of-the-art classification algorithms are not statistically significant. Consequently, we recommend to prefer algorithms with simple models like the linear support vector machine (SVM) as they allow for better subsequent interpretation without significant loss of accuracy.     

Comparison of mathematical models for the maternal age dependence of Down's syndrome rates

Summary The maternal age dependence of Down's syndrome rates was analyzed by two mathematical models, a discontinuous (DS) slope model which fits different exponential equations to different parts of the 20–49 age interval and a CPE model which fits a function that is the sum of a constant and exponential term over this whole 20–49 range. The CPE model had been considered but rejected by Penrose, who preferred models postulating changes with age assuming either a power function X¹⁰, where X is age or a Poisson model in which accumulation of 17 events was the assumed threshold for the occurrence of Down's syndrome. However, subsequent analyses indicated that the two models preferred by Penrose did not fit recent data sets as well as the DS or CPE model. Here we report analyses of broadened power and Poisson models in which n (the postulated number of independent events) can vary. Five data sets are analyzed. For the power models the range of the optimal n is 11 to 13; for the Poisson it is 17 to 25. The DS, Poisson, and power models each give the best fit to one data set; the CPE, to two sets. No particular model is clearly preferable. It appears unlikely that, with a data set from any single available source, a specific etiologic hypothesis for the maternal age dependence of Down's syndrome can be clearly inferred by the use of these or similar regression models.     

Deducing Underlying Mechanisms from Protein Recruitment Data

By using fluorescent labelling techniques, the distribution and dynamics of proteins can be measured within living cells, allowing to study in vivo the response of cells to a triggering event, such as DNA damage. In order to evaluate the reaction rate constants and to identify the proteins and reactions that are essential for the investigated process, mechanistic models are used, which often contain many proteins and associated parameters and are therefore underdetermined by the data. In order to establish criteria for assessing the significance of a model, we present here a systematic investigation of the information that can be reliably deduced from protein recruitment data, assuming that the complete set of reactions that affect the data of the considered protein species is not known. To this purpose, we study in detail models where one or two proteins that influence each other are recruited to a substrate. We show that in many cases the kind of interaction between the proteins can be deduced by analyzing the shape of the recruitment curves of one protein. Furthermore, we discuss in general in which cases it is possible to discriminate between different models and in which cases it is impossible based on the data. Finally, we argue that if different models fit experimental data equally well, conducting experiments with different protein concentrations would allow discrimination between the alternative models in many cases.     

Identifiability of Large Phylogenetic Mixture Models

Phylogenetic mixture models are statistical models of character evolution allowing for heterogeneity. Each of the classes in some unknown partition of the characters may evolve by different processes, or even along different trees. Such models are of increasing interest for data analysis, as they can capture the variety of evolutionary processes that may be occurring across long sequences of DNA or proteins. The fundamental question of whether parameters of such a model are identifiable is difficult to address, due to the complexity of the parameterization. Identifiability is, however, essential to their use for statistical inference.     

Models of the regulation of ribonucleotide reductase and their evaluation in intact mammalian cells

Enzymological studies have shown that ribonucleotide reductase is allosterically inhibited or stimulated by endproduct deoxyribonucleoside triphosphates, and various investigators have put forward schematized models of the regulation of this enzyme; the various models have in practice been considered to be equivalent or at least very similar. Here each of eleven published models is critically examined, and it is shown that there are important differences among them that have not previously been appreciated. In addition, studies using intact mammalian cells have generally been taken as being consistent with the enzymological data, but this point has not received much systematic attention. The available data are examined critically, and the implications of multiple, partially different models are considered.     

Cross-disciplinary information for understanding macroevolution

Many different macroevolutionary models can produce the same observations. Despite efforts in building more complex and realistic models, it may still be difficult to distinguish the processes that have generated the biodiversity we observe. In this opinion we argue that we can make new progress by reaching out across disciplines, relying on independent data and theory to constrain macroevolutionary inference. Using mainly paleontological insights and data, we illustrate how we can eliminate less plausible or implausible models, and/or parts of parameter space, while applying comparative phylogenetic approaches. We emphasize that such cross-disciplinary insights and data can be drawn between many other disciplines relevant to macroevolution. We urge cross-disciplinary training, and collaboration using common-use databases as a platform for increasing our understanding.     

Do metacommunity mass effects predict changes in species incidence and abundance?

Metacommunity matrices contain data on species incidence or abundance across sites, compactly portraying community composition and how it varies over sites. We constructed models based on an initial metacommunity matrix of either species incidence or abundance to test whether such data suffice to predict subsequent changes in incidence or abundance at each site. The models reflect both species and site mass effects in using products of the row and column totals to predict the incidence or abundance of each species expected at each site. We tested these models against empirical data on vascular plant incidence and abundance collected from two sets of forested sites in both the 1950s and 2000s. Predictions from these models parallel observed changes in species incidence and abundance in these distinctly different metacommunities and differ greatly from null model predictions. The abundance model shows greater power than the incidence model reflecting its higher information content. Predictions were more accurate for the more diverse forests of southern Wisconsin that are changing quickly in response to succession and fragmentation. Simulations show that these results are robust but sensitive to sampling intensity. Because these models require no data on site conditions or species’ characteristics, they provide a useful baseline to assess more complex models based on species’ functional traits, local site conditions, or landscape context. They may also prove useful to conservation biologists seeking to predict local population declines and extinction risks.     

Intraspecific trait variation across scales: implications for understanding global change responses

Recognition of the importance of intraspecific variation in ecological processes has been growing, but empirical studies and models of global change have only begun to address this issue in detail. This review discusses sources and patterns of intraspecific trait variation and their consequences for understanding how ecological processes and patterns will respond to global change. We examine how current ecological models and theories incorporate intraspecific variation, review existing data sources that could help parameterize models that account for intraspecific variation in global change predictions, and discuss new data that may be needed. We provide guidelines on when it is most important to consider intraspecific variation, such as when trait variation is heritable or when nonlinear relationships are involved. We also highlight benefits and limitations of different model types and argue that many common modeling approaches such as matrix population models or global dynamic vegetation models can allow a stronger consideration of intraspecific trait variation if the necessary data are available. We recommend that existing data need to be made more accessible, though in some cases, new experiments are needed to disentangle causes of variation.