Non‐equilibrium in plant distribution models – only an issue for introduced or dispersal limited species?

Species distribution models rely on the assumption that species' distributions are at equilibrium with environmental conditions within a region – i.e. they occur in all suitable habitats. If this assumption holds, species occurrence should be predictable from measures of the environment. Introduced species may be poor candidates for distribution models due to their presumed lack of equilibrium within the landscapes they occupy, although predicting their potential distributions is often of critical importance to natural resource managers. We determined if the accuracy of species distribution models differed between 17 native and 17 introduced riparian plant species in the western United States. We also assessed if model accuracy was associated with both environmental and biological factors that can influence dispersal. We used Random Forests to model species distributions and linear regression to determine if model accuracy was associated with dispersal‐related traits. Model accuracy for introduced species was higher than that for native species. Dispersal‐related traits did not affect model accuracy or improvement, though two other traits, family affiliation and rarity on the landscape, did have an effect. Distance‐based measures of dispersal potential improved model fit equally for both native and introduced species and for species with a variety of dispersal traits, suggesting that the importance of regional propagule pressure is relatively constant across species with different dispersal opportunities. Several lines of future questioning are suggested by our results, including why introduced species may in some cases produce more accurate distribution models than native species and how species dispersal traits relate to distribution model accuracy at different spatial scales.     

Spatial Ecological Hierarchies: Coexistence on Heterogeneous Landscapes via Scale Niche Diversification

Spatially heterogeneous environments are generally characterized by nested landscape patterns with resource aggregations on several scales. Empirical studies indicate that such nested landscape patterns impose selection constraints on the perceptive scales of animals, but the underlying selection mechanisms are unclear. We investigated the selection dynamics of perceptive scale within a spatial resource utilization model, where the environment is characterized by its resource distribution and species differ in their perceptive scales and resource preemption capabilities. Using three model landscapes with various resource distributions, we found that the optimal perceptive scale is determined by scale-specific attributes of the landscape pattern and that the number of coexisting species increases with the number of characteristic scales. Based on the results of this model, we argue that resource aggregations on different scales act as distinct resources and that animal species of particular perceptive scales are superior in utilizing resource aggregations of comparable spatial extent. Due to the allometric relationship between body size and perceptive scale, such fitness difference might result in discontinuous body mass distributions.     

Climatic associations of British species distributions show good transferability in time but low predictive accuracy for range change

Conservation planners often wish to predict how species distributions will change in response to environmental changes. Species distribution models (SDMs) are the primary tool for making such predictions. Many methods are widely used; however, they all make simplifying assumptions, and predictions can therefore be subject to high uncertainty. With global change well underway, field records of observed range shifts are increasingly being used for testing SDM transferability. We used an unprecedented distribution dataset documenting recent range changes of British vascular plants, birds, and butterflies to test whether correlative SDMs based on climate change provide useful approximations of potential distribution shifts. We modelled past species distributions from climate using nine single techniques and a consensus approach, and projected the geographical extent of these models to a more recent time period based on climate change; we then compared model predictions with recent observed distributions in order to estimate the temporal transferability and prediction accuracy of our models. We also evaluated the relative effect of methodological and taxonomic variation on the performance of SDMs. Models showed good transferability in time when assessed using widespread metrics of accuracy. However, models had low accuracy to predict where occupancy status changed between time periods, especially for declining species. Model performance varied greatly among species within major taxa, but there was also considerable variation among modelling frameworks. Past climatic associations of British species distributions retain a high explanatory power when transferred to recent time--due to their accuracy to predict large areas retained by species--but fail to capture relevant predictors of change. We strongly emphasize the need for caution when using SDMs to predict shifts in species distributions: high explanatory power on temporally-independent records--as assessed using widespread metrics--need not indicate a model's ability to predict the future.     

Scaling up from local competition to regional coexistence across two scales of spatial heterogeneity: insect larvae in the fruits of Apeiba membranacea

Species that live in patchy and ephemeral habitats can compete strongly for resources within patches at a small scale. The ramifications of these interactions for population dynamics and coexistence at regional scales will depend on the intraspecific and interspecific distributions of individuals among patches. Spatial heterogeneity due to independent aggregation of competitors among patchy habitats is an important mechanism maintaining species diversity. I describe regional patterns of aggregation for four species of insect larvae in the fruits of Apeiba membranacea, a Neotropical rainforest tree. This aggregation results from variation in densities at a small scale (among the fruits under a single tree), compounded by significant variation among trees in both mean densities and degrees of aggregation. Both the degrees of aggregation and mean densities are statistically independent within and across species at both spatial scales. I evaluate the regional consequences of these spatial patterns by using maximum likelihood methods to parameterize a model that includes both explicit measures of the strength of competition and spatial variation at both within- and among-tree spatial scales. Despite strong competitive interactions among these species, during 2 years the observed spatial variation at both scales combined was sufficient to explain the coexistence of these species, although other coexistence mechanisms may also operate simultaneously. The observed spatial variation at small spatial scales may not be sufficient for coexistence, indicating the importance of considering multiple sources of spatial heterogeneity when scaling up from experiments that investigate local interactions to regional patterns of coexistence.     

A dynamic multi‐scale occupancy model to estimate temporal dynamics and hierarchical habitat use for nomadic species

Distribution models are increasingly being used to understand how landscape and climatic changes are affecting the processes driving spatial and temporal distributions of plants and animals. However, many modeling efforts ignore the dynamic processes that drive distributional patterns at different scales, which may result in misleading inference about the factors influencing species distributions. Current occupancy models allow estimation of occupancy at different scales and, separately, estimation of immigration and emigration. However, joint estimation of local extinction, colonization, and occupancy within a multi‐scale model is currently unpublished. We extended multi‐scale models to account for the dynamic processes governing species distributions, while concurrently modeling local‐scale availability. We fit the model to data for lark buntings and chestnut‐collared longspurs in the Great Plains, USA, collected under the Integrated Monitoring in Bird Conservation Regions program. We investigate how the amount of grassland and shrubland and annual vegetation conditions affect bird occupancy dynamics and local vegetation structure affects fine‐scale occupancy. Buntings were prevalent and longspurs rare in our study area, but both species were locally prevalent when present. Buntings colonized sites with preferred habitat configurations, longspurs colonized a wider range of landscape conditions, and site persistence of both was higher at sites with greener vegetation. Turnover rates were high for both species, quantifying the nomadic behavior of the species. Our model allows researchers to jointly investigate temporal dynamics of species distributions and hierarchical habitat use. Our results indicate that grassland birds respond to different covariates at landscape and local scales suggesting different conservation goals at each scale. High turnover rates of these species highlight the need to account for the dynamics of nomadic species, and our model can help inform how to coordinate management efforts to provide appropriate habitat configurations at the landscape scale and provide habitat targets for local managers.     

Scaling up from local competition to regional coexistence across two scales of spatial heterogeneity: insect larvae in the fruits of <Emphasis Type="Italic">Apeiba membranacea</Emphasis>

Species that live in patchy and ephemeral habitats can compete strongly for resources within patches at a small scale. The ramifications of these interactions for population dynamics and coexistence at regional scales will depend on the intraspecific and interspecific distributions of individuals among patches. Spatial heterogeneity due to independent aggregation of competitors among patchy habitats is an important mechanism maintaining species diversity. I describe regional patterns of aggregation for four species of insect larvae in the fruits of Apeiba membranacea, a Neotropical rainforest tree. This aggregation results from variation in densities at a small scale (among the fruits under a single tree), compounded by significant variation among trees in both mean densities and degrees of aggregation. Both the degrees of aggregation and mean densities are statistically independent within and across species at both spatial scales. I evaluate the regional consequences of these spatial patterns by using maximum likelihood methods to parameterize a model that includes both explicit measures of the strength of competition and spatial variation at both within- and among-tree spatial scales. Despite strong competitive interactions among these species, during 2 years the observed spatial variation at both scales combined was sufficient to explain the coexistence of these species, although other coexistence mechanisms may also operate simultaneously. The observed spatial variation at small spatial scales may not be sufficient for coexistence, indicating the importance of considering multiple sources of spatial heterogeneity when scaling up from experiments that investigate local interactions to regional patterns of coexistence.     

Generalized models vs. classification tree analysis: Predicting spatial distributions of plant species at different scales

Abstract. Statistical models of the realized niche of species are increasingly used, but systematic comparisons of alternative methods are still limited. In particular, only few studies have explored the effect of scale in model outputs. In this paper, we investigate the predictive ability of three statistical methods (generalized linear models, generalized additive models and classification tree analysis) using species distribution data at three scales: fine (Catalonia), intermediate (Portugal) and coarse (Europe). Four Mediterranean tree species were modelled for comparison. Variables selected by models were relatively consistent across scales and the predictive accuracy of models varied only slightly. However, there were slight differences in the performance of methods. Classification tree analysis had a lower accuracy than the generalized methods, especially at finer scales. The performance of generalized linear models also increased with scale. At the fine scale GLM with linear terms showed better accuracy than GLM with quadratic and polynomial terms. This is probably because distributions at finer scales represent a linear sub‐sample of entire realized niches of species. In contrast to GLM, the performance of GAM was constant across scales being more data‐oriented. The predictive accuracy of GAM was always at least equal to other techniques, suggesting that this modelling approach is more robust to variations of scale because it can deal with any response shape.     

基于最大熵模型的不同尺度物种分布概率优化热点分析: 以红色木莲为例

单一空间尺度构建的最大熵(maximum entropy, MaxEnt)模型是否具有代表性, 是MaxEnt模型应用与发展中面临的重要问题。本研究基于有效的地理分布位点数据, 利用最小凸多边形法(the minimum convex polygon method)在三江并流、云南省及全国3个空间尺度下分别识别了红色木莲(Manglietia insignis)的建模区域, 并进一步建立MaxEnt模型: 使用ROC曲线分析法与遗漏率(omission rate, OR)检验评估MaxEnt模型预测精度; 基于ArcGIS分析分布概率及其热点区域的分布趋势, 并通过分区统计工具Zonal识别潜在适宜分布区域的质心位置; 采用刀切法检验环境因子贡献率。结果表明: (1)不同尺度下红色木莲的MaxEnt模型都有良好的预测效果, 三江并流、云南省及全国尺度下的AUC值分别为0.936、0.887和0.930, OR值分别为0.18、0.15和0.20; (2)各尺度红色木莲的适生区格局呈现一致性分布趋势, 集中在独龙江、怒江和澜沧江3个流域; (3) 3个空间尺度下红色木莲的地理分布受不同环境因子影响, 存在着尺度依赖效应。由此可见, 红色木莲在不同空间尺度下的预测模型有着稳定的性能表现与良好的预测效果。此外, 我们建议在野外实地调查与野生生物资源保护中加强对普通物种的关注, 在预测物种地理分布的研究中将MaxEnt模型与热点分析结合使用。     

Community assembly along a successional gradient in sub‐alpine meadows of the Qinghai‐Tibetan Plateau,China

Community assembly is a dynamic progression that reflects the interaction of several processes functioning at multiple scales. Understanding how these processes work in communities at different successional stages is important for identifying when regional or local processes are more important for community assembly, and for developing effective preservation and restoration strategies. We examined community assembly using a chronosequence of sub‐alpine meadows in Qinghai‐Tibetan Plateau that range from ‘natural’ (never farmed), to those that have been protected from agricultural exploitation for 1 to 10 years. We tested for shifts in species and traits among meadows and also for changes in environmental and spatial correlates of species distributions within meadows. We found that species richness increased and species composition returned to natural conditions within ten years of protection. These changes coincided with shifts in species traits; abundant species had high seed mass and specific leaf area in late‐successional meadows, whereas the opposite occurred in early‐successional meadows. Despite these shifts among meadows of different ages, spatial distributions of species within meadows did not change – when associated with abiotic variables, these spatial patterns reflected changes in soil pH and nitrogen. There was also no consistent change in the relative importance of environmental and spatial correlates of species distributions within meadows. These trends indicate that local processes of community assembly are similar within meadows even when species in those meadows differ. We conclude that successional change is a large‐scale process that alters the species pool and resulting suite of traits that are present within meadows. As a result, regional planning that incorporates successional age should be the focus for the conservation of diversity in this area. In contrast, local processes work within the constraints of the species pool set by successional age, producing consistent patterns within meadows of different ages.     

Semiparametric estimation of the covariate-specific ROC curve in presence of ignorable verification bias

Covariate-specific receiver operating characteristic (ROC) curves are often used to evaluate the classification accuracy of a medical diagnostic test or a biomarker, when the accuracy of the test is associated with certain covariates. In many large-scale screening tests, the gold standard is subject to missingness due to high cost or harmfulness to the patient. In this article, we propose a semiparametric estimation of the covariate-specific ROC curves with a partial missing gold standard. A location-scale model is constructed for the test result to model the covariates' effect, but the residual distributions are left unspecified. Thus the baseline and link functions of the ROC curve both have flexible shapes. With the gold standard missing at random (MAR) assumption, we consider weighted estimating equations for the location-scale parameters, and weighted kernel estimating equations for the residual distributions. Three ROC curve estimators are proposed and compared, namely, imputation-based, inverse probability weighted, and doubly robust estimators. We derive the asymptotic normality of the estimated ROC curve, as well as the analytical form of the standard error estimator. The proposed method is motivated and applied to the data in an Alzheimer's disease research.     

Improving species distribution models using biotic interactions: a case study of parasites,pollinators and plants

Biotic interactions have been considered as an important factor to be included in species distribution modelling, but little is known about how different types of interaction or different strategies for modelling affect model performance. This study compares different methods for including interspecific interactions in distribution models for bees, their brood parasites, and the plants they pollinate. Host–parasite interactions among bumble bees (genus Bombus: generalist pollinators and brood parasites) and specialist plant–pollinator interactions between Centris bees and Krameria flowers were used as case studies. We used 7 different modelling algorithms available in the BIOMOD R package. For Bombus, the inclusion of interacting species distributions generally increased model predictive accuracy. The improvement was better when the interacting species was included with its raw distribution rather than with its modeled suitability. However, incorporating the distributions of non‐interacting species sometimes resulted in similarly increased model accuracy despite their being no significance of any interaction for the distribution. For the Centris‐Krameria system the best strategy for modelling biotic interactions was to include the interacting species model‐predicted values. However, the results were less consistent than those for Bombus species, and most models including biotic interactions showed no significant improvement over abiotic models. Our results are consistent with previous studies showing that biotic interactions can be important in structuring species distributions at regional scales. However, correlations between species distributions are not necessarily indicative of interactions. Therefore, choosing the correct biotic information, based on biological and ecological knowledge, is critical to improve the accuracy of species distribution models and forecast distribution change.     

A test of the cross-scale resilience model: Functional richness in Mediterranean-climate ecosystems

Ecological resilience has been proposed to be generated, in part, in the discontinuous structure of complex systems. Environmental discontinuities are reflected in discontinuous, aggregated animal body mass distributions. Diversity of functional groups within body mass aggregations (scales) and redundancy of functional groups across body mass aggregations (scales) has been proposed to increase resilience. We evaluate that proposition by analyzing mammalian and avian communities of Mediterranean-climate ecosystems. We first determined that body mass distributions for each animal community were discontinuous. We then calculated the variance in richness of function across aggregations in each community, and compared observed values with distributions created by 1000 simulations using a null of random distribution of function, with the same n, number of discontinuities and number of functional groups as the observed data. Variance in the richness of functional groups across scales was significantly lower in real communities than in simulations in eight of nine sites. The distribution of function across body mass aggregations in the animal communities we analyzed was non-random, and supports the contentions of the cross-scale resilience model.     

The use of fractal image statistics in the estimation of lateral spatial extent

It has been argued that the characteristics of many commonly occurring surface textures are such that the resulting luminance distributions have the statistical properties of fractals, over a wide range of spatial scales. We show that, when fractal luminance distributions are spatially filtered, the spatial density of zero-crossings obtained is inversely proportional to the scale of filtering, and is not strongly dependent on the fractal dimension of the pattern used. We propose that this predictable property of natural images could provide a basis for the estimation of lateral spatial extent by counting zero-crossings within an interval at a variety of spatial scales, and averaging over spatial scale. We carried out experiments to compare the relative apparent lateral extents of fractal patterns and patterns of equally spaced bars, as a function of the number of bars. The results are in good agreement with theory.     

Biotic interactions improve prediction of boreal bird distributions at macro-scales

Aim The role of biotic interactions in influencing species distributions at macro‐scales remains poorly understood. Here we test whether predictions of distributions for four boreal owl species at two macro‐scales (10 × 10 km and 40 × 40 km grid resolutions) are improved by incorporating interactions with woodpeckers into climate envelope models. Location Finland, northern Europe. Methods Distribution data for four owl and six woodpecker species, along with data for six land cover and three climatic variables, were collated from 2861 10 × 10 km grid cells. Generalized additive models were calibrated using a 50% random sample of the species data from western Finland, and by repeating this procedure 20 times for each of the four owl species. Models were fitted using three sets of explanatory variables: (1) climate only; (2) climate and land cover; and (3) climate, land cover and two woodpecker interaction variables. Models were evaluated using three approaches: (1) examination of explained deviance; (2) four‐fold cross‐validation using the model calibration data; and (3) comparison of predicted and observed values for independent grid cells in eastern Finland. The model accuracy for approaches (2) and (3) was measured using the area under the curve of a receiver operating characteristic plot. Results At 10‐km resolution, inclusion of the distribution of woodpeckers as a predictor variable significantly improved the explanatory power, cross‐validation statistics and the predictive accuracy of the models. Inclusion of land cover led to similar improvements at 10‐km resolution, although these improvements were less apparent at 40‐km resolution for both land cover and biotic interactions. Main conclusions Predictions of species distributions at macro‐scales may be significantly improved by incorporating biotic interactions and land cover variables into models. Our results are important for models used to predict the impacts of climate change, and emphasize the need for comprehensive evaluation of the reliability of species–climate impact models.     

Modeling changes in predator functional response to prey across spatial scales

Extrapolation of predator functional responses from laboratory observations to the field is often necessary to predict predation rates and predator-prey dynamics at spatial and temporal scales that are difficult to observe directly. We use a spatially explicit individual-based model to explore mechanisms behind changes in functional responses when the scale of observation is increased. Model parameters were estimated from a predator-prey system consisting of the predator Delphastus catalinae (Coleoptera: Coccinellidae) and Bemisia tabaci biotype B (Hemiptera: Aleyrodidae) on tomato plants. The model explicitly incorporates prey and predator distributions within single plants, the search behavior of predators within plants, and the functional response to prey at the smallest scale of interaction (within leaflets) observed in the laboratory. Validation revealed that the model is useful in scaling up from laboratory observations to predation in whole tomato plants of varying sizes. Comparing predicted predation at the leaflet scale, as observed in laboratory experiments, with predicted predation on whole plants revealed that the predator functional response switches from type II within leaflets to type III within whole plants. We found that the magnitude of predation rates and the type of functional response at the whole plant scale are modulated by (1) the degree of alignment between predator and prey distributions and (2) predator foraging behavior, particularly the effect of area-concentrated search within plants when prey population density is relatively low. The experimental and modeling techniques we present could be applied to other systems in which active predators prey upon sessile or slow-moving species.     

Fluorescence polarization in a planar array of pigment molecules: theoretical treatment and application to flavins incorporated into artificial membranes.

A quantitative fluorescence polarization theory of molecules bound to two-dimensional plane layers has been developed when the electronic transition moments of absorption and emission are parallel within the fluorescent molecules. The transition moments are assumed to be in preferred orientation with respect to the normal to the plane and to be randomly oriented within the plane (rotational symmetry with the normal as axis of symmetry). Three basic model distributions of transition moments are investigated quantitatively. These model distributions represent a simplification but in most cases may be expected to describe reality with sufficient accuracy. For all distributions, two cases of different mobility of molecules are treated: (a) the lifetime of fluorescence is small compared with the characteristic relaxation time of the distribution, and (b) the lifetime of fluorescence is long, so that a complete reorientation of transition moments during the excited state can take place. From the quantitative calculations four characteristic quantities are derived, which are appropriate for the analysis of experimental data. Experiments are carried out with phosphatidylcholine bilayer membranes which contain three differently substituted amphiphilic flavins. All three flavins yield similar data. Their analyses predict free and fast mobility of the flavin chromophore.     

The relative importance of climate and habitat in determining the distributions of species at different spatial scales: a case study with ground beetles in Great Britain

Experimental studies have shown that many species show preferences for different climatic conditions, or may die in unsuitable conditions. Climate envelope models have been used frequently in recent years to predict the presence and absence of species at large spatial scales. However, many authors have postulated that the distributions of species at smaller spatial scales are determined by factors such as habitat availability and biotic interactions. Climatic effects are often assumed by modellers to be unimportant at fine resolutions, but few studies have actually tested this. We sampled the distributions of 20 beetle species of the family Carabidae across three study sites by pitfall trapping, and at the national scale from monitoring data. Statistical models were constructed to determine which of two sets of environmental variables (temperature or broad habitat type) best accounted for the observed data at the three sites and at the national (Great Britain) scale. High‐resolution temperature variables frequently produced better models (as determined by AIC) than habitat features when modelling the distributions of species at a local scale, within the three study sites. Conversely, habitat was always a better predictor than temperature when describing species’ distributions at a coarse scale within Great Britain. Northerly species were most likely to occur in cool micro‐sites within the study sites, whereas southerly species were most likely to occur in warm micro‐sites. Effects of microclimate were not limited to species at the edges of their distribution, and fine‐resolution temperature surfaces should therefore ideally be utilised when undertaking climate‐envelope modelling.     

Updating bird species distribution at large spatial scales: applications of habitat modelling to data from long-term monitoring programs

Mapping of species distributions at large spatial scales has been often based on the representation of gathered observations in a general grid atlas framework. More recently, subsampling and subsequent interpolation or habitat spatial modelling techniques have been incorporated in these projects to allow more detailed species mapping. Here, we explore the usefulness of data from long-term monitoring (LTM) projects, primarily aimed at estimating trends in species abundance and collected at shorter time intervals (usually yearly) than atlas data, to develop predictive habitat models. We modelled habitat occupancy for 99 species using a bird LTM program and evaluated the predictive accuracy of these models using independent data from a contemporary and comprehensive breeding bird atlas project from the same region. Habitat models from LTM data using generalized linear modelling were significant for all the species and generally showed a high predictive power, albeit lower than that from atlas models. Sample size and species range size and niche breadth were the most important factors behind variability in model predictive accuracy, whereas the spatial distribution of sampling units at a given sample size had minor effects. Although predictive accuracy of habitat modelling was strongly species dependent, increases in sample size and, secondarily, a better spatial distribution of sampling units should lead to more powerful predictive distribution models. We suggest that data from LTM programs, now established in a large number of countries, has the potential for being a major source of good quality data suitable for the estimation and regularly update of distributions at large spatial scales for a number of species.     

Occupancy frequency distributions: patterns,artefacts and mechanisms

Numerous hypotheses have been proposed to explain the shape of occupancy frequency distributions (distributions of the numbers of species occupying different numbers of areas). Artefactual effects include sampling characteristics, whereas biological mechanisms include organismal, niche-based and meta-population models. To date, there has been little testing of these models. In addition, although empirically derived occupancy distributions encompass an array of taxa and spatial scales, comparisons between them are often not possible because of differences in sampling protocol and method of construction. In this paper, the effects of sampling protocol (grain, sample number, extent, sampling coverage and intensity) on the shape of occupancy distributions are examined, and approaches for minimising artefactual effects recommended. Evidence for proposed biological determinants of the shape of occupancy distributions is then examined. Good support exists for some mechanisms (habitat and environmental heterogeneity), little for others (dispersal ability), while some hypotheses remain untested (landscape productivity, position in geographic range, range size frequency distributions), or are unlikely to be useful explanations for the shape of occupancy distributions 'species specificity and adaptation to habitat, extinction-colonization dynamics). The presence of a core (class containing species with the highest occupancy) mode in occupancy distributions is most likely to be associated with larger sample units, and small homogenous sampling areas positioned well within and towards the range centers of a sufficient proportion of the species in the assemblage. Satellite (class with species with the lowest occupancy) modes are associated with sampling large, heterogeneous areas that incorporate a large proportion of the assemblage range. However, satellite modes commonly also occur in the presence of a core mode, and rare species effects are likely to contribute to the presence of a satellite mode at most sampling scales. In most proposed hypotheses, spatial scale is an important determinant of the shape of the observed occupancy distribution. Because the attributes of the mechanisms associated with these hypotheses change with spatial scale, their predictions for the shape of occupancy distributions also change. To understand occupancy distributions and the mechanisms underlying them, a synthesis of pattern documentation and model testing across scales is thus needed. The development of null models, comparisons of occupancy distributions across spatial scales and taxa, documentation of the movement of individual species between occupancy classes with changes in spatial scale, as well as further testing of biological mechanisms are all necessary for an improved understanding of the distribution of species and assemblages within their geographic ranges.     

Simulation modeling of pooling for combinatorial protein engineering

Pooling in directed-evolution experiments will greatly increase the throughput of screening systems, but important parameters such as the number of good mutants created and the activity level increase of the good mutants will depend highly on the protein being engineered. The authors developed and validated a Monte Carlo simulation model of pooling that allows the testing of various scenarios in silico before starting experimentation. Using a simplified test system of 2 enzymes, betagalactosidase (supermutant, or greatly improved enzyme) and beta-glucuronidase (dud, or enzyme with ancestral level of activity), the model accurately predicted the number of supermutants detected in experiments within a factor of 2. Additional simulations using more complex activity distributions show the versatility of the model. Pooling is most suited to cases such as the directed evolution of new function in a protein, where the background level of activity is minimized, making it easier to detect small increases in activity level. Pooling is most successful when a sensitive assay is employed. Using the model will increase the throughput of screening procedures for directed-evolution experiments and thus lead to speedier engineering of proteins.