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Many population statistics describe the characteristics of populations within and among species. These are useful for describing population dynamics, understanding how environmental factors alter demographic patterns, testing hypotheses related to the evolution of life history characteristics and informing the effective management of populations.In this study, we propose a population statistic: the interstage flow. The interstage flow is defined as the product of the element in the ith row, the jth column of the population projection matrix and the jth element of the normalized stable stage distribution.The sum of the interstage flow matrix elements is equal to the population growth rate (PGR), which is the dominant eigenvalue of the population projection matrix. The interstage flow matrix elements allow decomposition of PGR into component contributions made by transitions between developmental stages.We demonstrate the utility of interstage flow matrices using matrix population models from the COMPADRE plant matrix database. We compared interstage flows among four life history/functional groups (FGs) (semelparous herbs, iteroparous herbs, shrubs and trees) and described how PGR reflected individual transitions related to stasis, fecundity and growth. We found that the individual flows are different among FGs.Synthesis. The proposed population statistic, the interstage flow matrix, describes the contribution of individual developmental stage transitions to the PGR. The flow of individuals between developmental stages differs in distinctive ways among different life histories and FGs. The interstage flow matrix is a valuable statistic for describing these differences. [ABSTRACT FROM AUTHOR]

Many models have been developed to predict the combined effect of drugs and chemicals. Most models are classified into two additive models: independent action (IA) and concentration addition (CA). It is generally considered if the modes of action of chemicals are similar then the combined effect obeys CA; however, many empirical studies report nonlinear effects deviating from the predictions by CA. Such deviations are termed synergism and antagonism. Synergism, which leads to a stronger toxicity, requires more careful management, and hence it is important to understand how and which combinations of chemicals lead to synergism. In this paper, three types of chemical reactions are mathematically modeled and the cause of the nonlinear effects among chemicals with similar modes of action was investigated. Our results show that combined effects obey CA only when the modes of action are exactly the same. Contrary to existing knowledge, combined effects are generally nonlinear even if the modes of action of the chemicals are similar. Our results further show that the nonlinear effects vanish out when the chemical concentrations are low, suggesting that the current management procedure of assuming CA is rarely inappropriate because environmental concentrations of chemicals are generally low. [ABSTRACT FROM AUTHOR]

Assessing the vulnerability and adaptive capacity of species, communities, and ecosystems is essential for successful conservation. Climate change, however, induces extreme uncertainty in various pathways of assessments, which hampers robust decision-making for conservation. Here, we developed a framework that allows us to quantify the level of acceptable uncertainty as a metric of ecosystem robustness, considering the uncertainty due to climate change. Under the framework, utilizing a key concept from info-gap decision theory, vulnerability is measured as the inverse of maximum acceptable uncertainty to fulfill the minimum required goal for conservation. We applied the framework to 42 natural forest ecosystems and assessed their acceptable uncertainties in terms of maintenance of species richness and forest functional type. Based on best-guess estimate of future temperature in various GCM models and RCP scenarios, and assuming that tree species survival is primarily determined by mean annual temperature, we performed simulations with increasing deviation from the best-guess temperature. Our simulations indicated that the acceptable uncertainty varied greatly among the forest plots, presumably reflecting the distribution of ecological traits and niches among species within the communities. Our framework provides acceptable uncertainty as an operational metric of ecosystem robustness under uncertainty, while incorporating both system properties and socioeconomic conditions. We argue that our framework can enhance social consensus building and decision-making in the face of the extreme uncertainty induced by global climate change. [ABSTRACT FROM AUTHOR]

Highlights: [•] We present a new approach to set effluent limits under severe uncertainty. [•] Our framework allows effluent limits to be set with only a partial risk assessment. [•] We incorporate the trade-off between ecological risk and economic cost. [ABSTRACT FROM AUTHOR]

Population viability analyses are widely used to support decisions for the management of single species, but there are few studies that explicitly take into account realistic economic costs. In this study we determine the most cost-efficient conservation management options for the white-banded tanager (Neothraupis fasciata) in the protected areas of the Cerrado in central Brazil. We use the PVA model VORTEX to simulate the ability of different management options to improve population persistence and then assess the effectiveness of each option given a fixed budget. We discover that the best strategy for improving the viability of white-banded tanager populations is to use fire management and nest protection to increase fecundity. In small reserves and a low budget then fire management alone is the best strategy, but if the budget is larger fire management with nest protection as a mixed strategy is better. In large reserves the best strategy is to do nest protection and with large budgets there is a negligible difference between spending all the money on nest protection versus a mixed strategy. If we had not included financial considerations in our analysis of management options then we would have discarded fire management as an option, even though it can be the best strategy. [Copyright &y& Elsevier]

Abstract: Alien species are often a major threat to native species. We consider optimal conservation strategies for a population whose viability is affected both by an alien species (such as a competitor, a predator, or a pathogen) and by random fluctuations of the environment (e.g. precipitation, temperature). We assume that the survivorship of the native population can be improved by providing resources such as food and shelter, and also by an extermination effort that decreases the abundance of the alien species. These efforts decrease the extinction probability of the native population, but they are accompanied by economic costs. We search for the optimal strategy that minimizes the weighted sum of the extinction probability and the economic costs over a single year. We derive conditions under which investment should be made in both resource-enhancement and extermination, and examine how the optimal effort levels change with parameters. When the optimal strategy includes both types of efforts, the optimal extermination effort level turns out to be independent of the density and economic value of the native species, or the variance of the environmental fluctuation. Furthermore, the optimal resource-enhancement effort is then independent of the density of the alien species. However, the parameter dependencies greatly change if one of the efforts becomes zero. We also examine the situation in which the impact of the alien species is uncertain. The optimal extermination effort increases with the uncertainty of this impact except when the cost of extermination is very high. [Copyright &y& Elsevier]

Mate-choice copying by females has been reported in fishes (e.g., guppies) and lekking birds. Presumably, females assess males' quality using both information from direct observation of males and information acquired by observing other females' choices. Here, we study mathematically the conditions under which matechoice copying is advantageous on the basis of Bayesian decision theory. A female may observe the mate choice of another female, called the model female, who has performed an optimal choice based on her own judgment. The conditions required for the focal female to choose the same mate as that chosen by the model female should depend on the male's appearance to her, the reliability of her own judgment of male quality, and the reliability of the model females. When three or more females are involved, the optimal mate choice critically depends on whether multiple model females make decisions independently or they themselves copy the choices of others. If two equally reliable females choose different males, the choice of the second female, made knowing the choice of the first, should have a stronger effect on the choice of the third (focal) female. This "lastchoice precedence" should be tested experimentally. [ABSTRACT FROM AUTHOR]

We consider optimal conservation strategies for an endangered population. We assume that juvenile survival is affected by unpredictable environmental fluctuation and can be improved by costly conservation effort. The initial population size is not accurately known at the time that the conservation effort level is chosen, but the uncertainty of its estimate can be reduced by a costly monitoring effort. In a previous paper, we analysed the optimal management strategy that minimizes a weighted sum of extinction probability and economic costs when only a single year is considered. Here we examine the case in which the conservation period lasts for several years by dynamic programming with incompletely observed process states. We study the optimal levels of the conservation and the monitoring efforts, and their dependence on the length of the conservation period and other parameters. The main conclusions are: (1) The optimal conservation effort in the first year depends on the accuracy of the information on the population size in the first year, but is almost independent of the accuracy of the information in later years. (2) When the risk of population extinction is small, the optimal conservation effort increases with the uncertainty of the population size. In contrast when the population is endangered, the optimal conservation effort decreases with the uncertainty of the population size. (3) The optimal conservation and monitoring efforts both increase with the length of the conservation period, provided that the population is relatively safe. However, if the population is endangered, both types of effort become smaller when the conservation period increases. [Copyright &y& Elsevier]

We consider optimal conservation strategies for endangered populations. We assume that the survival of the population is affected by unpredictable environmental fluctuation and can be improved by conservation effort. Furthermore, the exact value of the initial population size is assumed to be unknown. The conservation strategy involves two aspects: investment of assessment effort, to improve the estimate of the initial population size and investment of conservation effort. Both types of effort imply economic costs. The optimal management strategy is assumed to minimize the weighted sum of extinction probability and the economic cost of the conservation and the assessment effort. (1) We first analyse the optimal conservation effort when the current population size is known accurately. (2) Next, we consider the situation in which there is limited information (i.e. a cue) on population size. (3) We subsequently discuss the cases where the cue accuracy can be improved by assessment of the population. We study the optimal level of the assessment effort and discuss its dependence on various parameters. [Copyright &y& Elsevier]

We study the optimal conservation effort for a population in a fluctuating environment. The survivorship of a population is affected by unpredictable environmental fluctuation (noise) and can be improved by conservation effort accompanied by a cost. The optimal effort level is the one that minimizes the total cost, defined as the weighted sum of the population extinction risk and the economic cost of conservation effort. The optimal effort depends on the variance and the probability distribution of the noise, the relative importance of the population''s survival vs. the economic cost, the effectiveness of conservation effort, and the time scope over which we optimize. The analysis of dynamic programming illustrates that the choice of extinction risk function greatly affects the optimal effort level. The conservation effort level that is the best solution of a multiple-year optimization may be higher than that for the corresponding single-year optimization, if the population is relatively safe. However, the conservation level for the multiple-year optimization becomes lower than for the single-year optimization if the population is endangered. In a similar manner, the optimal conservation effort level for the problem with a short time scope is either higher or lower than that for the problem with a long time scope, depending on the extinction risk of the population. Next, for each parameter of the model, we define five different sensitivities of extinction probability or of the total cost. We then study the mean increase in the total cost caused by the uncertainty of parameters. To achieve the best conservation result, we need to invest the limited research effort to the parameter with the largest effect to the optimal effort level, rather than to those with large impacts on the extinction probability or on the total cost. The recommended policy should depend critically on the choice of the criterion to optimize, which shows the importance of theoretical study of the relationship in performing proper decision making in conservation practice. [Copyright &y& Elsevier]

Climate warming is of concern as a key factor in the worldwide decline in insect populations. In Japan, numbers of a common dragonfly in rice paddy fields, Sympetrum frequens, decreased sharply in the 1990s. Because S. frequens migrates to cooler mountains in summer, climate warming has been suggested as one of the main causes of the population decline in addition to agronomic factors. Here, we analysed the relation between summer temperatures and population densities of S. frequens and the related S. infuscatum, which does not migrate to mountains in summer, using published population monitoring data and temperature data from three regions (Toyama, Ishikawa, and Shizuoka) in Japan. Decadal differences in summer temperatures lay within the range of fluctuations among years, suggesting that an increase in summer temperatures cannot explain the past sharp population declines. However, regression analyses using monitoring data from Toyama showed that the population dynamics of both species in autumn are negatively correlated with summer temperatures in the same year. These results suggest that high temperatures in summer directly affect adult mortality to an extent that results in a decrease in population growth. [ABSTRACT FROM AUTHOR]

Abstract Predicting chemical mixture toxicity is an important issue for risk assessment. Loewe's concentration addition (CA) is a major model for predicting such toxicity. The CA is an additivity-based model, and if the results of toxicity test deviate from the CA prediction, it is considered that the toxic effect of the mixture is non-additive, and that "interaction" has played some role. In the present study, using as an example a biotic ligand model (BLM), which predicts metal toxicities, we theoretically investigated the toxic effect of mixture and found that the effects are almost always non-additive if the effects are evaluated by total metal concentrations, and the non-additivity is not derived by interactions among metals but by a combination of processes of metal kinetics. Once non-additive effects are observed in chemical mixture, it is often expected that there should be some complex toxic mechanisms or some toxic interaction. Our results suggest that the expectation may not be always true. Since at least two processes are entrained in the metal toxicity (metal speciation and binding of metals to biotic ligand in BLM framework), there is a possibility that the non-additivity is generated by the combination of processes and interaction is nothing to do with it. Our results imply that toxic effects of metal mixture can be predicted more easily than we generally expected. [ABSTRACT FROM AUTHOR]

The relative ability of the NOEC (no-observed-effect concentration) and ECx (the effect concentration corresponding to x-percent response) to determine benchmark toxicant concentrations, which are expected to ensure environmental safety, when there are large uncertainties in data was investigated with Monte Carlo simulations. We assumed a hypothetical true concentration-response function, and examined how random fluctuations of responses around the true responses affected the NOEC and ECx values. For assessment of the relative performances of these endpoints, we adopted two criteria: how large uncertainties were allowed for the minimum requirement for safety to be met, and the probability with which the estimated endpoints exceeded the minimum requirement for safety. The results of simulations indicated that, when there were small uncertainties in the data, performance of the NOEC was comparable with or slightly better than the ECx (EC5 and EC10) in providing benchmark concentrations that satisfied the minimum requirement for safety. With larger random variation of data (the coefficient of variation in responses between replicates within treatments or in the control was noticeably larger than 10 percent), the NOEC performed considerably worse than the ECx in terms of the frequency of simulated runs in which the endpoints exceeded the minimum requirement of safety. We conclude that the NOEC is as relevant as the ECx for risk assessment of chemicals under limited situations. [ABSTRACT FROM AUTHOR]

Application of herbicides to paddy fields in Japan has strong seasonality, and their environmental concentrations exhibit clear spatiotemporal variation. The authors developed an approach that combines a multimedia environmental exposure model (Grid- Catchment Integrated Modeling System) and density dynamics models for algae. This approach enabled assessment of ecological risk when the exposure concentration shows spatiotemporal variation. First, risk maps of 5 herbicides (pretilachlor, butachlor, simetryn, mefenacet, and esprocarb) were created from the spatial predictions of environmental concentrations and 50% inhibitory concentrations of the herbicides. Simulations of algal density dynamics at high-risk sites were then conducted by incorporating the predicted temporal dynamics of the environmental concentration of each herbicide at the sites. The results suggested that the risk of pretilachlor was clearly the highest of the 5 herbicides, in terms of both the spatial distributions and the temporal durations. The present study highlights the importance of integrating exposure models and effect models to clarify spatial and temporal risk and to develop management plans for chemical exposure that shows high spatiotemporal variation. [ABSTRACT FROM AUTHOR]

An amendment to this paper has been published and can be accessed via a link at the top of the paper. [ABSTRACT FROM AUTHOR]

Abstract: To succeed in combating lake eutrophication, cooperation of local inhabitants, small factories, and farmers in reducing phosphorus discharge is very important. But the willingness of each player to cooperate would depend on the cooperation of other players and on the level of environmental concern of the society in general. Here we study the integrated dynamics of people''s choice of behavior and the magnitude of eutrophication. Assumptions are: there are a number of players who choose between alternative options: a cooperative and environment-oriented option is more costly than the other. The decision of each player is affected by “social pressure” as well as by economical cost of the options. The lake pollution increases with the total phosphorus released, and a high pollution level in the lake would enhance the social pressure. The model includes a positive and a negative feedback loops which create diverse dynamical behavior. The model often shows bistability — having an equilibrium with a high level of cooperation among people and clean water, and the other equilibrium with low cooperation and polluted water, which are simultaneously stable. The model also shows fluctuation between a high and a low levels of cooperation in alternating years, cycle with a longer periodicity, or chaotic fluctuation. Conservatism of people stabilizes the system and sometimes helps maintaining cooperation. The system may show unexpected parameter dependence — the improved phosphorus removing efficiency might make water more polluted if it causes the decline in the environmental concern and cooperation among people. [Copyright &y& Elsevier]

Neonicotinoid insecticides pose risks that need to be managed for conservation of aquatic ecosystems. In this study, we evaluated the associations between the estimated environmental concentrations of two neonicotinoid insecticides (imidacloprid and dinotefuran) and the total abundances of seven functional feeding groups (FFGs) of benthic invertebrate communities in rivers in urban rice-paddy areas in four Japanese regions. Regional datasets of benthic invertebrate communities and environmental variables available for Japan were analyzed. The associations between neonicotinoid exposure and benthic functional groups in each region were evaluated by applying a partial redundancy analysis to each regional dataset. We then examined whether there was an interregionally consistent pattern in the observed associations to ascertain the general applicability of the associations. In two of the four regions, the associations of the total abundances of the seven FFGs with neonicotinoid concentrations were significant, suggesting negative effects of imidacloprid and dinotefuran on river ecosystem functions in these two Japanese regions. Moreover, although the associations in the remaining two regions were not significant, the pattern of associations of the total abundances of six of the FFGs (shredders, filter feeders, collectors, grazers, predators, and scavengers) with imidacloprid concentrations seemed to be consistent among the four regions. This implies broad-scale negative effects of imidacloprid on river ecosystem functions in urban rice-paddy areas. We did not, however, find any interregionally consistent patterns in the associations with dinotefuran concentrations. This may be related to the multicollinearity with the imidacloprid concentrations and/or the low maximum dinotefuran concentration relative to the toxicity values of this neonicotinoid. Therefore, the association between dinotefuran and river ecosystem functions requires additional investigation. We believe that this type of hypotheses-generating research using country-wide biomonitoring and exposure databases can be a great aid in future ecological risk assessment studies. Unlabelled Image • Neonicotinoid (NN) risk assessment requires the use of observational field datasets. • Data from country-wide biomonitoring and exposure databases were analyzed. • Associations of functional groups of benthic invertebrates with NNs were evaluated. • Consistency in the associations among four Japanese regions were also examined. • Broad-scale effects of imidacloprid use on river ecosystem functions were found. [ABSTRACT FROM AUTHOR]

• Abandoned farmlands in paddy rice field has increased due to the social, financial reasons. • Farmers should grow rice and clean their common waterway to maintain the landscape of paddy rice field. • We build an agent-based model to study balancing combinations of the two efforts. • We find that the neighbor-based management is effective to sustain the cultivation. The evolution of group cooperation is still an evolutionary puzzle and has been studied from the perspective of not only evolutionary ecology but also social sciences. Some socio-ecological problems are caused by collapse of group cooperation. By applying theoretical studies about the evolution of cooperation, we can elucidate what causes the problems and find solutions. One of the appropriate examples is maintaining rice paddy field landscapes, which are a grand spectacle in Asia, and some are UNESCO world heritage sites. These magnificent landscapes and the associated biodiversity are at risk of abandonment for social and financial reasons. Rice paddy fields can be preserved not only by regular cultivation, which requires farmers to invest effort in cultivation, but also by the maintenance of common facilities such as irrigation canals. To investigate how this landscape might be preserved, we developed an agent-based model in which each farmer makes two types of efforts: an effort for land cultivation and an effort for collective action such as common facility maintenance. Additionally, we consider the side effects of rice production such as field deterioration from abandonment and water use competition. These factors determine the utility of each player who imitates the level of efforts necessary to invest in land cultivation and common facility maintenance of one with higher utility. This decision-making of each player can be described by the evolutionary game theory. We find that maintenance effort promotes cultivation effort, but not vice versa, even though we usually consider that each farmer's cultivation effort makes rice field landscape sustainable. We also find that if players and their near neighbors are responsible for maintaining their common facilities together, they continue to maintain them and cultivate, but if all players are responsible for maintaining all facilities in the whole farmland, players are likely to quit facility maintenance and stop cultivation. Competition for water use among all players, however, promotes cultivation more than competition among neighbors only. Therefore, rice paddy field landscapes can be sustainable if neighbors, but not the whole players, are responsible for maintaining their common facilities and cooperate together, and if the water usage of all players, but not neighbors, influences the productivity of each rice field. [ABSTRACT FROM AUTHOR]

• Dragonfly abundance in Japan's agricultural landscapes has decreased. • We monitored the population density of the dragonfly Sympetrum frequens. • We estimated systemic insecticide use and analyzed its effect on the dragonfly. • The results suggest a negative effect of systemic insecticide use on population size. • Some agronomic factors need to be further examined as potential confounders. Since the mid-1990s, populations of the common Japanese dragonfly Sympetrum frequens in rice fields have declined severely. Application of systemic insecticides—especially fipronil—to nursery boxes of rice seedlings is suspected to be the main cause of the decline. However, until now there have been insufficient population data to test the causality. We conducted a dragonfly survey from 2009 to 2016 in four prefectures of Japan and compiled the data to enable the comparison of population growth rates along five main census routes over the years. We also estimated the use ratio of each insecticide applied to nursery boxes in rice fields (i.e., the area exposed to insecticide as a ratio of the total rice field area) by prefecture. We then statistically analyzed the effects of the insecticides on the dragonfly's population growth rates, taking into account the potential confounding factors based on current knowledge. There was a significant negative association between the annual increase in use ratio of the sum of systemic insecticides (e.g., fipronil, imidacloprid, and chlorantraniliprole) and the annual population growth rate of S. frequens. This association suggests that systemic insecticide use affected the decrease in population density of the dragonfly, although some agronomic factors need to be further examined as potential confounders. [ABSTRACT FROM AUTHOR]

Ecological niche models (ENMs) are widely used in spatial prioritization for biodiversity conservation (e.g. selecting conservation areas). However, it is unclear whether ENMs are always beneficial for such purposes. We quantified the benefit of using ENMs in conservation prioritization, comparing the numbers of species covered by conservation areas selected on the basis of probabilities estimated by ENMs (ENM approach) and those selected on the basis of raw observation data (raw-data approach), while controlling survey range, survey bias, and target size of conservation area. We evaluated three ENM algorithms (GLM, GAM, and random forests). We used virtual community data generated by simulation for the evaluation. ENM approach was effective when survey bias is strong, survey range is narrow, and target size of conservation area is moderate. The percentage of cases in which the ENM approach outperformed the raw-data approach ranged from 0.0 to 33% (GLM), 31% (GAM), and 75% (random forests) depending on conditions. The number of rare species (< 20 presence records) included in the conservation area based on the ENM approach was less than, or the same as, that of the raw-data approach. The unexpectedly limited cases in which the ENM approach was effective in the present research may depend on the conservation target we used (to cover as many species as possible in conservation area). Our results highlight urgent need for evaluating ENM's effectiveness under other conservation targets for wise use of ENM in conservation prioritization. [ABSTRACT FROM AUTHOR]

Field surveys provide valuable empirical information about the effects of heavy metals on the biological integrity of river ecosystems. To evaluate the effect of nickel (Ni) on aquatic organisms, we conducted field surveys of benthic invertebrates and Ni concentrations at 45 sites in 19 rivers in Japan. We examined the relationships between 11 structural or functional measures of benthic invertebrate communities and free Ni ion concentrations with a 90th quantile regression model. Among the measures, Ephemeroptera, Plecoptera, and Trichoptera (EPT) richness, total wet biomass of all invertebrates, and total abundance of filter feeders were negatively associated with free Ni ion concentrations. The total abundance of mud burrowers and their percentage contribution to the abundance of all invertebrates as well as the total abundances of collector‐gatherers and predators were positively associated with the Ni ion concentrations. The free ion concentrations of Ni associated with a 5% reduction of one of the 3 measures from its 90th quantile value at reference sites (EC5) were estimated to be 0.2 to 7.6 µg/L. The point estimates of EC5 were similar in order of magnitude to the environmental quality standard for Ni in the European Union. However, the usefulness of simple point estimates of effective concentrations based on quantile regression lines should be carefully examined because the uncertainties in our EC5 values were large. Environ Toxicol Chem 2019;38:1728–1737. © 2019 SETAC [ABSTRACT FROM AUTHOR]

Dispersal as well as population growth is a key demographic process that determines population dynamics. However, determining the effects of environmental covariates on dispersal from spatial‐temporal abundance proxy data is challenging owing to the complexity of model specification for directional dispersal permeability and the extremely high computational loads for numerical integration. In this paper, we present a case study estimating how environmental covariates affect the dispersal of Japanese sika deer by developing a spatially explicit state‐space matrix model coupled with an improved numerical integration technique (Markov chain Monte Carlo with particle filters). In particular, we explored the environmental drivers of inhomogeneous range expansion, characteristic of animals with short dispersal. Our model framework successfully reproduced the complex population dynamics of sika deer, including rapid changes in densely populated areas and distribution fronts within a decade. Furthermore, our results revealed that the inhomogeneous range expansion of sika deer seemed to be primarily caused by the dispersal process (i.e., movement barriers in fragmented forests) rather than population growth. Our state‐space matrix model enables the inference of population dynamics for a broad range of organisms, even those with low dispersal ability, in heterogeneous landscapes, and could address many pressing issues in conservation biology and ecosystem management. We present a case study estimating how environmental elements affect the dispersal of Japanese sika deer by developing a spatially explicit state‐space matrix model coupled with an improved numerical integration technique. Our results revealed that the inhomogeneous range expansion of sika deer was primarily caused by the dispersal process (i.e., movement barriers in fragmented forests) rather than population growth. [ABSTRACT FROM AUTHOR]

We review and synthesize recent developments in the study of the invasion of communities in heterogeneous environments, considering both the invasibility of the community and impacts to the community. We consider both empirical and theoretical studies. For each of three major kinds of environmental heterogeneity (temporal, spatial and invader-driven), we find evidence that heterogeneity is critical to the invasibility of the community, the rate of spread, and the impacts on the community following invasion. We propose an environmental heterogeneity hypothesis of invasions, whereby heterogeneity both increases invasion success and reduces the impact to native species in the community, because it promotes invasion and coexistence mechanisms that are not possible in homogeneous environments. This hypothesis could help to explain recent findings that diversity is often increased as a result of biological invasions. It could also explain the scale dependence of the diversity–invasibility relationship. Despite the undoubted importance of heterogeneity to the invasion of communities, it has been studied remarkably little and new research is needed that simultaneously considers invasion, environmental heterogeneity and community characteristics. As a young field, there is an unrivalled opportunity for theoreticians and experimenters to work together to build a tractable theory informed by data. [ABSTRACT FROM AUTHOR]