Social network properties within a fish assemblage invaded by non-native sunbleak Leucaspius delineatus

Network theory is commonly used to reveal social interactions and the organisation of interconnected nodes—but has not yet been applied to animal invasions. Non-native species invasions are now considered one of the foremost threats to natural ecosystems and biodiversity. This is the first attempt to assess social network properties within a freshwater fish assemblage invaded by a non-native fish species. We show that invasive sunbleak Leucaspius delineatus is socially more strongly interconnected with native species than the native species with each other. The social networks also reveal characteristics of a ‘small world’ such as low clustering coefficients C and short path lengths L. The findings may indicate potential traits of successful invaders and the implication for the spread of pathogens between individuals within a group of animals that contain a non-native invasive species. The success of establishment and subsequent invasion may be highlighted not only by the capacity of the new species to adapt to the new environment, but also in its capacity to penetrate the social circle of the native community.     

Worldwide effects of non-native species on species–area relationships

Non-native species have invaded most parts of the world, and the invasion process is expected to continue and accelerate. Because many invading non-native species are likely to become permanent inhabitants, future consideration of species-area relationships (SARs) should account for non-native species, either separately or jointly with native species. If non-native species occupy unused niches and space in invaded areas and extinction rate of native species remains low (especially for plants), the resultant SARs (with both native and non-native species) will likely be stronger. We used published and newly compiled data (35 data sets worldwide) to examine how species invasions affect SARs across selected taxonomic groups and diverse ecosystems around the world. We first examined the SARs for native, non-native, and all species. We then investigated with linear regression analyses and paired or unpaired t tests how degree of invasion (proportion of non-native species) affected postinvasion SARs. Postinvasion SARs for all species (native plus non-native) became significantly stronger as degree of invasion increased (r² = 0.31, p = 0.0006), thus, reshaping SARs worldwide. Overall, native species still showed stronger and less variable SARs. Also, slopes for native species were steeper than for non-native species (0.298 vs. 0.153). There were some differences among non-native taxonomic groups in filling new niches (especially for birds) and between islands and mainland ecosystems. We also found evidence that invasions may increase equilibrial diversity. Study of such changing species–area curves may help determine the probability of future invasions and have practical implications for conservation.     

Eradication via destratification: whole-lake mixing to selectively remove rainbow smelt, a cold-water invasive species

Invasive species can have severe effects on aquatic ecosystems. After invasions occur, eradication should be considered whenever the potential loss of ecosystem services outweighs the cost of the eradication method. Here we evaluate the possibility of destratifying Crystal Lake, Wisconsin, USA, to eradicate the invasive fish rainbow smelt (Osmerus mordax). We modeled the effects of three destratification scenarios (non-, low-, and high-mixing) using both physical and biological models. Field observations were used to calibrate the models. Water temperatures estimated from 18 unique DYRESM simulations were used in a bioenergetics model to estimate growth of five age classes of rainbow smelt under normal and destratified conditions. Our simulations indicate that destratification can eliminate optimal rainbow smelt thermal habitat resulting in mortality. Destratified lake temperatures also surpassed several physiological critical temperatures. Bioenergetics simulations predicted a weight loss of 45-55% in yearling and adult rainbow smelt. We found that destratification is potentially effective for eradicating cold-water species in temperate lakes.     

Invasive species in Europe: ecology, status, and policy

Globalization of trade and travel has facilitated the spread of non-native species across the earth. A proportion of these species become established and cause serious environmental, economic, and human health impacts. These species are referred to as invasive, and are now recognized as one of the major drivers of biodiversity change across the globe. As a long-time centre for trade, Europe has seen the introduction and subsequent establishment of at least several thousand non-native species. These range in taxonomy from viruses and bacteria to fungi, plants, and animals. Although invasive species cause major negative impacts across all regions of Europe, they also offer scientists the opportunity to develop and test theory about how species enter and leave communities, how non-native and native species interact with each other, and how different types of species affect ecosystem functions. For these reasons, there has been recent growth in the field of invasion biology as scientists work to understand the process of invasion, the changes that invasive species cause to their recipient ecosystems, and the ways that the problems of invasive species can be reduced. This review covers the process and drivers of species invasions in Europe, the socio-economic factors that make some regions particularly strongly invaded, and the ecological factors that make some species particularly invasive. We describe the impacts of invasive species in Europe, the difficulties involved in reducing these impacts, and explain the policy options currently being considered. We outline the reasons that invasive species create unique policy challenges, and suggest some rules of thumb for designing and implementing management programs. If new management programs are not enacted in Europe, it is inevitable that more invasive species will arrive, and that the total economic, environmental, and human health impacts from these species will continue to grow.     

Assessing ecosystem vulnerability to invasive rusty crayfish (Orconectes rusticus)

Despite the widespread introduction of nonnative species and the heterogeneity of ecosystems in their sensitivity to ecological impacts, few studies have assessed ecosystem vulnerability to the entire invasion process, from arrival to establishment and impacts. Our study addresses this challenge by presenting a probabilistic, spatially explicit approach to predicting ecosystem vulnerability to species invasions. Using the freshwater-rich landscapes of Wisconsin, USA, we model invasive rusty crayfish (Orconectes rusticus) as a function of exposure risk (i.e., likelihood of introduction and establishment of O. rusticus based on a species distribution model) and the sensitivity of the recipient community (i.e., likelihood of impacts on native O. virilis and O. propinquus based on a retrospective analysis of population changes). Artificial neural networks predicted that approximately 10% of 4200 surveyed lakes (n = 388) and approximately 25% of mapped streams (23 523 km total length) are suitable for O. rusticus introduction and establishment. A comparison of repeated surveys before vs. post-1985 revealed that O. virilis was six times as likely and O. propinquus was twice as likely to be extirpated in streams invaded by O. rusticus, compared to streams that were not invaded. Similarly, O. virilis was extirpated in over three-quarters of lakes invaded by O. rusticus compared to half of the uninvaded lakes, whereas no difference was observed for O. propinquus. We identified 115 lakes (approximately 3% of lakes) and approximately 5000 km of streams (approximately 6% of streams) with a 25% chance of introduction, establishment, and extirpation by O. rusticus of either native congener. By identifying highly vulnerable ecosystems, our study offers an effective strategy for prioritizing on-the-ground management action and informing decisions about the most efficient allocation of resources. Moreover, our results provide the flexibility for stakeholders to identify priority sites for prevention efforts given a maximum level of acceptable risk or based on budgetary or time restrictions. To this end, we incorporate the model predictions into a new online mapping tool with the intention of closing the communication gap between academic research and stakeholders that requires information on the prospects of future invasions.     

Earthworm Invasion as the Driving Force Behind Plant Invasion and Community Change in Northeastern North American Forests

Abstract:  Identification of factors that drive changes in plant community structure and contribute to decline and endangerment of native plant species is essential to the development of appropriate management strategies. Introduced species are assumed to be driving causes of shifts in native plant communities, but unequivocal evidence supporting this view is frequently lacking. We measured native vegetation, non-native earthworm biomass, and leaf-litter volume in 15 forests in the presence and absence of 3 non-native plant species ( Microstegium vimineum, Alliaria petiolata, Berberis thunbergii ) to assess the general impact of non-native plant and earthworm invasions on native plant communities in northeastern United States. Non-native plant cover was positively correlated with total native plant cover and non-native earthworm biomass. Earthworm biomass was negatively associated with cover of native woody and most herbaceous plants and with litter volume. Graminoid cover was positively associated with non-native earthworm biomass and non-native plant cover. These earthworm-associated responses were detected at all sites despite differences in earthworm species and abundance, composition of the native plant community, identity of invasive plant species, and geographic region. These patterns suggest earthworm invasion, rather than non-native plant invasion, is the driving force behind changes in forest plant communities in northeastern North America, including declines in native plant species, and earthworm invasions appear to facilitate plant invasions in these forests. Thus, a focus on management of invasive plant species may be insufficient to protect northeastern forest understory species.     

Aquatic plant community invasibility and scale-dependent patterns in native and invasive species richness

Invasive species richness often is negatively correlated with native species richness at the small spatial scale of sampling plots, but positively correlated in larger areas. The pattern at small scales has been interpreted as evidence that native plants can competitively exclude invasive species. Large-scale patterns have been understood to result from environmental heterogeneity, among other causes. We investigated species richness patterns among submerged and floating-leaved aquatic plants (87 native species and eight invasives) in 103 temperate lakes in Connecticut (northeastern USA) and found neither a consistently negative relationship at small (3-m2) scales, nor a positive relationship at large scales. Native species richness at sampling locations was uncorrelated with invasive species richness in 37 of the 60 lakes where invasive plants occurred; richness was negatively correlated in 16 lakes and positively correlated in seven. No correlation between native and invasive species richness was found at larger spatial scales (whole lakes and counties). Increases in richness with area were uncorrelated with abiotic heterogeneity. Logistic regression showed that the probability of occurrence of five invasive species increased in sampling locations (3 m2, n = 2980 samples) where native plants occurred, indicating that native plant species richness provided no resistance against invasion. However, the probability of three invasive species' occurrence declined as native plant density increased, indicating that density, if not species richness, provided some resistance with these species. Density had no effect on occurrence of three other invasive species. Based on these results, native species may resist invasion at small spatial scales only in communities where density is high (i.e., in communities where competition among individuals contributes to community structure). Most hydrophyte communities, however, appear to be maintained in a nonequilibrial condition by stress and/or disturbance. Therefore, most aquatic plant communities in temperate lakes are likely to be vulnerable to invasion.     

Rethinking the native range concept

A species is not native outside its native range, but native range is not precisely defined. The invasion literature contains wide discussion of the core concepts such as naturalization, invasiveness, and ecological impact, but the concept of native range has received so little attention that a formal definition does not exist. I considered, among other impediments to a formal definition of native range, the sometimes arbitrariness of the spatial and temporal limits assigned to native range. Broad questions that remain include whether invasion theory can be used to define the native range for species without non-native ranges.     

Effectiveness of terrestrial protected areas for conservation of lake fish communities

Freshwater protected areas are rare even though freshwater ecosystems are among the most imperiled in the world. Conservation actions within terrestrial protected areas (TPAs) such as development or resource extraction regulations may spill over to benefit freshwater ecosystems within their boundaries. Using data from 175 lakes across Ontario, Canada, we compared common indicators of fish‐assemblage status (i.e., species richness, Shannon diversity index, catch per unit effort, and normalized‐length size spectrum slopes) to evaluate whether TPAs benefit lake fish assemblages. Nearest neighbor cluster analysis was used to generate pairs of lakes: inside versus outside, inside versus bordering, and bordering versus outside TPAs based on lake characteristics. The diversity and abundance indicators did not differ significantly across comparisons, but normalized‐length size spectrum slopes (NLSS) were significantly steeper in lakes outside parks. The latter indicated assemblage differences (greater abundances of small‐bodied species) and less‐efficient energy transfer through the trophic levels of assemblages outside parks. Although not significantly different, pollution‐ and turbidity‐tolerant species were more abundant outside parks, whereas 3 of the 4 pollution‐intolerant species were more abundant within parks. Twenty‐one percent of the difference in slopes was related to higher total dissolved solids concentrations and angling pressure. Our results support the hypothesis that TPAs benefit lake fish assemblages and suggest that NLSS slopes are informative indicators for aquatic protected area evaluations because they represent compositional and functional aspects of communities.     

Native fish diversity alters the effects of an invasive species on food webs

Aquatic communities have been altered by invasive species, with impacts on native biodiversity and ecosystem function. At the same time, native biodiversity may mitigate the effects of an invader. Common carp (Cyprinus carpio) is a ubiquitous, invasive fish species that strongly influences community and ecosystem processes. We used common carp to test whether the potential effects of an invasive species are altered across a range of species diversity in native communities. In mesocosms, treatments of zero, one, three, and six native fish species were used to represent the nested subset patterns observed in fish communities of lakes in Illinois, USA. The effect of the invader was tested across fish richness treatments by adding common carp to the native community and substituting native biomass with common carp. Native species and intraspecific effects reduced invader growth. The invader reduced native fish growth; however, the negative effect was minimized with increasing native richness. The zooplankton grazer community was modified by a top-down effect from the invader that increased the amount of phytoplankton. Neither the invader nor richness treatments influenced total phosphorus or community metabolism. Overall, the invader reduced resources for native species; and the effect scaled with how the invader was incorporated into the community. Higher native diversity mitigated the impact of the invader, confirming the need to consider biodiversity when predicting the impacts of invasive species.     

A simulation model to evaluate the impacts of invasive earthworms on soil carbon dynamics

Recent studies have reported that earthworm invasions alter native communities and impact nutrient cycling in terrestrial ecosystems. We developed a simulation model to evaluate the potential impacts of earthworm invasions on carbon dynamics, taking into consideration earthworm feeding strategies and priming effects on the microorganisms through their casting activities. Responses of carbon stocks (forest litter, soil organic matter, microbial biomass and earthworm populations) and carbon fluxes (litter decomposition, earthworm consumption, and microbial respiration) were used to evaluate an earthworm invasion of a forest ecosystem. Data from a northern temperate forest (Arnot Forest, New York) were adapted for model calibration and evaluation. Simulation results suggest that the impact and outcome of earthworm invasions are affected by pre-invasion resource availability (litter and soil organic matter), invasive earthworm assemblages (particularly feeding strategy), and invasion history (associated with earthworm population dynamics). The abovementioned factors may also determine invasion progress of earthworm species. The accuracy of the model could be improved by the addition of environmental modules (e.g., soil water regimes), precise parameters accounting for individual species attributes under different environmental conditions (e.g. utilization ability of different types of food resources), as well as earthworm population dynamics (size and structure) and interactions with predators and other invasive/indigenous species during the invasion progress. Such an earthworm invasion model could provide valuable evaluation of the complicated responses of carbon dynamics to earthworm invasions in a range of forest ecosystems, particularly under global change scenarios.     

Predicting the Range of Chinese Mitten Crabs in Europe

Abstract:  Ecological niche modeling provides a means for predicting the potential future distribution of a nonindigenous species based on environmental characteristics of the species' native range. We applied this method to the Chinese mitten crab (Eriocheir sinensis) , a catadromous crustacean with a long history of invasion in Europe. We used genetic algorithm for rule-set prediction to predict the potential European distribution of mitten crab based on its distribution in 42 locations in its native Asia. The climatic variables, air temperature, number of days, amount of precipitation, and wetness index, contributed significantly to predictions of native distribution limits. Although the genetic algorithm for rule-set prediction model was developed for the native range, the species' extensive distribution in Europe ( n = 434) allowed independent validation of the predictions. Application of the model to Europe was successful, with 84% of occurrences in regions predicted to be suitable by >80% of the models and <4% of occurrences in areas predicted suitable by <50% of the models (mainly along the northern range). At the watershed scale, areas with established mitten crab populations had significantly higher habitat matching than sites that were not invaded. The independent validation of the Asian-based model by the European distribution revealed that predictions were highly accurate. The model also identified large areas of Europe, particularly along the Mediterranean coast, as vulnerable to future invasion. These predictions can be used to develop strategies to control the spread of mitten crab by preventing introductions into vulnerable areas.     

Effect of Invasive Plant Species on Temperate Wetland Plant Diversity

Abstract:  Invasive species are a major threat to global biodiversity and an important cause of biotic homogenization of ecosystems. Exotic plants have been identified as a particular concern because of the widely held belief that they competitively exclude native plant species. We examined the correlation between native and invasive species richness in 58 Ontario inland wetlands. The relationship between exotic and native species richness was positive even when we controlled for important covarying factors. In addition, we examined the relationship between the abundance of four native species (  Typha latifolia, T. angustifolia, Salix petiolaris, Nuphar variegatum ) and four invasive species (  Lythrum salicaria, Hydrocharis morsus-ranae, Phalaris arundinacea, Rhamnus frangula ) that often dominate temperate wetlands and native and rare native species richness. Exotic species were no more likely to dominate a wetland than native species, and the proportion of dominant exotic species that had a significant negative effect on the native plant community was the same as the proportion of native species with a significant negative effect. We conclude that the key to conservation of inland wetland biodiversity is to discourage the spread of community dominants, regardless of geographical origin.     

Invasion, Disturbance, and Competition: Modeling the Fate of Coastal Plant Populations

Abstract:  Wetland habitats are besieged by biotic and abiotic disturbances such as invasive species, hurricanes, habitat fragmentation, and salinization. Predicting how these factors will alter local population dynamics and community structure is a monumental challenge. By examining ecologically similar congeners, such as Iris hexagona and I. pseudacorus (which reproduce clonally and sexually and tolerate a wide range of environmental conditions), one can identify life-history traits that are most influential to population growth and viability. We combined empirical data and stage-structured matrix models to investigate the demographic responses of native ( I. hexagona ) and invasive ( I. pseudacorus ) plant populations to hurricanes and salinity stress in freshwater and brackish wetlands. In our models I. hexagona and I. pseudacorus responded differently to salinity stress, and species coexistence was rare. In 82% of computer simulations of freshwater marsh, invasive iris populations excluded the native species within 50 years, whereas native populations excluded the invasive species in 99% of the simulations in brackish marsh. The occurrence of hurricanes allowed the species to coexist, and species persistence was determined by the length of time it took the ecosystem to recover. Rapid recovery (2 years) favored the invasive species, whereas gradual recovery (30 years) favored the native species. Little is known about the effects of hurricanes on competitive interactions between native and invasive plant species in marsh ecosystems. Our models contribute new insight into the relationship between environmental disturbance and invasion and demonstrate how influential abiotic factors such as climate change will be in determining interspecific interactions.     

Long-term dynamics of biotic and abiotic resistance to exotic species invasion in restored vernal pool plant communities

Invasion of native ecosystems by exotic species can seriously threaten native biodiversity, alter ecosystem function, and inhibit conservation. Moreover, restoration of native plant communities is often impeded by competition from exotic species. Exotic species invasion may be limited by unfavorable abiotic conditions and by competition with native species, but the relative importance of biotic and abiotic factors remains controversial and may vary during the invasion process. We used a long-term experiment involving restored vernal pool plant communities to characterize the temporal dynamics of exotic species invasion, and to evaluate the relative support for biotic and abiotic factors affecting invasion resistance. Experimental pools (n=256) were divided among controls and several seeding treatments. In most treatments, native vernal pool species were initially more abundant than exotic species, and pools that initially received more native seeds exhibited lower frequencies of exotic species over time. However, even densely seeded pools were eventually dominated by exotic species, following extreme climatic events that reduced both native and exotic plant densities across the study site. By the sixth year of the experiment, most pools supported more exotics than native vernal pool species, regardless of seeding treatment or pool depth. Although deeper pools were less invaded by exotic species, two exotics (Hordeum marinum and Lolium multiflorum) were able to colonize deeper pools as soon as the cover of native species was reduced by climatic extremes. Based on an information-theoretic analysis, the best model of invasion resistance included a nonlinear effect of seeding treatment and both linear and nonlinear effects of pool depth. Pool depth received more support as a predictor of invasion resistance, but seeding intensity was also strongly supported in multivariate models of invasion, and was the best predictor of resistance to invasion by H. marinum and L. multilorum. We conclude that extreme climatic events can facilitate exotic species invasions by both reducing abiotic constraints and weakening biotic resistance to invasion.     

Assessing the Effects of Climate Change on Aquatic Invasive Species

Abstract:  Different components of global environmental change are typically studied and managed independently, although there is a growing recognition that multiple drivers often interact in complex and nonadditive ways. We present a conceptual framework and empirical review of the interactive effects of climate change and invasive species in freshwater ecosystems. Climate change is expected to result in warmer water temperatures, shorter duration of ice cover, altered streamflow patterns, increased salinization, and increased demand for water storage and conveyance structures. These changes will alter the pathways by which non-native species enter aquatic systems by expanding fish-culture facilities and water gardens to new areas and by facilitating the spread of species during floods. Climate change will influence the likelihood of new species becoming established by eliminating cold temperatures or winter hypoxia that currently prevent survival and by increasing the construction of reservoirs that serve as hotspots for invasive species. Climate change will modify the ecological impacts of invasive species by enhancing their competitive and predatory effects on native species and by increasing the virulence of some diseases. As a result of climate change, new prevention and control strategies such as barrier construction or removal efforts may be needed to control invasive species that currently have only moderate effects or that are limited by seasonally unfavorable conditions. Although most researchers focus on how climate change will increase the number and severity of invasions, some invasive coldwater species may be unable to persist under the new climate conditions. Our findings highlight the complex interactions between climate change and invasive species that will influence how aquatic ecosystems and their biota will respond to novel environmental conditions.     

Multi-trophic invasion resistance in Hawaii: bioacoustics, field surveys, and airborne remote sensing

We used airborne imaging spectroscopy and scanning light detection and ranging (LiDAR), along with bioacoustic recordings, to determine how a plant species invasion affects avian abundance and community composition across a range of Hawaiian submontane ecosystems. Total avian abundance and the ratio of native to exotic avifauna were highest in habitats with the highest canopy cover and height. Comparing biophysically equivalent sites, stands dominated by native Metrosideros polymorpha trees hosted larger native avian communities than did mixed stands of Metrosideros and the invasive tree Morella faya. A multi-trophic analysis strongly suggests that native avifauna provide biotic resistance against the invasion of Morella trees and exotic birds, thus slowing invasion "meltdowns" that disrupt the functioning of native Hawaiian ecosystems.     

Synergisms among Habitat Fragmentation, Livestock Grazing, and Biotic Invasions in Southwestern Australia

Abstract: The agricultural development of southern Australia over the past 200 years has resulted in extensively fragmented systems, often with only small, isolated remnants of native vegetation remaining. Grazing by sheep and cattle has affected both the remaining fragments and the surrounding matrix, and non-native plant and animal species have had dramatic effects on the native biota. Invasive plant species have the potential to significantly alter ecosystem composition and functioning, and invasive animals, particularly rabbits ( Oryctolagus cuniculatus ), foxes (    Vulpes vulpes ) and cats (    Felis catus ) effectively alter habitat and drive native fauna to local extinction. These different influences often interact. For instance, smaller fragments are often more prone to plant invasion and are more likely to have been grazed in the past. Invasion of plant species is often linked with livestock grazing or rabbit invasion, and other higher-order interactions are also apparent. Classical fragmentation studies that concentrate on parameters such as habitat area and isolation but ignore changes in habitat condition brought about by livestock and invasive species are unlikely to yield meaningful results. Similarly, management of fragmented ecosystems must account for not only the spatial characteristics of the remaining habitat but also the importance of other influences, particularly those that impinge on fragments from the surrounding matrix.     

酸雨对外来植物入侵的影响

酸雨和外来种入侵都是全球关注的问题。结合外来入侵植物的生态适应特性以及酸雨的危害特征,系统分析了酸雨对外来植物入侵产生的影响。酸雨对外来植物入侵的影响是复杂多样的。酸雨导致群落冠层稀疏,群落透光率增加,加之氮沉降后土壤、水体氮素的增加,有利于生长力强的外来喜阳植物入侵;酸雨加速土壤酸化,促使基本离子淋失以及A1毒等危害植物的生长发育,植物的内源激素以及化感作用发生改变,适应力和耐受力强的外来植物在与本地植物竞争中处于相对优势而成为入侵种;酸雨以及外来植物入侵改变了土壤微生物群落结构,影响本地植物的生长而促使外来植物的入侵。     

Microplastic contamination in Great Lakes fish

Freshwater ecosystems, generally adjacent to human population and more contaminated relative to adjacent marine ecosystems, are vulnerable to microplastic contamination. We sampled 7 species of fish from Lake Ontario and Lake Superior and assessed their gastrointestinal (GI) tracts to quantify ingested microplastics and other anthropogenic particles. A subset of the microparticles were chemically analyzed to confirm polymer types and anthropogenic origins. We documented the highest concentration of microplastics and other anthropogenic microparticles ever reported in bony fish. We found 12,442 anthropogenic microparticles across 212 fish (8 species) from nearshore Lake Ontario, 943 across 50 fish (1 species) from Humber River, and 3094 across 119 fish (7 species) from Lake Superior. Fish from Lake Ontario had the greatest mean abundance of anthropogenic microparticles in their GI tracts (59 particles/fish [SD 104]), with up to 915 microparticles in a single fish. Fish from Lake Superior contained a mean [SD] of 26 [74] particles/fish, and fish from Humber River contained 19 [14] particles/fish. Most particles were microfibers. Overall, ≥90% of particles were anthropogenic, of which 35-59% were microplastics. Polyethylene (24%), polyethylene terephthalate (20%), and polypropylene (18%) were the most common microplastics. Ingestion of anthropogenic particles was significantly different among species within Lake Ontario (p < 0.05), and the abundance of anthropogenic particles increased as fish length increased in Lake Ontario (ρ = 0.62). Although we cannot extrapolate the concentration of microplastics in the water and sediments of these fish, the relatively high abundance of microplastics in the GI tracts of fish suggests environmental exposure may be above threshold concentrations for risk.