How population loss through habitat boundaries determines the dynamics of a predator–prey system

The increased persistence of predator–prey systems when interactions are distributed through the space has been acknowledged by both empirical and theoretical studies. One salient feature of predator–prey interactions in heterogeneous space, for example, is the existence of cycles with reduced amplitude when compared with a homogeneous landscape. Although the role of spatial interactions in shaping the dynamics of predator–prey systems has been extensively studied, still very few works have focused on the effects of habitat loss and fragmentation on these systems. In this work, we study the population dynamics of a predator–prey system in a single finite habitat with flux at the boundaries. Species movement and growth are described through a reaction–diffusion model with Rosenzweig–MacArthur type local interactions. Conforming with the existing literature, we find that the reduction of habitat size, or increasing of species movement rates equivalently, has the potential to decrease the amplitude of oscillations and even bring the system to a steady coexistence equilibrium above a threshold. We observe, however, situations in which this trend is reversed. This occurs when species movement rates and response at patch boundaries interact to induce non-trivial patterns of species distributions. These distributions are characterized by anti-correlation between predator and prey, creating then spatial refugia for prey. Our results highlight the role of population loss through habitat boundaries in determining the dynamics of predator–prey interactions.     

Population consequences of movement decisions in a patchy landscape

Complex, human‐dominated landscapes provide unique challenges to animals. In landscapes fragmented by human activity, species whose home ranges ordinarily consist of continuous habitat in pristine environments may be forced to forage among multiple smaller habitat patches embedded in an inhospitable environment. Furthermore, foragers often must decide whether to traverse a heterogeneous suite of landscape elements that differ in risk of predation or energetic costs. We modeled population consequences of foraging decisions for animals occupying patches embedded in a heterogeneous landscape. In our simulations, animals were allowed to use three different rules for moving between patches: a) optimal selection resulting from always choosing the least‐cost path; b) random selection of a movement path; and c) probabilistic selection in which path choice was proportional to an animal's probability of survival while traversing the path. The resulting distribution of the population throughout the landscape was dependent on the movement rule used. Least‐cost movement rules (a) produced landscapes that contained the highest average density of consumers per patch. However, optimal movement resulted in an all‐or‐none pattern of occupancy and a coupling of occupied patches into pairs that effectively reduced the population to a set of sub‐populations. Random and probabilistic rules, (b and c), in relatively safe landscapes produced similar average densities and 100% occupancy of patches. However, as the level of risk associated with travel between patches increased, random movement resulted in an all‐or‐none occupancy pattern while occupied patches in probabilistic populations went extinct independently of the other patches. Our results demonstrate strong effects of inter‐patch heterogeneity and movement decisions on population dynamics, and suggest that models investigating the persistence of species in complex landscapes should take into account the effects of the intervening landscape on behavioral decisions affecting animal movements between patches.     

Behavioral states help translate dispersal movements into spatial distribution patterns of floaters

Within the field of spatial ecology, it is important to study animal movements in order to better understand population dynamics. Dispersal is a nonlinear process through which different behavioral mechanisms could affect movement patterns. One of the most common approaches to analyzing the trajectories of organisms within patches is to use random-walk models to describe movement features. These models express individual movements within a specific area in terms of random-walk parameters in an effort to relate movement patterns to the distributions of organisms in space. However, only using the movement trajectories of individuals to predict the spatial spread of animal populations may not fit the complex distribution of individuals across heterogeneous environments. When we empirically tested the results from a random-walk model (a residence index) used to predict the spatial equilibrium distribution of individuals, we found that the index severely underestimated the spatial spread of dispersing individuals. We believe this is because random-walk models only account for the effects of environmental conditions on individual movements, completely overlooking the crucial influence of behavior changes over time. In the future, both aspects should be accounted for when predicting general rules of (meta)population abundance, distribution, and dynamics from patterns of animal movements.     

Linking habitat structure and orientation in an arboreal species Gehyra variegata (Gekkonidae)

Understanding how organisms move through landscapes is important for predicting the effects of landscape structure on the population dynamics and spatial distribution of organisms. Despite the accepted importance, the ability to orientate when moving is a poorly studied phenomenon. In this study we report on a translocation experiment in which we used fluorescent powder to study the ability of the arboreal gecko Gehyra variegata to orientate successfully between trees. The relocation experiment demonstrated the ability of translocated geckos to return to the tree of initial capture. Further, we investigated the set of rules geckos employ, when travelling through their structured habitat. Computer simulations relating capture-mark-recapture data to structural components of the habitat revealed that movement rules taking vision into account showed the best fit to the empirical data. The movement rule: "move randomly to one of the three next neighbouring trees that are visible" described the observed movement best. This movement rule connects all trees in the habitat and lowers the predation risk during movement.     

Lost in space? Searching for directions in the spatial modelling of individuals,populations and species ranges

The workshop ‘Spatial models in animal ecology, management and conservation’ held at Silwood Park (UK), 9–11 March 2010, aimed to synthesize recent progress in modelling the spatial dynamics of individuals, populations and species ranges and to provide directions for research. It brought together marine and terrestrial researchers working on spatial models at different levels of organization, using empirical as well as theory-driven approaches. Different approaches, temporal and spatial scales, and practical constraints predominate at different levels of organization and in different environments. However, there are theoretical concepts and specific methods that can fruitfully be transferred across levels and systems, including: habitat suitability characterization, movement rules, and ways of estimating uncertainty.     

Modeling bird species distribution change in fire prone Mediterranean landscapes: incorporating species dispersal and landscape dynamics

Species distribution models (SDMs) have traditionally been founded on the assumption that species distributions are in equilibrium with environmental conditions and that these species–environment relationships can be used to estimate species responses to environmental changes. Insight into the validity of this assumption can be obtained from comparing the performance of correlative species distribution models with more complex hybrid approaches, i.e. correlative and process‐based models that explicitly include ecological processes, thereby accounting for mismatches between habitat suitability and species occupancy patterns. Here we compared the ability of correlative SDMs and hybrid models, which can accommodate non‐equilibrium situations arising from dispersal constraints, to reproduce the distribution dynamics of the ortolan bunting Emberiza hortulana in highly dynamic, early successional, fire driven Mediterranean landscapes. Whereas, habitat availability was derived from a correlative statistical SDM, occupancy was modeled using a hybrid approach combining a grid‐based, spatially‐explicit population model that explicitly included bird dispersal with the correlative model. We compared species occupancy patterns under the equilibrium assumption and different scenarios of species dispersal capabilities. To evaluate the predictive capability of the different models, we used independent species data collected in areas affected to different degree by fires. In accordance with the view that disturbance leads to a disparity between the suitable habitat and the occupancy patterns of the ortolan bunting, our results indicated that hybrid modeling approaches were superior to correlative models in predicting species spatial dynamics. Furthermore, hybrid models that incorporated short dispersal distances were more likely to reproduce the observed changes in ortolan bunting distribution patterns, suggesting that dispersal plays a key role in limiting the colonization of recently burnt areas. We conclude that SDMs used in a dynamic context can be significantly improved by using combined hybrid modeling approaches that explicitly account for interactions between key ecological constraints such as dispersal and habitat suitability that drive species response to environmental changes.     

A spatial theory for emergent multiple predator–prey interactions in food webs

Predator–prey interaction is inherently spatial because animals move through landscapes to search for and consume food resources and to avoid being consumed by other species. The spatial nature of species interactions necessitates integrating spatial processes into food web theory and evaluating how predators combine to impact their prey. Here, we present a spatial modeling approach that examines emergent multiple predator effects on prey within landscapes. The modeling is inspired by the habitat domain concept derived from empirical synthesis of spatial movement and interactions studies. Because these principles are motivated by synthesis of short‐term experiments, it remains uncertain whether spatial contingency principles hold in dynamical systems. We address this uncertainty by formulating dynamical systems models, guided by core habitat domain principles, to examine long‐term multiple predator–prey spatial dynamics. To describe habitat domains, we use classical niche concepts describing resource utilization distributions, and assume species interactions emerge from the degree of overlap between species. The analytical results generally align with those from empirical synthesis and present a theoretical framework capable of demonstrating multiple predator effects that does not depend on the small spatial or temporal scales typical of mesocosm experiments, and help bridge between empirical experiments and long‐term dynamics in natural systems.     

Ecological correlates of population genetic structure: a comparative approach using a vertebrate metacommunity

Identifying ecological factors associated with population genetic differentiation is important for understanding microevolutionary processes and guiding the management of threatened populations. We identified ecological correlates of several population genetic parameters for three interacting species (two garter snakes and an anuran) that occupy a common landscape. Using multiple regression analysis, we found that species interactions were more important in explaining variation in population genetic parameters than habitat and nearest-neighbour characteristics. Effective population size was best explained by census size, while migration was associated with differences in species abundance. In contrast, genetic distance was poorly explained by the ecological correlates that we tested, but geographical distance was prominent in models for all species. We found substantially different population dynamics for the prey species relative to the two predators, characterized by larger effective sizes, lower gene flow and a state of migration-drift equilibrium. We also identified an escarpment formed by a series of block faults that serves as a barrier to dispersal for the predators. Our results suggest that successful landscape-level management should incorporate genetic and ecological data for all relevant species, because even closely associated species can exhibit very different population genetic dynamics on the same landscape.     

Dynamic versus instantaneous models of diet choice

We investigate the dynamics of a series of two-prey-one-predator models in which the predator exhibits adaptive diet choice based on the different energy contents and/or handling times of the two prey species. The predator is efficient at exploiting its prey and has a saturating functional response; these two features combine to produce sustained population cycles over a wide range of parameter values. Two types of models of behavioral change are compared. In one class of models ("instantaneous choice"), the probability of acceptance of the poorer prey by the predator instantaneously approximates the optimal choice, given current prey densities. In the second class of models ("dynamic choice"), the probability of acceptance of the poorer prey is a dynamic variable, which begins to change in an adaptive direction when prey densities change but which requires a finite amount of time to approach the new optimal behavior. The two types of models frequently predict qualitatively different population dynamics of the three-species system, with chaotic dynamics and complex cycles being a common outcome only in the dynamic choice models. In dynamic choice models, factors that reduce the rate of behavioral change when the probability of accepting the poorer prey approaches extreme values often produce complex population dynamics. Instantaneous and dynamic models often predict different average population densities and different indirect interactions between prey species. Alternative dynamic models of behavior are analyzed and suggest, first, that instantaneous choice models may be good approximations in some circumstances and, second, that different types of dynamic choice models often lead to significantly different population dynamics. The results suggest possible behavioral mechanisms leading to complex population dynamics and highlight the need for more empirical study of the dynamics of behavioral change.     

The effects of spatial movement and group interactions on disease dynamics of social animals

The effects of spatial movements of infected and susceptible individuals on disease dynamics is not well understood. Empirical studies on the spatial spread of disease and behaviour of infected individuals are few and theoretical studies may be useful to explore different scenarios. Hence due to lack of detail in empirical studies, theoretical models have become necessary tools in investigating the disease influence in host-pathogen systems. In this paper we developed and analysed a spatially explicit model of two interacting social groups of animals of the same species. We investigated how the movement scenarios of susceptible and infected individuals together with the between-group contact parameter affect the survival rate of susceptible individuals in each group. This work can easily be applied to various host-pathogen systems. We define bounds on the number of susceptibles which avoid infection once the disease has died out as a function of the initial conditions and other model parameters. For example, once disease has passed through the populations, a larger diffusion coefficient for each group can result in higher population levels when there is no between-group interaction but in lower levels when there is between-group interaction. Numerical simulations are used to demonstrate these bounds and behaviours and to describe the different outcomes in ecological terms.     

The Dispersal System of a Butterfly: A Test of Source-Sink Theory Suggests the Intermediate-Scale Hypothesis

Theory predicts source-sink dynamics can occur in species with the ideal preemptive distribution but not with the ideal free distribution. Source-sink dynamics can also occur in species with passive dispersal, in which a fixed fraction of the population disperses each generation. However, in nature, dispersal often approximates random diffusion rather than ideal choices or fixed probabilities. Here, I ask which dispersal system occurred in a butterfly (Euphydryas editha) known to have source-sink dynamics. The study used 13 experimental sites, where vacant and occupied habitat patches were juxtaposed. I estimated movement during the flight season and tested hypotheses about the type of dispersal system. Ideal free and ideal preemptive models were rejected because per capita movement rates were density independent. Passive dispersal was rejected because per capita rates were related to patch area and habitat preference. The diffusion model best explained the data because it predicted both the area relationship and an odd feature of the habitat preference: immigration was not higher in preferred habitat; rather, emigration was lower. The diffusion model implied that source-sink dynamics were driven by diffusion from areas of high to low population density. Existing source-sink theory assumes fine-scale patchiness, in which animals have perfect knowledge and ease of mobility. The results from the butterfly suggest that source-sink dynamics arise at coarser spatial scales, where diffusion models apply.     

Population biology of two rare fern species: long life and long-lasting stability

? Premise of the study: This study describes the population dynamics of two rare fern species and evaluates the prospects of their survival. This is the first detailed demography study of ferns using transition matrix models. The study species, Asplenium adulterinum and A. cuneifolium, are restricted to serpentine rocks and differ in ploidy level and partly in habitat requirements. Both species are of interest in nature conservation. ? Methods: Single life-history traits were evaluated and transition matrix models were used to describe the dynamics of the populations. Population growth rates, elasticity values, and life-table response experiments were used to compare the dynamics between species, years, and different habitat types. Predicted population performance based on models was compared with real data on population growth. ? Key Results: All populations of both species are growing. Stable stage distribution based on stochastic simulation corresponds to current stage distribution. The most critical phase of the life cycle is stasis of large adult plants. Reproduction is of low importance. Extinction probability of small populations is low. Mean life span of individuals of both species is 30-50 yr. When compared with real data, the model successfully predicted population performance over 10 yr. ? Conclusion: Populations in the study region are not endangered, and current population dynamics are stable. Differences in life-history traits between species, probability of extinction between species and habitat, and different ploidy-and, thus, probably different dispersal ability-suggest the existence of metapopulation dynamics.     

Dynamics of populations with individual variation in dispersal on bounded domains

Most classical models for the movement of organisms assume that all individuals have the same patterns and rates of movement (for example, diffusion with a fixed diffusion coefficient) but there is empirical evidence that movement rates and patterns may vary among different individuals. A simple way to capture variation in dispersal that has been suggested in the ecological literature is to allow individuals to switch between two distinct dispersal modes. We study models for populations whose members can switch between two different nonzero rates of diffusion and whose local population dynamics are subject to density dependence of logistic type. The resulting models are reaction–diffusion systems that can be cooperative at some population densities and competitive at others. We assume that the focal population inhabits a bounded region and study how its overall dynamics depend on the parameters describing switching rates and local population dynamics. (Traveling waves and spread rates have been studied for similar models in the context of biological invasions.) The analytic methods include ideas and results from reaction–diffusion theory, semi-dynamical systems, and bifurcation/continuation theory.     

How to understand species’ niches and range dynamics: a demographic research agenda for biogeography

Range dynamics causes mismatches between a species’ geographical distribution and the set of suitable environments in which population growth is positive (the Hutchinsonian niche). This is because source–sink population dynamics cause species to occupy unsuitable environments, and because environmental change creates non‐equilibrium situations in which species may be absent from suitable environments (due to migration limitation) or present in unsuitable environments that were previously suitable (due to time‐delayed extinction). Because correlative species distribution models do not account for these processes, they are likely to produce biased niche estimates and biased forecasts of future range dynamics. Recently developed dynamic range models (DRMs) overcome this problem: they statistically estimate both range dynamics and the underlying environmental response of demographic rates from species distribution data. This process‐based statistical approach qualitatively advances biogeographical analyses. Yet, the application of DRMs to a broad range of species and study systems requires substantial research efforts in statistical modelling, empirical data collection and ecological theory. Here we review current and potential contributions of these fields to a demographic understanding of niches and range dynamics. Our review serves to formulate a demographic research agenda that entails: (1) advances in incorporating process‐based models of demographic responses and range dynamics into a statistical framework, (2) systematic collection of data on temporal changes in distribution and abundance and on the response of demographic rates to environmental variation, and (3) improved theoretical understanding of the scaling of demographic rates and the dynamics of spatially coupled populations. This demographic research agenda is challenging but necessary for improved comprehension and quantification of niches and range dynamics. It also forms the basis for understanding how niches and range dynamics are shaped by evolutionary dynamics and biotic interactions. Ultimately, the demographic research agenda should lead to deeper integration of biogeography with empirical and theoretical ecology.     

Population turnover and habitat dynamics in Notonecta (Hemiptera: Notonectidae) metapopulations

Simple metapopulation models assume that local populations occur in patches of uniform quality habitat separated by non-habitat. However field metapopulations tend to show considerable spatial and temporal variation in patch quality, and hence probability of occupancy. This may have implications for the adequacy of simple metapopulation models in describing and predicting regional population dynamics of natural systems. This study investigated the effects of habitat characteristics on landscape-scale occupancy dynamics of two species of backswimmer (Notonecta, Hemiptera: Notonectidae) in small freshwater ponds. The results demonstrated clear links between habitat, pond occupancy and population turnover, particularly local extinction. There were considerable changes in the habitat of individual ponds between years, but local changes were not spatially correlated and the frequency distribution of habitat conditions at the landscape level remained similar in different years. Stable occupancy levels of Notonecta species appears to result from a balance of the rates of creation and loss of suitable habitat due to spatially uncorrelated habitat change. Systems such as this, where turnover is driven by habitat dynamics, demonstrate the potential value of incorporating the dynamics of habitat change into metapopulation models. Such developments are likely to improve predictions of landscape-scale occupancy dynamics, whilst also allowing patch-level predictions of occupancy, based on local habitat conditions. Received: 18 August 1999 / Accepted: 3 December 1999     

Spatial dynamics in model plant communities: what do we really know?

A variety of models have shown that spatial dynamics and small-scale endogenous heterogeneity (e.g., forest gaps or local resource depletion zones) can change the rate and outcome of competition in communities of plants or other sessile organisms. However, the theory appears complicated and hard to connect to real systems. We synthesize results from three different kinds of models: interacting particle systems, moment equations for spatial point processes, and metapopulation or patch models. Studies using all three frameworks agree that spatial dynamics need not enhance coexistence nor slow down dynamics; their effects depend on the underlying competitive interactions in the community. When similar species would coexist in a nonspatial habitat, endogenous spatial structure inhibits coexistence and slows dynamics. When a dominant species disperses poorly and the weaker species has higher fecundity or better dispersal, competition-colonization trade-offs enhance coexistence. Even when species have equal dispersal and per-generation fecundity, spatial successional niches where the weaker and faster-growing species can rapidly exploit ephemeral local resources can enhance coexistence. When interspecific competition is strong, spatial dynamics reduce founder control at large scales and short dispersal becomes advantageous. We describe a series of empirical tests to detect and distinguish among the suggested scenarios.     

Stabilization through spatial pattern formation in metapopulations with long-range dispersal

Many studies of metapopulation models assume that spatially extended populations occupy a network of identical habitat patches, each coupled to its nearest neighbouring patches by density-independent dispersal. Much previous work has focused on the temporal stability of spatially homogeneous equilibrium states of the metapopulation, and one of the main predictions of such models is that the stability of equilibrium states in the local patches in the absence of migration determines the stability of spatially homogeneous equilibrium states of the whole metapopulation when migration is added. Here, we present classes of examples in which deviations from the usual assumptions lead to different predictions. In particular, heterogeneity in local habitat quality in combination with long-range dispersal can induce a stable equilibrium for the metapopulation dynamics, even when within-patch processes would produce very complex behaviour in each patch in the absence of migration. Thus, when spatially homogeneous equilibria become unstable, the system can often shift to a different, spatially inhomogeneous steady state. This new global equilibrium is characterized by a standing spatial wave of population abundances. Such standing spatial waves can also be observed in metapopulations consisting of identical habitat patches, i.e. without heterogeneity in patch quality, provided that dispersal is density dependent. Spatial pattern formation after destabilization of spatially homogeneous equilibrium states is well known in reaction–diffusion systems and has been observed in various ecological models. However, these models typically require the presence of at least two species, e.g. a predator and a prey. Our results imply that stabilization through spatial pattern formation can also occur in single-species models. However, the opposite effect of destabilization can also occur: if dispersal is short range, and if there is heterogeneity in patch quality, then the metapopulation dynamics can be chaotic despite the patches having stable equilibrium dynamics when isolated. We conclude that more general metapopulation models than those commonly studied are necessary to fully understand how spatial structure can affect spatial and temporal variation in population abundance.     

Dynamics of species coexistence: maintenance of a plant-ant competitive metacommunity

The metacommunity approach is an adequate framework to study coexistence between interacting species at different spatial scales. However, empirical evidence from natural metacommunities necessary to evaluate the predictive power of theoretical models of species coexistence remains sparse. We use two African ant species, Cataulacus mckeyi and Petalomyrmex phylax , symbiotically associated with the myrmecophyte Leonardoxa africana africana , to examine spatio-temporal dynamics of species coexistence and to investigate which environmental and life-history parameters may contribute to the maintenance of species diversity in this guild of symbiotic ants. Using environmental niche partitioning as a conceptual framework, we combined data on habitat variation, social structure of colonies, and population genetics with data from a colonisation experiment and from observation of temporal dynamics. We propose that the dynamics of ant species colonisation and replacement at local and regional scales can be explained by a set of life history traits for which the two ants exhibit hierarchies, coupled with strong environmental differences between the different patches in the level of environmental disturbances. The role of the competition–colonisation tradeoff is discussed and we propose that interspecific tradeoffs for traits related to dispersal and to reproduction are also determinant for species coexistence. We therefore suggest that species-sorting mechanisms are predominant in the dynamics of this metacommunity, but we also emphasise that there may be many ways for two symbionts in competition for the same host to coexist. The results speak in favour of a more complete integration of the various metacommunity models in a single theoretical framework.     

Habitat fragmentation and population extinction of birds

It has not been established that a major cause of extinction in birds or any other taxa is failure of metapopulation dynamics: the collapse of a network of ephemeral but discrete populations as movement between them becomes increasingly infrequent. The few data on who goes where and who mates with whom suggest that most species are structured as either a single large population or a small set of source populations and a larger set of sinks. The extinction of the latter is irrelevant to the persistence of the species. However, regional decline of a species in the face of habitat destruction and fragmentation can mimic a failure of metapopulation dynamics, because distinct aggregations of individuals will disappear much as they would if populations in an interacting network were eliminated one by one. Any species with highly restricted range is at great risk of extinction from spatially localized forces, such as cyclones or deforestation. Restricted range rather than inherent weakness is the main reason that so many island species have gone extinct or are endangered. Species with small populations in contact with much larger heterospecific ones with which they are interfertile are threatened with extinction by hybridization. Finally, the disappearance of a species from a site may be due to subtle habitat change, even if this observation seems superficially consistent with some general population theory, such as the dynamic equilibrium theory of island biogeography. Current theory is an inadequate substitute for intensive field studies as a means to address the conservation problems of individual species.     

Lasting effects of maternal behaviour on the distribution of a dispersive stream insect

1. Predicting population dynamics at large spatial scales requires integrating information about spatial distribution patterns, inter-patch movement rates and within-patch processes. Advective dispersal of aquatic species by water movement is considered paramount to understanding their population dynamics. Rivers are model advective systems, and the larvae of baetid mayflies are considered quintessential dispersers. Egg laying of baetids along channels is patchy and reflects the distribution of oviposition sites, but larvae are assumed to drift frequently and far, thereby erasing patterns created during oviposition. Dispersal kernels are often overestimated, however, and empirical tests of such assumptions are warranted because of the pivotal role distribution patterns can have on populations. 2. We tested empirically whether the egg distribution patterns arising from oviposition behaviours persisted and were reflected in the distribution patterns of larval Baetis rhodani. In field surveys, we tested for associations between egg mass and larval densities over 1 km lengths of four streams. A control species, the mayfly Ephemerella ignita, was employed to test for covarying environmental factors. We estimated drift rates directly to test whether larvae dispersed between riffles (patches of high egg mass density) and whether drift rates were density-dependent or density-related - expected outcomes if drift erases patterns established by maternal behaviours. 3. Positive associations between egg masses and larval benthic densities were found for neonate and mid-stage larvae of Baetis, but not the control species, suggesting persistence of the patchy distribution patterns established at oviposition. Drift rates were high, and riffles were net exporters of neonate and mid-stage larvae, but drift rates were unrelated to benthic densities and few drifters reached the next riffle. Riffles were sinks for large larvae, suggesting ontogenetic shifts in habitat use, but little long-distance dispersal. 4. Overall, the results suggest that most neonate and mid-stage larvae of B. rhodani remain close to the natal riffle, and late-stage larvae disperse shorter distances than routinely assumed. The persistence of maternal effects on distribution patterns well into juvenile life of an allegedly iconic disperser suggests that traditional models of how dispersal influences the population dynamics of many lotic invertebrates may be incorrect.