Comparing the qualitatively different effects rapidly evolving and rapidly induced defences have on predator-prey interactions

The double-edged sword of inducible defences: costs and benefits of maladaptive switching from the individual to the community level

Phenotypic plasticity can increase individual fitness when environmental conditions change over time. Inducible defences are a striking example, allowing species to react to fluctuating predation pressure by only expressing their costly defended phenotype under high predation risk. Previous theoretical investigations have focused on how this affects predator–prey dynamics, but the impact on competitive outcomes and broader community dynamics has received less attention. Here we use a small food web model, consisting of two competing plastic autotrophic species exploited by a shared consumer, to study how the speed of inducible defences across three trade-off constellations affects autotroph coexistence, biomasses across trophic levels, and temporal variability. Contrary to the intuitive idea that faster adaptation increases autotroph fitness, we found that higher switching rates reduced individual fitness as it consistently provoked more maladaptive switching towards undefended phenotypes under high predation pressure. This had an unexpected positive impact on the consumer, increasing consumer biomass and lowering total autotroph biomass. Additionally, maladaptive switching strongly reduced autotroph coexistence through an emerging source-sink dynamic between defended and undefended phenotypes. The striking impact of maladaptive switching on species and food web dynamics indicates that this mechanism may be of more critical importance than previously recognized.

How does genetic architecture affect eco-evolutionary dynamics? A theoretical perspective

Recent studies have revealed the importance of feedbacks between contemporary rapid evolution (i.e. evolution that occurs through changes in allele frequencies) and ecological dynamics. Despite its inherent interdisciplinary nature, however, studies on eco-evolutionary feedbacks have been mostly ecological and tended to focus on adaptation at the phenotypic level without considering the genetic architecture of evolutionary processes. In empirical studies, researchers have often compared ecological dynamics when the focal species under selection has a single genotype with dynamics when it has multiple genotypes. In theoretical studies, common approaches are models of quantitative traits where mean trait values change adaptively along the fitness gradient and Mendelian traits with two alleles at a single locus. On the other hand, it is well known that genetic architecture can affect short-term evolutionary dynamics in population genetics. Indeed, recent theoretical studies have demonstrated that genetic architecture (e.g. the number of loci, linkage disequilibrium and ploidy) matters in eco-evolutionary dynamics (e.g. evolutionary rescue where rapid evolution prevents extinction and population cycles driven by (co)evolution). I propose that theoretical approaches will promote the synthesis of functional genomics and eco-evolutionary dynamics through models that combine population genetics and ecology as well as nonlinear time-series analyses using emerging big data.

This article is part of the theme issue ‘Genetic basis of adaptation and speciation: from loci to causative mutations’.

Evolutionary and Plastic Phenotypic Change Can Be Just as Fast as Changes in Population Densities

AbstractEvolution and plasticity can drive population-level phenotypic change (e.g., changes in the mean phenotype) on timescales comparable to changes in population densities. However, it is unclear whether phenotypic change has the potential to be just as fast as changes in densities or whether comparable rates of change occur only when densities are changing slow enough for phenotypes to keep pace. Moreover, it is unclear whether this depends on the mode of adaptation. Using scaling theory and fast-slow dynamical systems theory, we develop a method for comparing maximum rates of density and phenotypic change estimated from population-level time-series data. We apply our method to 30 published empirical studies where changes in morphological traits are caused by evolution, plasticity, or an unknown combination. For every study, the maximum rate of phenotypic change was between 0.5 and 2.5 times faster than the maximum rate of change in density. Moreover, there were no systematic differences between systems with different modes of adaptation. Our results show that plasticity and evolution can drive phenotypic change just as fast as changes in densities. We discuss the implications of our results in terms of the strengths of feedbacks between population densities and traits.

Rethinking trophic niches: Speed and body mass colimit prey space of mammalian predators

Realized trophic niches of predators are often characterized along a one-dimensional range in predator-prey body mass ratios. This prey range is constrained by an "energy limit" and a "subdue limit" toward small and large prey, respectively. Besides these body mass ratios, maximum speed is an additional key component in most predator-prey interactions.Here, we extend the concept of a one-dimensional prey range to a two-dimensional prey space by incorporating a hump-shaped speed-body mass relation. This new "speed limit" additionally constrains trophic niches of predators toward fast prey.To test this concept of two-dimensional prey spaces for different hunting strategies (pursuit, group, and ambush predation), we synthesized data on 63 terrestrial mammalian predator-prey interactions, their body masses, and maximum speeds.We found that pursuit predators hunt smaller and slower prey, whereas group hunters focus on larger but mostly slower prey and ambushers are more flexible. Group hunters and ambushers have evolved different strategies to occupy a similar trophic niche that avoids competition with pursuit predators. Moreover, our concept suggests energetic optima of these hunting strategies along a body mass axis and thereby provides mechanistic explanations for why there are no small group hunters (referred to as "micro-lions") or mega-carnivores (referred to as "mega-cheetahs").Our results demonstrate that advancing the concept of prey ranges to prey spaces by adding the new dimension of speed will foster a new and mechanistic understanding of predator trophic niches and improve our predictions of predator-prey interactions, food web structure, and ecosystem functions.

Diversity and coexistence are influenced by time-dependent species interactions in a predator-prey system

Although numerous studies show that communities are jointly influenced by predation and competitive interactions, few have resolved how temporal variability in these interactions influences community assembly and stability. Here, we addressed this challenge in experimental microbial microcosms by employing empirical dynamic modelling tools to: (1) detect causal interactions between prey species in the absence and presence of a predator; (2) quantify the time-varying strength of these interactions and (3) explore stability in the resulting communities. Our findings show that predators boost the number of causal interactions among community members, and lead to reduced dynamic stability, but higher coexistence among prey species. These results correspond to time-varying changes in species interactions, including emergence of morphological characteristics that appeared to reduce predation, and indirectly facilitate growth of predator-susceptible species. Jointly, our findings suggest that careful consideration of both context and time may be necessary to predict and explain outcomes in multi-trophic systems.

Reversed predator-prey cycles are driven by the amplitude of prey oscillations

Ecoevolutionary feedbacks in predator-prey systems have been shown to qualitatively alter predator-prey dynamics. As a striking example, defense-offense coevolution can reverse predator-prey cycles, so predator peaks precede prey peaks rather than vice versa. However, this has only rarely been shown in either model studies or empirical systems. Here, we investigate whether this rarity is a fundamental feature of reversed cycles by exploring under which conditions they should be found. For this, we first identify potential conditions and parameter ranges most likely to result in reversed cycles by developing a new measure, the effective prey biomass, which combines prey biomass with prey and predator traits, and represents the prey biomass as perceived by the predator. We show that predator dynamics always follow the dynamics of the effective prey biomass with a classic ¼-phase lag. From this key insight, it follows that in reversed cycles (i.e., ¾-lag), the dynamics of the actual and the effective prey biomass must be in antiphase with each other, that is, the effective prey biomass must be highest when actual prey biomass is lowest, and vice versa. Based on this, we predict that reversed cycles should be found mainly when oscillations in actual prey biomass are small and thus have limited impact on the dynamics of the effective prey biomass, which are mainly driven by trait changes. We then confirm this prediction using numerical simulations of a coevolutionary predator-prey system, varying the amplitude of the oscillations in prey biomass: Reversed cycles are consistently associated with regions of parameter space leading to small-amplitude prey oscillations, offering a specific and highly testable prediction for conditions under which reversed cycles should occur in natural systems.

Eco-Evolutionary Dynamics of Ecological Stoichiometry in Plankton Communities

Nitrogen (N) and phosphorus (P) limit primary production in many aquatic ecosystems, with major implications for ecological interactions in plankton communities. Yet it remains unclear how evolution may affect the N∶P stoichiometry of phytoplankton-zooplankton interactions. Here, we address this issue by analyzing an eco-evolutionary model of phytoplankton-zooplankton interactions with explicit nitrogen and phosphorus dynamics. In our model, investment of phytoplankton in nitrogen versus phosphorus uptake is an evolving trait, and zooplankton display selectivity for phytoplankton with N∶P ratios matching their nutritional requirements. We use this model to explore implications of the contrasting N∶P requirements of copepods versus cladocerans. The model predicts that selective zooplankton strongly affect the N∶P ratio of phytoplankton, resulting in deviations from their optimum N∶P ratio. Specifically, selective grazing by nitrogen-demanding copepods favors dominance of phytoplankton with low N∶P ratios, whereas phosphorus-demanding cladocerans favor dominance of phytoplankton with high N∶P ratios. Interestingly, selective grazing by nutritionally balanced zooplankton leads to the occurrence of alternative stable states, where phytoplankton may evolve either low, optimum, or high N∶P ratios, depending on the initial conditions. These results offer a new perspective on commonly observed differences in N∶P stoichiometry between plankton of freshwater and those of marine ecosystems and indicate that selective grazing by zooplankton can have a major impact on the stoichiometric composition of phytoplankton.

Changes in predator exposure, but not in diet, induce phenotypic plasticity in scorpion venom

Animals embedded between trophic levels must simultaneously balance pressures to deter predators and acquire resources. Venomous animals may use venom toxins to mediate both pressures, and thus changes in this balance may alter the composition of venoms. Basic theory suggests that greater exposure to a predator should induce a larger proportion of defensive venom components relative to offensive venom components, while increases in arms races with prey will elicit the reverse. Alternatively, reducing the need for venom expenditure for food acquisition, for example because of an increase in scavenging, may reduce the production of offensive venom components. Here, we investigated changes in scorpion venom composition using a mesocosm experiment where we manipulated scorpions' exposure to a surrogate vertebrate predator and live and dead prey. After six weeks, scorpions exposed to surrogate predators exhibited significantly different venom chemistry compared with naive scorpions. This change included a relative increase in some compounds toxic to vertebrate cells and a relative decrease in some compounds effective against their invertebrate prey. Our findings provide, to our knowledge, the first evidence for adaptive plasticity in venom composition. These changes in venom composition may increase the stability of food webs involving venomous animals.

Disentangling eco-evolutionary dynamics of predator-prey coevolution: the case of antiphase cycles

The impact of rapid predator-prey coevolution on predator-prey dynamics remains poorly understood, as previous modelling studies have given rise to contradictory conclusions and predictions. Interpreting and reconciling these contradictions has been challenging due to the inherent complexity of model dynamics, defying mathematical analysis and mechanistic understanding. We develop a new approach here, based on the Geber method for deconstructing eco-evolutionary dynamics, for gaining such understanding. We apply this approach to a co-evolutionary predator-prey model to disentangle the processes leading to either antiphase or ¼-lag cycles. Our analysis reveals how the predator-prey phase relationship is driven by the temporal synchronization between prey biomass and defense dynamics. We further show when and how prey biomass and trait dynamics become synchronized, resulting in antiphase cycles, allowing us to explain and reconcile previous modelling and empirical predictions. The successful application of our proposed approach provides an important step towards a comprehensive theory on eco-evolutionary feedbacks in predator-prey systems.

Energetics and evasion dynamics of large predators and prey: pumas vs. hounds

Quantification of fine-scale movement, performance, and energetics of hunting by large carnivores is critical for understanding the physiological underpinnings of trophic interactions. This is particularly challenging for wide-ranging terrestrial canid and felid predators, which can each affect ecosystem structure through distinct hunting modes. To compare free-ranging pursuit and escape performance from group-hunting and solitary predators in unprecedented detail, we calibrated and deployed accelerometer-GPS collars during predator-prey chase sequences using packs of hound dogs (Canis lupus familiaris, 26 kg, n = 4-5 per chase) pursuing simultaneously instrumented solitary pumas (Puma concolor, 60 kg, n = 2). We then reconstructed chase paths, speed and turning angle profiles, and energy demands for hounds and pumas to examine performance and physiological constraints associated with cursorial and cryptic hunting modes, respectively. Interaction dynamics revealed how pumas successfully utilized terrain (e.g., fleeing up steep, wooded hillsides) as well as evasive maneuvers (e.g., jumping into trees, running in figure-8 patterns) to increase their escape distance from the overall faster hounds (avg. 2.3× faster). These adaptive strategies were essential to evasion in light of the mean 1.6× higher mass-specific energetic costs of the chase for pumas compared to hounds (mean: 0.76 vs. 1.29 kJ kg-1 min-1, respectively). On an instantaneous basis, escapes were more costly for pumas, requiring exercise at ≥90% of predicted [Formula: see text] and consuming as much energy per minute as approximately 5 min of active hunting. Our results demonstrate the marked investment of energy for evasion by a large, solitary carnivore and the advantage of dynamic maneuvers to postpone being overtaken by group-hunting canids.

Expanded view of ecosystem stability: A grazed grassland case study

Analysis of stability under linearized dynamics is central to ecology. We highlight two key limitations of the widely used traditional analysis. First, we note that while stability at fixed points is often the focus, ecological systems may spend less time near fixed points, and more time responding to stochastic environmental forcing by exhibiting wide zero-mean fluctuations about those states. If non-steady, uniquely precarious states along the nonlinear flow are analyzed instead of fixed points, transient growth is possible and indeed common for ecosystems with stable attractive fixed points. Second, we show that in either steady or non-steady states, eigenvalue based analysis can misleadingly suggest stability while eigenvector geometry arising from the non-self-adjointness of the linearized operator can yield large finite-time instabilities. We offer a simple alternative to eigenvalue based stability analysis that naturally and straightforwardly overcome these limitations.

Trait adaptation promotes species coexistence in diverse predator and prey communities

Species can adjust their traits in response to selection which may strongly influence species coexistence. Nevertheless, current theory mainly assumes distinct and time-invariant trait values. We examined the combined effects of the range and the speed of trait adaptation on species coexistence using an innovative multispecies predator-prey model. It allows for temporal trait changes of all predator and prey species and thus simultaneous coadaptation within and among trophic levels. We show that very small or slow trait adaptation did not facilitate coexistence because the stabilizing niche differences were not sufficient to offset the fitness differences. In contrast, sufficiently large and fast trait adaptation jointly promoted stable or neutrally stable species coexistence. Continuous trait adjustments in response to selection enabled a temporally variable convergence and divergence of species traits; that is, species became temporally more similar (neutral theory) or dissimilar (niche theory) depending on the selection pressure, resulting over time in a balance between niche differences stabilizing coexistence and fitness differences promoting competitive exclusion. Furthermore, coadaptation allowed prey and predator species to cluster into different functional groups. This equalized the fitness of similar species while maintaining sufficient niche differences among functionally different species delaying or preventing competitive exclusion. In contrast to previous studies, the emergent feedback between biomass and trait dynamics enabled supersaturated coexistence for a broad range of potential trait adaptation and parameters. We conclude that accounting for trait adaptation may explain stable and supersaturated species coexistence for a broad range of environmental conditions in natural systems when the absence of such adaptive changes would preclude it. Small trait changes, coincident with those that may occur within many natural populations, greatly enlarged the number of coexisting species.

Maternal effects on offspring consumption can stabilize fluctuating predator-prey systems

Maternal effects, where the conditions experienced by mothers affect the phenotype of their offspring, are widespread in nature and have the potential to influence population dynamics. However, they are very rarely included in models of population dynamics. Here, we investigate a recently discovered maternal effect, where maternal food availability affects the feeding rate of offspring so that well-fed mothers produce fast-feeding offspring. To understand how this maternal effect influences population dynamics, we explore novel predator-prey models where the consumption rate of predators is modified by changes in maternal prey availability. We address the 'paradox of enrichment', a theoretical prediction that nutrient enrichment destabilizes populations, leading to cycling behaviour and an increased risk of extinction, which has proved difficult to confirm in the wild. Our models show that enriched populations can be stabilized by maternal effects on feeding rate, thus presenting an intriguing potential explanation for the general absence of 'paradox of enrichment' behaviour in natural populations. This stabilizing influence should also reduce a population's risk of extinction and vulnerability to harvesting.

Intraguild predation leads to genetically based character shifts in the threespine stickleback

Intraguild predation is a common ecological interaction that occurs when a species preys upon another species with which it competes. The interaction is potentially a mechanism of divergence between intraguild prey (IG-prey) populations, but it is unknown if cases of character shifts in IG-prey are an environmental or evolutionary response. We investigated the genetic basis and inducibility of character shifts in threespine stickleback from lakes with and without prickly sculpin, a benthic intraguild predator (IG-predator). Wild populations of stickleback sympatric with sculpin repeatedly show greater defensive armor and water column height preference. We laboratory-raised stickleback from lakes with and without sculpin, as well as marine stickleback, and found that differences between populations in armor, body shape, and behavior persisted in a common garden. Within the common garden, we raised stickleback half-families from multiple populations in the presence and absence of sculpin. Although the presence of sculpin induced trait changes in the marine stickleback, we did not observe an induced response in the freshwater stickleback. Behavioral and morphological trait differences between freshwater populations thus have a genetic basis and suggest an evolutionary response to intraguild predation.

Mass enhances speed but diminishes turn capacity in terrestrial pursuit predators

The dynamics of predator-prey pursuit appears complex, making the development of a framework explaining predator and prey strategies problematic. We develop a model for terrestrial, cursorial predators to examine how animal mass modulates predator and prey trajectories and affects best strategies for both parties. We incorporated the maximum speed-mass relationship with an explanation of why larger animals should have greater turn radii; the forces needed to turn scale linearly with mass whereas the maximum forces an animal can exert scale to a 2/3 power law. This clarifies why in a meta-analysis, we found a preponderance of predator/prey mass ratios that minimized the turn radii of predators compared to their prey. It also explained why acceleration data from wild cheetahs pursuing different prey showed different cornering behaviour with prey type. The outcome of predator prey pursuits thus depends critically on mass effects and the ability of animals to time turns precisely.

DOI:http://dx.doi.org/10.7554/eLife.06487.001

A pursuit between a predator and its prey involves complex strategies. Prey often make sudden sharp turns when running to evade a predator. Any predator that cannot turn quickly enough will have to run further to catch up with the prey again, thus potentially allowing the prey to pull away from the predator. The timing of these turns is crucial; if the prey turns when the predator is too far away, the predator can cut the corner off the turn and catch up with the prey more easily.

The speed at which animals can turn depends on the forces involved in cornering, and larger animals need to produce greater forces for any given turn. However, larger animals can apply relatively less force than smaller animals for turns and so cannot turn as rapidly. The effect of the relationship between mass and turning ability on the strategies used during land-based pursuits had not been investigated.

Wilson et al. have now created a mathematical model that considers how the mass of a predator and its prey influences the course and strategies used in a land-based pursuit. The model is based in part on a mathematical problem called the ‘homicidal chauffeur game’, where a car driver attempts to run over a pedestrian. Wilson et al.'s model predicts that chases between large predators and smaller prey should feature frequent sharp turns, as the prey try to exploit their superior turning ability. However, when the predators and prey are of similar size, the prey gain little or no advantage from executing high-speed turns. Indeed, as turning slows the prey down, turning may often be disadvantageous, and so fewer turns should be seen during a pursuit.

The predictions of the model were compared with the pursuit strategies of wild cheetahs, which were studied using collars equipped with tags to measure acceleration as the predators chased prey of different sizes—from hares to large antelopes called gemsboks. The tracking data confirmed the predictions of the model; thereby revealing that body mass and the ability of animals to choose when best to turn strongly determine the outcome of predator-prey pursuits.

DOI:http://dx.doi.org/10.7554/eLife.06487.002

Form of an evolutionary tradeoff affects eco-evolutionary dynamics in a predator-prey system

Evolution on a time scale similar to ecological dynamics has been increasingly recognized for the last three decades. Selection mediated by ecological interactions can change heritable phenotypic variation (i.e., evolution), and evolution of traits, in turn, can affect ecological interactions. Hence, ecological and evolutionary dynamics can be tightly linked and important to predict future dynamics, but our understanding of eco-evolutionary dynamics is still in its infancy and there is a significant gap between theoretical predictions and empirical tests. Empirical studies have demonstrated that the presence of genetic variation can dramatically change ecological dynamics, whereas theoretical studies predict that eco-evolutionary dynamics depend on the details of the genetic variation, such as the form of a tradeoff among genotypes, which can be more important than the presence or absence of the genetic variation. Using a predator-prey (rotifer-algal) experimental system in laboratory microcosms, we studied how different forms of a tradeoff between prey defense and growth affect eco-evolutionary dynamics. Our experimental results show for the first time to our knowledge that different forms of the tradeoff produce remarkably divergent eco-evolutionary dynamics, including near fixation, near extinction, and coexistence of algal genotypes, with quantitatively different population dynamics. A mathematical model, parameterized from completely independent experiments, explains the observed dynamics. The results suggest that knowing the details of heritable trait variation and covariation within a population is essential for understanding how evolution and ecology will interact and what form of eco-evolutionary dynamics will result.

Coevolution can reverse predator-prey cycles

A hallmark of Lotka-Volterra models, and other ecological models of predator-prey interactions, is that in predator-prey cycles, peaks in prey abundance precede peaks in predator abundance. Such models typically assume that species life history traits are fixed over ecologically relevant time scales. However, the coevolution of predator and prey traits has been shown to alter the community dynamics of natural systems, leading to novel dynamics including antiphase and cryptic cycles. Here, using an eco-coevolutionary model, we show that predator-prey coevolution can also drive population cycles where the opposite of canonical Lotka-Volterra oscillations occurs: predator peaks precede prey peaks. These reversed cycles arise when selection favors extreme phenotypes, predator offense is costly, and prey defense is effective against low-offense predators. We present multiple datasets from phage-cholera, mink-muskrat, and gyrfalcon-rock ptarmigan systems that exhibit reversed-peak ordering. Our results suggest that such cycles are a potential signature of predator-prey coevolution and reveal unique ways in which predator-prey coevolution can shape, and possibly reverse, community dynamics.

Reciprocal behavioral plasticity and behavioral types during predator-prey interactions

How predators and prey interact has important consequences for population dynamics and community stability. Here we explored how predator-prey interactions are simultaneously affected by reciprocal behavioral plasticity (i.e., plasticity in prey defenses countered by plasticity in predator offenses and vice versa) and consistent individual behavioral variation (i.e., behavioral types) within both predator and prey populations. We assessed the behavior of a predator species (northern pike) and a prey species (three-spined stickleback) during one-on-one encounters. We also measured additional behavioral and morphological traits in each species. Using structural equation modeling, we found that reciprocal behavioral plasticity as well as predator and prey behavioral types influenced how individuals behaved during an interaction. Thus, the progression and ultimate outcome of predator-prey interactions depend on both the dynamic behavioral feedback occurring during the encounter and the underlying behavioral type of each participant. We also examined whether predator behavioral type is underlain by differences in metabolism and organ size. We provide some of the first evidence that behavioral type is related to resting metabolic rate and size of a sensory organ (the eyes). Understanding the extent to which reciprocal behavioral plasticity and intraspecific behavioral variation influence the outcome of species interactions could provide insight into the maintenance of behavioral variation as well as community dynamics.

Coexistence in a variable environment: eco-evolutionary perspectives

A central question in community ecology is the means by which species coexist. Models of coexistence often assume that species have fixed trait values and consider questions such as how tradeoffs and environmental variation influence coexistence and diversity. However, species traits can be dynamic, varying between populations and individuals and changing over time as species adapt and evolve, at rates that are relevant to ecological processes. Consequently, adding evolution to ecological coexistence models may modify their predictions and stability in complex or unexpected ways. We extend a well-studied coexistence mechanism depending on resource fluctuations by allowing evolution along a tradeoff between maximum growth rate and competitive ability. Interactions between favorable season length and the period of fluctuations constrain coexistence, with two species coexistence favored by intermediate season length and arising through evolutionary branching or non-local invasion. However, these results depend on the relative rates of ecological and evolutionary processes: rapid evolution leads to a complete breakdown of otherwise stable coexistence. Other coexistence mechanisms should be evaluated from an evolutionary perspective to examine how evolutionary forces may alter predicted ecological dynamics.

Evolutionary and plastic rescue in multitrophic model communities

Under changing environmental conditions, intraspecific variation can potentially rescue populations from extinction. There are two principal sources of variation that may ultimately lead to population rescue: genetic diversity and phenotypic plasticity. We compared the potential for evolutionary rescue (through genetic diversity) and plastic rescue (through phenotypic plasticity) by analysing their differential ability to produce dynamical stability and persistence in model food webs. We also evaluated how rescue is affected by the trophic location of variation. We tested the following hypotheses: (i) plastic communities are more likely to exhibit stability and persistence than communities in which genetic diversity provides the same range of traits. (ii) Variation at the lowest trophic level promotes stability and persistence more than variation at higher levels. (iii) Communities with variation at two levels have greater probabilities of stability and persistence than communities with variation at only one level. We found that (i) plasticity promotes stability and persistence more than genetic diversity; (ii) variation at the second highest trophic level promotes stability and persistence more than variation at the autotroph level; and (iii) more than variation at two trophic levels. Our study shows that proper evaluation of the rescue potential of intraspecific variation critically depends on its origin and trophic location.