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Even when environments deteriorate gradually, ecosystems may shift abruptly from one state to another. Such catastrophic shifts are difficult to predict and reverse (hysteresis). While well studied in simplified contexts, we lack a general understanding of how catastrophic shifts spread in realistic spatial contexts. For different types of landscape structure, including typical terrestrial modular and riverine dendritic networks, we here investigate landscape-scale stability in metapopulations made of bistable patches. We find that such metapopulations usually exhibit large scale catastrophic shifts and hysteresis, and that the properties of these shifts depend strongly on metapopulation spatial structure and dispersal rate: intermediate dispersal rates and a riverine spatial structure can largely reduce hysteresis size. Interestingly, our study suggests that large-scale restoration is easier with spatially clustered restoration efforts and in populations characterized by an intermediate dispersal rate.

1. Dispersal is a central life history trait that affects the ecological and evolutionary dynamics of populations and communities. The recent use of experimental evolution for the study of dispersal is a promising avenue for demonstrating valuable proofs of concept, bringing insight into alternative dispersal strategies and tradeoffs, and testing the repeatability of evolutionary outcomes. 2. Practical constraints restrict experimental evolution studies of dispersal to a set of typically small, short-lived organisms reared in artificial laboratory conditions. Here, we argue that despite these restrictions, inferences from these studies can reinforce links between theoretical predictions and empirical observations and advance our understanding of the eco-evolutionary consequences of dispersal. 3. We illustrate how applying an integrative framework of theory, experimental evolution and natural systems can improve our understanding of dispersal evolution under more complex and realistic biological scenarios, such as the role of biotic interactions and complex dispersal syndromes.

Population and community ecology traditionally has a very strong theoretical foundation with well-known dynamical models, such as the logistic and its variations, and many modification of the classical Lotka-Volterra predator-prey and interspecific competition models. More and more, these classical models are being confronted with data via fitting to empirical time series for purposes of projections or for estimating model parameters of interest. However, using statistical models to fit theoretical models to data is far from trivial, especially for time series data where subsequent measurements are not independent. This raises the question of whether statistical inferences using pure observation error models, such as simple (non-)linear regressions, are biased, and whether more elaborate process error models or state-space models have to be used to address this complexity.In order to help empiricists, especially researchers working with experimental laboratory populations in micro- and mesocosms, make informed decisions about the statistical formalism to use, we here compare different error structures one could use when fitting classical deterministic ODE models to empirical data. We consider a large range of biological scenarios and theoretical models, from single species to community dynamics and trophic interactions. In order to compare the performance of different error structure models, we use both realistically simulated data and empirical data from microcosms in a Bayesian framework.We find that many model parameters can be estimated precisely with an appropriate choice of error structure using pure observation error or state-space models, if observation errors are not too high. However, Allee effect models are typically hard to identify and state-space models should be preferred when model complexity increases.Our work shows that, at least in the context of low environmental stochasticity and high quality observations, deterministic models can be used to describe stochastic population dynamics that include process variability and observation error. We discuss when more complex state-space model formulations may be required for obtaining accurate parameter estimates. Finally, we provide a comprehensive tutorial for fitting these models in R.Open researchCode for stochastic individual-based simulations is available fromhttps://doi.org/10.5281/zenodo.5500442. A tutorial for fitting ODE models to time series data in R is presented in the Supplementary Information and is also available onlinehttps://github.com/benjamin-rosenbaum/fittingdeterministic population models. Data (Fronhofer et al., 2020) will be provided via GitHub and Zenodo.

Predicting range expansion dynamics is an important goal of both fundamental and applied research in conservation and global change biology. However, this is challenging if ecological and evolutionary processes occur on the same time scale. Using the freshwater ciliate Paramecium caudatum, we combined experimental evolution and mathematical modeling to assess the predictability of evolutionary change during range expansions. In the experiment, we followed ecological dynamics and trait evolution in independently replicated microcosm populations in range core and front treatments, where episodes of natural dispersal alternated with periods of population growth. These eco-evolutionary conditions were recreated in a predictive mathematical model, parametrized with dispersal and growth data of the 20 founder strains in the experiment. We found that short-term evolution was driven by selection for increased dispersal in the front treatment and general selection for higher growth rates in all treatments. There was a good quantitative match between predicted and observed trait changes. Phenotypic divergence was further mirrored by genetic divergence between range core and front treatments. In each treatment, we found the repeated fixation of the same cytochrome c oxidase I (COI) marker genotype, carried by strains that also were the most likely winners in our model. Long-term evolution in the experimental range front lines resulted in the emergence of a dispersal syndrome, namely a competition—colonization trade-off. Altogether, both model and experiment highlight the potential importance of dispersal evolution as a driver of range expansions. Thus, evolution at range fronts may follow predictable trajectories, at least for simple scenarios, and predicting these dynamics may be possible from knowledge of few key parameters.

Contemporary evolution has the potential to significantly alter biotic responses to global change, including range expansion dynamics and biological invasions. However, predictive models often make highly simplifying assumptions about the genetic architecture underlying relevant traits. This can be problematic since genetic architecture defines evolvability, that is, evolutionary rates, and higher order evolutionary processes, which determine whether evolution will be able to keep up with environmental change or not. Therefore, we here study the impact of the genetic architecture of dispersal and local adaptation, two central traits of high relevance for range expansion dynamics, on the speed and variability of range expansions into an environmental gradient, such as temperature. In our theoretical model we assume that dispersal and local adaptation traits result from the products of two non-interacting gene-regulatory networks (GRNs). We compare our model to simpler quantitative genetics models and show that in the GRN model, range expansions are accelerated, faster and more variable. Increased variability implies that these evolutionary changes reduce predictability. We further find that acceleration in the GRN model is primarily driven by an increase in the rate of local adaptation to novel habitats which results from greater sensitivity to mutation (decreased robustness) and increased gene expression. Our results highlight how processes at microscopic scales, here, within genomes, can impact the predictions of large scale, macroscopic phenomena, such as range expansions, by modulating the rate of evolution.

Populations that expand their range can undergo rapid evolutionary adaptation of life-history traits, dispersal behaviour and adaptation to the local environment. Such adaptation may be aided or hindered by sexual reproduction, depending on the context. However, few empirical and experimental studies have investigated the genetic basis of adaptive evolution during range expansions. Even less attention has been given to the question how sexual reproduction may modulate such adaptive evolution during range expansions. We here studied genomic adaptation during experimental range expansions of the protist Tetrahymena thermophila in landscapes with a uniform environment or a pH gradient. Specifically, we investigated two aspects of genomic adaptation during range expansion. First, we investigated adaptive genetic change in terms of the underlying numbers of allele frequency changes from standing genetic variation and de novo variants. We focused on how sexual reproduction may alter this adaptive genetic change. Second, we identified genes subject to selection caused by the expanding range itself, and directional selection due to the presence or absence of the pH gradient. We focused this analysis on alleles with large frequency changes that occurred in parallel in more than one population to identify the most likely candidate targets of selection. We found that sexual reproduction altered adaptive genetic change both in terms of de novo variants and standing genetic variation. However, sexual reproduction affected allele frequency changes in standing genetic variation only in the absence of long-distance gene flow. Adaptation to the range expansion affected genes involved in cell divisions and DNA repair, whereas adaptation to the pH gradient additionally affected genes involved in ion balance and oxidoreductase reactions. These genetic changes may result from selection on growth and adaptation to low pH. In the absence of gene flow, sexual reproduction may have aided genetic adaptation. Gene flow may have swamped expanding populations with maladapted alleles, thus reducing the extent of evolutionary adaptation during range expansion. Sexual reproduction also altered the genetic basis of adaptation in our evolving populations via de novo variants, possibly by purging deleterious mutations or by revealing fitness benefits of rare genetic variants.

Dispersal is a central determinant of spatial dynamics in communities and ecosystems, and various ecological factors can shape the evolution of constitutive and plastic dispersal behaviours. One important driver of dispersal plasticity is the biotic environment. Parasites, for example, influence the internal condition of infected hosts and define external patch quality. Thus state-dependent dispersal may be determined by infection status and context-dependent dispersal by the abundance of infected hosts in the population. A prerequisite for such dispersal plasticity to evolve is a genetic basis on which natural selection can act. Using interconnected microcosms, we investigated dispersal in experimental populations of the freshwater protist Paramecium caudatum in response to the bacterial parasite Holospora undulata. For a collection of 20 natural host strains, we found substantial variation in constitutive dispersal, and to a lesser degree in dispersal plasticity. First, infection tended to increase or decrease dispersal relative to uninfected controls, depending on strain identity, potentially indicative of state-dependent dispersal plasticity. Infection additionally decreased host swimming speed compared to the uninfected counterparts. Second, for certain strains, there was a weak negative association between dispersal and infection prevalence, such that uninfected hosts tended to disperse less when infection was more frequent in the population, indicating context-dependent dispersal plasticity. Future experiments may test whether the observed differences in dispersal plasticity are sufficiently strong to react to natural selection. The evolution of dispersal plasticity as a strategy to mitigate parasite effects spatially may have important implications for epidemiological dynamics.

Anthropogenic activities are increasingly affecting ecosystems across the globe. Meanwhile, empirical and theoretical evidence suggest that natural systems can exhibit abrupt collapses in response to incremental increases in the stressors, sometimes with dramatic ecological and economic consequences. These catastrophic shifts are faster and larger than expected from the changes in the stressors and happen once a tipping point is crossed. The primary mechanisms that drive ecosystem responses to perturbations lie in their architecture of relationships, i.e. how species interact with each other and with the physical environment and the spatial structure of the environment. Nonetheless, existing theoretical work on catastrophic shifts has so far largely focused on relatively simple systems that have either few species and/or no spatial structure. This work has laid a critical foundation for understanding how abrupt responses to incremental stressors are possible, but it remains difficult to predict (let alone manage) where or when they are most likely to occur in more complex real-world settings. Here, we discuss how scaling up our investigations of catastrophic shifts from simple to more complex—species rich and spatially structured—systems could contribute to expanding our understanding of how nature works and improve our ability to anticipate the effects of global change on ecological systems. This article is part of the theme issue ‘Ecological complexity and the biosphere: the next 30 years’.

Temperatures are increasing due to global changes, putting biodiversity at risk. Organisms are faced with a limited set of options to cope with this situation: adapt, disperse or die. We here focus on the first possibility, more specifically, on evolutionary adaptations to temperature. Ectotherms are usually characterized by a hump-shaped relationship between fitness and temperature, a non-linear reaction norm that is referred to as thermal performance curve (TPC). To understand and predict impacts of global change, we need to know whether and how such TPCs evolve.Therefore, we performed a systematic literature search and a statistical meta-analysis focusing on experimental evolution and artificial selection studies. This focus allows us to directly quantify relative fitness responses to temperature selection by calculating fitness differences between TPCs from ancestral and derived populations after thermal selection.Out of 7561 publications screened, we found 47 studies corresponding to our search criteria representing taxa across the tree of life, from bacteria, to plants and vertebrates. We show that, independently of species identity, the studies we found report a positive response to temperature selection. Considering entire TPC shapes, adaptation to higher temperatures traded off with fitness at lower temperatures, leading to niche shifts. Effects were generally stronger in unicellular organisms. By contrast, we do not find statistical support for the often discussed “Hotter is better” hypothesis.While our meta-analysis provides evidence for adaptive potential of TPCs across organisms, it also highlights that more experimental work is needed, especially for under-represented taxa, such as plants and non-model systems.

Human activities put ecosystems under increasing pressure, often resulting in local extinctions. However, it is unclear how local extinctions affect regional processes, such as the distribution of diversity in space, especially if extinctions show spatial patterns, such as being clustered. Therefore, it is crucial to investigate extinctions and their consequences in a spatially explicit framework. Using highly controlled microcosm experiments and theoretical models, we ask here how the number and spatial autocorrelation of extinctions interactively affect metacommunity dynamics. We found that local patch extinctions increased local diversity ( α -diversity) and inter-patch diversity ( β -diversity) by delaying the exclusion of inferior competitors. Importantly, recolonization dynamics depended more strongly on the spatial distribution than on the number of patch extinctions: clustered local patch extinctions resulted in slower recovery, lower α -diversity and higher β -diversity. Our results highlight that the spatial distribution of perturbations should be taken into account when studying and managing spatially structured communities.

Exploitative parasites are predicted to evolve in highly connected populations or in expanding epidemics. However, many parasites rely on host dispersal to reach new populations, potentially causing conflict between local transmission and global spread. We performed experimental range expansions in interconnected microcosms of the protozoan Paramecium caudatum, allowing natural dispersal of hosts infected with the bacterial parasite Holospora undulata. Parasites from range front treatments facilitated host dispersal and were less virulent, but also invested less in horizontal transmission than parasites from range cores. These differences were consistent with parameter estimates derived from an epidemiological model fitted on population-level time-series data. Our results illustrate how dispersal selection can have profound consequences for the evolution of parasite life history and virulence. Decrypting the eco-evolutionary processes that shape parasite 'dispersal syndromes' may be important for the management of spreading epidemics in changing environments, biological invasions or in other spatial non-equilibrium settings.

Dispersal is a central biological process tightly integrated into life-histories, morphology, physiology and behaviour. Such associations, or syndromes, are anticipated to impact the eco-evolutionary dynamics of spatially structured populations, and cascade into ecosystem processes. As for dispersal on its own, these syndromes are likely neither fixed nor random, but conditional on the experienced environment. We experimentally studied how dispersal propensity varies with individuals' phenotype and local environmental harshness using 15 species ranging from protists to vertebrates. We reveal a general phenotypic dispersal syndrome across studied species, with dispersers being larger, more active and having a marked locomotion-oriented morphology and a strengthening of the link between dispersal and some phenotypic traits with environmental harshness. Our proof-of-concept metacommunity model further reveals cascading effects of context-dependent syndromes on the local and regional organisation of functional diversity. Our study opens new avenues to advance our understanding of the functioning of spatially structured populations, communities and ecosystems.

A major focus of ecology is to understand and predict ecosystem function across scales. Many ecosystem functions are measured only at local scales, while their effects occur at a landscape level. Here we investigate how landscape-scale predictions of ecosystem function depend on intraspecific competition, a fine-scale process, by manipulating intraspecific density of shredding macroinvertebrates and examining effects on leaf litter decomposition, a key function in freshwater ecosystems. For two species, we found that per capita leaf processing rates declined with increasing density following power functions with negative exponents, likely due to interference competition. To demonstrate consequences of this nonlinearity, we scaled up estimates of leaf litter processing from shredder abundance surveys in 10 replicated headwater streams. In accordance with Jensen's inequality, applying density-dependent consumption rates reduced estimates of catchment-scale leaf consumption by an order of magnitude relative to density-independent rates. Density-dependent consumption estimates aligned closely with metabolic requirements in catchments with large-but not small-shredder populations. Importantly, shredder abundance was not limited by leaf litter availability, and catchment-level leaf litter supply was much higher than estimated consumption. Thus leaf litter processing was not limited by resource supply. Our work highlights the need for scaling up, which accounts for intraspecific interactions.

Theory predicts that the distribution of genetic diversity in a landscape is strongly dependent on the connectivity of the metapopulation and the dispersal of individuals between patches. However, the influence of explicit spatial configurations such as dendritic landscapes on the genetic diversity of metapopulations is still understudied, and theoretical corroborations of empirical patterns are largely lacking. Here, we used microsatellite data and stochastic simulations of two metapopulations of freshwater amphipods in a 28,000 km2 riverine network to study the influence of spatial connectivity and dispersal strategies on the spatial distribution of their genetic diversity. We found a significant imprint of the effects of riverine network connectivity on the local and global genetic diversity of both amphipod species. Data from 95 sites showed that allelic richness significantly increased towards more central nodes of the network. This was also seen for observed heterozygosity, yet not for expected heterozygosity. Genetic differentiation increased with instream distance. In simulation models, depending on the mutational model assumed, upstream movement probability and dispersal rate, respectively, emerged as key factors explaining the empirically observed distribution of local genetic diversity and genetic differentiation. Surprisingly, the role of site-specific carrying capacities, for example by assuming a direct dependency of population size on local river size, was less clear cut: while our best fitting model scenario included this feature, over all simulations, scaling of carrying capacities did not increase data-model fit. This highlights the importance of dispersal behaviour along spatial networks in shaping population genetic diversity.

International audience; Ecology and evolution unfold in spatially structured communities, where dispersal links dynamics across scales. Because dispersal is multicausal, identifying general drivers remains challenging. In a coordinated distributed experiment spanning organisms from protozoa to vertebrates, we tested whether two fundamental determinants of local dynamics, top-down and bottom-up control, generally explain active dispersal. We show that both factors consistently increased emigration rates and use metacommunity modelling to highlight consequences on local and regional dynamics.

L31-34: “by allowing... by making... by exerting...” a little bit hard to follow, rephrase? I would add the sample size in the abstract becauseit is important to know it to understand the conclusion of the study . And I think references can be removed from the abstract, it will make space for a sentence or two about the touchscreen task maybe?

A recommendation – based on reviews by Two anonymous reviewers – of the article: Sevchik, A., Logan, C. J., McCune, K. B., Blackwell, A., Rowney, C. and Lukas, D. (2021) Investigating sex differences in genetic relatedness in great-tailed grackles in Tempe, Arizona to infer potential sex biases in dispersal. EcoEvoRxiv, osf.io/t6beh, ver. 5 peer-reviewed and recommended by Peer community in Ecology. doi: https://doi.org/10.32942/osf.io/t6beh

Theory predicts that the distribution of genetic diversity in a landscape is strongly dependent on the connectivity of the metapopulation and the dispersal of individuals between patches. However, the influence of explicit spatial configurations such as dendritic landscapes on the genetic diversity and structure of metapopulations is still understudied, and theoretical corroborations of empirical patterns are largely lacking. Here, we used real-world microsatellite data and stochastic simulations of two metapopulations of freshwater amphipods in a 28,000 km2riverine network to study the influence of spatial connectivity and dispersal strategies on their spatial genetic diversity and structure. We found a significant imprint of the riverine network connectivity on the genetic diversity of both amphipod species. Data from 95 sites showed that allelic richness and observed heterozygosity significantly increased towards more central nodes of the network. In simulation models, dispersal rate was suggested to be the key factor explaining the empirically observed distribution of genetic diversity. Contrary to often-claimed expectations, however, the relevance of directionality of dispersal was only minor. Surprisingly, also the consideration of site-specific carrying capacities, for example by assuming a direct dependency of population size with local river size, substantially decreased the model fit to empirical data. This highlights that directional dispersal and the spatial arrangement of population sizes may have a smaller relevance in shaping population genetic diversity of riverine organisms than previously thought, and that dispersal along the river network is the single-most important determinant of population genetic diversity.

While host–parasite interactions are ubiquitous, the large‐scale consequences of parasite infections are mainly driven by the spatial context. One trait of pivotal importance for the eco‐evolutionary dynamics of such metapopulations is the spatial behaviour of hosts, that is, their dispersal. It is well established that dispersal is not a random process, rather dispersal is informed and may depend on internal and external factors. In host–parasite metapopulations, dispersal may be a function of a host's infection state, but also of the local context, such as host density or parasite prevalence. Using a dynamical host–parasite metapopulation model of a parasite that reduces host fecundity (sterilizing parasite), we explore whether host dispersal evolves to be state‐ and context‐dependent and what shapes the evolutionarily stable dispersal reaction norms have. We show that state‐dependent dispersal readily evolves in the sense that hosts disperse more when infected, except when infected hosts pay significantly higher dispersal costs. This dispersal bias evolves due to kin selection, which is consistent with previous studies. Most importantly, we show that prevalence‐dependent dispersal evolves, especially when virulence is high and epidemiological dynamics have predictable signatures. The observed evolutionary outcome, a negatively prevalence‐dependent dispersal reaction norm for susceptible hosts at high virulence, seems counter‐intuitive at first. However, our results can be readily explained by the emergent epidemiological dynamics, especially their spatial and temporal correlation patterns. Finally, we show that context‐dependency in dispersal may rely on both, prevalence, and host density cues. Our work provides new insights into the evolution of complex dispersal phenotypes in host–parasite metapopulations as well as on feedbacks with epidemiological dynamics.

Eco-evolutionary processes may play an important role in the spatial spread of infectious disease. Current theory predicts more exploitative parasites to evolve in highly connected populations or at the front of spreading epidemics. However, many parasites rely on host dispersal to reach new populations. This may lead to conflict between local transmission and global spread, possibly counteracting selection for higher virulence. Here, we used the freshwater host Paramecium caudatum and its bacterial parasite Holospora undulata to investigate parasite evolution under an experimental range expansion scenario with natural host dispersal. We find that parasites evolving at experimental range fronts favoured higher dispersal rates of infected hosts than did parasites evolving in core populations. Front parasites further showed lower levels of virulence (host division and survival) and delayed development of infection, consistent with parameter estimates from an epidemiological model that we fitted on experimental time-series data. This combined evidence suggests an evolutionary trade-off between virulence and host-mediated dispersal, with a concomitant reduction in the investment into horizontal transmission. Our experiment illustrates how parasite evolution can be shaped by divergent selection encountered in different segments of an epidemic wave. Such an interplay between demography and spatial selection has important implications for the understanding and management of emerging diseases, and, more generally, for biological invasions and other non-equilibrium scenarios of spreading populations.SIGNIFICANCE STATEMENTWhat drives parasite evolution in spatially expanding epidemics? Many parasites require dispersal of infected hosts to reach new patches, and this may produce specific adaptations enhancing spatial spread. We performed experimental range expansions in an aquatic model system, with natural dispersal of infected hosts. Parasites from experimental range fronts were less virulent and interfered less with host dispersal, but also invested less in horizontal transmission than parasites from the range core. Thus, dispersal adaptation at the front may come at a cost of reduced horizontal transmission, a trade-off rarely considered in theoretical models on parasite virulence evolution. These results have important implications in the context of emerging diseases, and for parasite evolution during biological invasions or other spatial non-equilibrium scenarios.

International audience; Environmental change can alter species’ abundances within communities consistently; for example, increasing all abundances by the same percentage, or more idiosyncratically. Here, we show how comparing effects of temperature on species grown in isolation and when grown together helps our understanding of how ecological communities more generally respond to environmental change. In particular, we find that the shape of the feasibility domain (the parameter space of carrying capacities compatible with positive species’ abundances) helps to explain the composition of experimental microbial communities under changing environmental conditions. First, we introduce a measure to quantify the asymmetry of a community’s feasibility domain using the column vectors of the corresponding interaction matrix. These column vectors describe the effects each species has on all other species in the community (hereafter referred to as species’ multidimensional effects). We show that as the asymmetry of the feasibility domain increases the relationship between species’ abundance when grown together and when grown in isolation weakens. We then show that microbial communities experiencing different temperature environments exhibit patterns consistent with this theory. Specifically, communities at warmer temperatures show relatively more asymmetry; thus, the idiosyncrasy of responses is higher compared with that in communities at cooler temperatures. These results suggest that while species’ interactions are typically defined at the pairwise level, multispecies dynamics can be better understood by focusing on the effects of these interactions at the community level.

Predator–prey interactions heavily influence the dynamics of many ecosystems. An increasing body of evidence suggests that rapid evolution and coevolution can alter these interactions, with important ecological implications, by acting on traits determining fitness, including reproduction, anti-predatory defence and foraging efficiency. However, most studies to date have focused only on evolution in the prey species, and the predator traits in (co)evolving systems remain poorly understood. Here, we investigated changes in predator traits after approximately 600 generations in a predator–prey (ciliate–bacteria) evolutionary experiment. Predators independently evolved on seven different prey species, allowing generalization of the predator's evolutionary response. We used highly resolved automated image analysis to quantify changes in predator life history, morphology and behaviour. Consistent with previous studies, we found that prey evolution impaired growth of the predator, although the effect depended on the prey species. By contrast, predator evolution did not cause a clear increase in predator growth when feeding on ancestral prey. However, predator evolution affected morphology and behaviour, increasing size, speed and directionality of movement, which have all been linked to higher prey search efficiency. These results show that in (co)evolving systems, predator adaptation can occur in traits relevant to foraging efficiency without translating into an increased ability of the predator to grow on the ancestral prey type.

At species’ range edges, individuals often face novel environmental conditions that may limit range expansion until populations adapt. The potential to adapt depends on genetic variation upon which selection can act. However, populations at species’ range edges are often genetically depauperate. One mechanism increasing genetic variation is reshuffling existing variation through sex. Sex, however, can potentially limit adaptation by breaking up existing beneficial allele combinations (recombination load). The gene swamping hypothesis predicts this is specifically the case when populations expand along an abiotic gradient and asymmetric dispersal leads to numerous maladapted dispersers from the range core swamping the range edge. We used the ciliate Tetrahymena thermophila as a model for testing the gene swamping hypothesis. We performed replicated range expansions in landscapes with or without a pH-gradient, while simultaneously manipulating the occurrence of gene flow and sexual versus asexual reproduction. We show that sex accelerated evolution of local adaptation in the absence of gene flow, but hindered it in the presence of gene flow. However, sex affected adaptation independently of the pH-gradient, indicating that both abiotic gradients and the biotic gradient in population density lead to gene swamping. Overall, our results show that gene swamping alters adaptation in life-history strategies.

While host-parasite interactions are ubiquitous, the large scale consequences of parasite infections are mainly driven by the spatial context. One trait of pivotal importance for the eco-evolutionary dynamics of such metapopulations is the spatial behaviour of hosts, that is, their dispersal. It is well established that dispersal is not a random process, rather dispersal is informed and may depend on internal and external factors. In host-parasite metapopulations, dispersal may be a function of a host’s infection state, but also of the local context, such as host density or parasite prevalence. Using a dynamical host-parasite metapopulation model, we explore whether host dispersal evolves to be state- and context-dependent and what shapes the evolutionarily stable dispersal reaction norms have. We show that state-dependent dispersal readily evolves in the sense that hosts disperse more when infected. This dispersal bias evolves due to kin selection which is consistent with previous studies. Most importantly, we show that prevalence-dependent dispersal evolves, especially when virulence is high and epidemiological dynamics have predictable signatures. The observed evolutionary outcome, a negatively prevalence-dependent dispersal reaction norm for susceptible hosts, seems counter-intuitive at first. However, our results can be readily explained by the emergent epidemiological dynamics, especially their spatial and temporal correlation patterns. Finally, we show that context-dependency in dispersal may rely on both, prevalence, but also host density cues. Our work provides new insights into the evolution of complex dispersal phenotypes in host-parasite metapopulations as well as on associated feedbacks between ecological dynamics and evolutionary change.

Cross-ecosystem subsidies are studied with a focus on resource exchange at local ecosystem boundaries. This perspective ignores regional dynamics that can emerge via constraints imposed by the landscape, potentially leading to spatially-dependent effects of subsidies and spatial feedbacks. Using miniaturized landscape analogues of river dendritic and terrestrial lattice spatial networks, we manipulated and studied resource exchange between the two whole networks. We found that community composition in dendritic networks depended on the resource pulse from the lattice network, with the strength of this effect declining in larger downstream patches. In turn, this spatially-dependent effect imposed constraints on the lattice network with populations in that network reaching higher densities when connected to more central patches in the dendritic network. Consequently, localized cross-ecosystem fluxes, and their respective effects on recipient ecosystems, must be studied in a perspective taking into account the explicit spatial configuration of the landscape.Statement of authorshipEH, IG, EAF and FA designed the research; EH conducted the lab experiment with support from IG, EAF and FA, processed the experimental data with methodological developments from IG, and carried out the analysis of experimental data; all authors participated in results interpretation; EH wrote the first draft of the manuscript; All authors significantly contributed to further manuscript revisions.

Several key processes in freshwater ecology are governed by the connectivity inherent to dendritic river networks. These have extensively been analyzed from a geomorphological and hydrological viewpoint, yet structures classically used in ecological modeling have been poorly representative of the structure of real river basins, often failing to capture well‐known scaling features of natural rivers. Pioneering work identified optimal channel networks (OCNs) as spanning trees reproducing all scaling features characteristic of natural stream networks worldwide. While OCNs have been used to create landscapes for studies on metapopulations, biodiversity, and epidemiology, their generation has not been generally accessible.Given the increasing interest in dendritic riverine networks by ecologists and evolutionary biologists, we here present a method to generate OCNs and, to facilitate its application, we provide the R‐package OCNet. Owing to the stochastic process generating OCNs, multiple network replicas spanning the same surface can be built; this allows performing computational experiments whose results are irrespective of the particular shape of a single river network. The OCN construct also enables the generation of elevational gradients derived from the optimal network configuration, which can constitute three‐dimensional landscapes for spatial studies in both terrestrial and freshwater realms. Moreover, the package provides functions that aggregate OCNs into an arbitrary number of nodes, calculate several descriptors of river networks, and draw relevant network features.We describe the main functionalities of the package and its integration with other R‐packages commonly used in spatial ecology. Moreover, we exemplify the generation of OCNs and discuss an application to a metapopulation model for an invasive riverine species.In conclusion, OCNet provides a powerful tool to generate realistic river network analogues for various applications. It thereby allows the design of spatially realistic studies in increasingly impacted ecosystems and enhances our knowledge on spatial processes in freshwater ecology in general., Recently, research on spatial dynamics in ecology and evolution has bloomed. However, spatial structures used in theoretical and empirical ecological studies are often not representative of realistic landscapes. This is particularly true for river networks, which are of paramount interest to ecologists owing to their wide (but currently severely declining) biodiversity. Indeed, most of ecological work has been neglecting the scaling character of real river networks, despite well‐established knowledge in the fields of geomorphology and hydrology. Here, we present a method to create optimal channel networks (OCNs, i.e., river network analogues reproducing all topographic and scaling features of natural rivers), and the respective R‐package allowing their generation and analysis. We review the theoretical background underlying the OCN concept, present the main package functionalities, discuss possible applications in the realm of ecology and evolution, and detail how the package can be integrated with other popular R‐packages in spatial ecology.

Human activities lead more and more to the disturbance of plant and animal communities with local extinctions as a consequence. While these negative effects are clearly visible at a local scale, it is less clear how such local patch extinctions affect regional processes, such as metacommunity dynamics and the distribution of diversity in space. Since local extinctions may not be isolated events in space but rather cluster together, it is crucial to investigate their effects in a spatially explicit framework.Here, we use experimental microcosms and numerical simulations to understand the relationship between local patch extinctions and metacommunity dynamics. More specifically, we investigate the effects of the amount and spatial autocorrelation of extinctions in a full factorial design. Experimentally, we found that local patch extinctions increased inter-patch (β-) diversity by creating differences between perturbed and unperturbed patches and at the same time increased local (α-) diversity by delaying the competitive exclusion of inferior competitors. Most importantly, recolonization dynamics depended more strongly on the spatial distribution of patch extinctions than on the amount of extinctions per se. Clustered local patch extinctions reduced mixing between perturbed and unperturbed patches which led to slower recovery, lower α-diversity in unperturbed patches and higher β-diversity. Results from a metacommunity model matched the experimental observations qualitatively when the model included ranked competitive interactions, giving a hint at the underlying mechanisms.Our results highlight that local patch extinctions can increase the diversity within and between communities, that the strength of these effects depends on the spatial distribution of extinctions and that the effects of local patch extinctions can spread regionally, throughout a landscape. These findings are highly relevant for conservation and management of spatially structured communities under global change.

Range expansions and biological invasions are prime examples of transient processes that are likely impacted by rapid evolutionary changes. As a spatial process, range expansions are driven by dispersal and movement behaviour. Although it is widely accepted that dispersal and movement may be context-dependent, for instance density-dependent, and best represented by reaction norms, the evolution of density-dependent movement during range expansions has received little experimental attention. We therefore tested current theory predicting the evolution of increased movement at low densities at range margins using highly replicated and controlled range expansion experiments across multiple genotypes of the protist model system Tetrahymena thermophila. Although rare, we found evolutionary changes during range expansions even in the absence of initial standing genetic variation. Range expansions led to the evolution of negatively density-dependent movement at range margins. In addition, we report the evolution of increased intrastrain competitive ability and concurrently decreased population growth rates in range cores. Our findings highlight the importance of understanding movement and dispersal as evolving reaction norms and plastic life-history traits of central relevance for range expansions, biological invasions and the dynamics of spatially structured systems in general.

Dispersal is a process of central importance for the ecological and evolutionary dynamics of populations and communities, because of its diverse consequences for gene flow and demography. It is subject to evolutionary change, which begs the question, what is the genetic basis of this potentially complex trait? To address this question, we (i) review the empirical literature on the genetic basis of dispersal, (ii) explore how theoretical investigations of the evolution of dispersal have represented the genetics of dispersal, and (iii) discuss how the genetic basis of dispersal influences theoretical predictions of the evolution of dispersal and potential consequences. Dispersal has a detectable genetic basis in many organisms, from bacteria to plants and animals. Generally, there is evidence for significant genetic variation for dispersal or dispersal-related phenotypes or evidence for the micro-evolution of dispersal in natural populations. Dispersal is typically the outcome of several interacting traits, and this complexity is reflected in its genetic architecture: while some genes of moderate to large effect can influence certain aspects of dispersal, dispersal traits are typically polygenic. Correlations among dispersal traits as well as between dispersal traits and other traits under selection are common, and the genetic basis of dispersal can be highly environment-dependent. By contrast, models have historically considered a highly simplified genetic architecture of dispersal. It is only recently that models have started to consider multiple loci influencing dispersal, as well as non-additive effects such as dominance and epistasis, showing that the genetic basis of dispersal can influence evolutionary rates and outcomes, especially under non-equilibrium conditions. For example, the number of loci controlling dispersal can influence projected rates of dispersal evolution during range shifts and corresponding demographic impacts. Incorporating more realism in the genetic architecture of dispersal is thus necessary to enable models to move beyond the purely theoretical towards making more useful predictions of evolutionary and ecological dynamics under current and future environmental conditions. To inform these advances, empirical studies need to answer outstanding questions concerning whether specific genes underlie dispersal variation, the genetic architecture of context-dependent dispersal phenotypes and behaviours, and correlations among dispersal and other traits.

1. Understanding the consequences of spatial structure on ecological dynamics is a central theme in ecology. Recently, research has recognised the relevance of river and river-analogue network structures, because these systems are not only highly diverse but also rapidly changing due to habitat modifications or species invasions. 2. Much of the previous work on ecological and evolutionary dynamics in metapop- ulations and metacommunities in dendritic river networks has been either using comparative approaches or was purely theoretical. However, the use of micro- cosm experiments provides the unique opportunity to study large-scale questions in a causal and experimental framework. 3. We conducted replicated microcosm experiments, in which we manipulated the spatially explicit network configuration of a landscape and addressed how linear versus dendritic connectivity affects population dynamics, specifically the spatial distribution of population densities, and movement behaviour of the protist model organism Tetrahymena pyriformis. We tracked population densities and individual-level movement behaviour of thousands of individuals over time. 4. At the end of the experiment, we found more variable population densities between patches in dendritic networks compared to linear networks, as pre- dicted by theory. Specifically, in dendritic networks, population densities were higher at nodes that connected to headwaters compared to the headwaters themselves and to more central nodes in the network. These differences follow theoretical predictions and emerged from the different network topologies per se. These differences in population densities emerged despite weakly density- dependent movement. 5. We show that differences in network structure alone can cause characteristic spatial variation in population densities. While such differences have been postu- lated by theoretical work and are the underlying precondition for differential dis- persal evolution in heterogeneous networks, our results may be the first experimental demonstration thereof. Furthermore, these population-level dynam- ics may affect extinction risks and can upscale to previously shown metacommu- nity level diversity dynamics. Given that many species in natural river systems exhibit strong spatiotemporal patterns in population densities, our work suggests that abundance patterns should not only be addressed from a local environmental perspective, but may be the outcome of processes that are inher- ently driven by the respective habitat network structure.

Eco-evolutionary dynamics are now recognized to be highly relevant for population and community dy- namics. However, the impact of evolutionary dynamics on spatial patterns, such as the occurrence of clas- sical metapopulation dynamics, is less well appreciated. Here, we analyse the evolutionary consequences of spatial network connectivity and topology for dispersal strategies and quantify the eco-evolutionary feedback in terms of altered classical metapopulation dynamics. We find that network properties, such as topology and connectivity, lead to predictable spatio-temporal correlations in fitness expectations. These spatio-temporally stable fitness patterns heavily impact evolutionarily stable dispersal strategies and lead to eco-evolutionary feedbacks on landscape level metrics, such as the number of occupied patches, the number of extinctions and recolonizations as well as metapopulation extinction risk and genetic struc- ture. Our model predicts that classical metapopulation dynamics are more likely to occur in dendritic networks, and especially in riverine systems, compared to other types of landscape configurations. As it remains debated whether classical metapopulation dynamics are likely to occur in nature at all, our work provides an important conceptual advance for understanding the occurrence of classical metapopulation dynamics which has implications for conservation and management of spatially structured populations.

Aim Globally, the geographical distributions of species are dynamic and strongly influenced by dispersal. At the same time, range dynamics feed back and may select for increased dispersal at expanding range fronts. This interplay between macroecological and evolutionary dynamics happens almost universally across environmental gradients and such gradients can have a direct impact on the fitness of organisms due to the match or mismatch between an individual's environmental optimum and the current conditions along the gradient. Importantly, gradients also provide individuals with information on environmental changes because dispersing individuals may sense whether environmental conditions improve or deteriorate. However, the ability of organisms to use this information on the environment and to subsequently adjust dispersal decisions plastically, that is, deciding to further disperse into the gradient or not, has been largely ignored and the macroecological consequences remain unclear. We here aim to demonstrate the impact of informed dispersal on the eco-evolutionary dynamics of ranges. Location Laboratory and theoretical. Methods We used individual-based simulations and controlled experiments in replicated microcosm landscapes. Range expansions of the protist model organism Tetrahymena were tracked using video recording and analysis. Results We show that information on environmental gradients had a severe impact on range dynamics and inverted the spatial distribution of population densities in comparison with controls where this information was not provided. Additionally, the use of information on gradients prevented evolutionary changes in dispersal rates and an acceleration of range expansion. Main conclusions We demonstrate the strong impact of informed dispersal and subsequent behavioural changes on range dynamics in environmental gradients. More generally, our findings highlight the importance of informed dispersal for spatial ecological and evolutionary dynamics.

It is widely recognized that ecological dynamics influence evolutionary dynamics, and conversely that evolutionary changes alter ecological processes. Because fragmentation impacts all biological levels (from individuals to ecosystems) through isolation and reduced habitat size, it strongly affects the links among evolutionary and ecological processes such as population dynamics, local adaptation, dispersal and speciation. Here, we review our current knowledge of the eco-evolutionary dynamics in fragmented landscapes, focusing on both theory and experimental studies. We then suggest future experimental directions to study eco-evolutionary dynamics and/or feedbacks in fragmented landscapes, especially to bridge the gap between theoretical predictions and experimental validations. This article is protected by copyright. All rights reserved.

Abiotic stress is a major force of selection that organisms are constantly facing. While the evolutionary effects of various stressors have been broadly studied, it is only more recently that the relevance of interactions between evolution and underlying ecological conditions, that is, eco-evolutionary feedbacks, have been highlighted. Here, we experimentally investigated how populations adapt to pH-stress under high population densities. Using the protist speciesTetrahymena thermophila, we studied how four different genotypes evolved in response to stressfully low pH conditions and high population densities. We found that genotypes underwent evolutionary changes, some shifting up and others shifting down their intrinsic rates of increase (r0). Overall, evolution at low pH led to the convergence ofr0and intraspecific competitive ability (α) across the four genotypes. Given the strong correlation betweenr0andα, we argue that this convergence was a consequence of selection for increased density-dependent fitness at low pH under the experienced high density conditions. Increased density-dependent fitness was either attained through increase inr0, or decrease ofα, depending on the genetic background. In conclusion, we show that demography can influence the direction of evolution under abiotic stress.

Predator-prey interactions are key for the dynamics of many ecosystems. An increasing body of evidence suggests that rapid evolution and co-evolution can alter these interactions, with important ecological implications, by acting on traits determining fitness, including reproduction, anti-predatory defense and foraging efficiency. However, most studies to date have focused only on evolution in the prey species, and the predator traits in (co-)evolving systems remain poorly understood. Here we investigated changes in predator traits after ~600 generations in a predator-prey (ciliate-bacteria) evolutionary experiment. Predators independently evolved on seven different prey species, allowing generalization of the predator’s evolutionary response. We used highly resolved automated image analysis to quantify changes in predator life history, morphology and behavior. Consistent with previous studies, we found that prey evolution impaired growth of the predator. In contrast, predator evolution did not cause a clear increase in fitness when feeding on ancestral prey. However, predator evolution affected morphology and behavior, increasing size, speed and directionality of movement, which have all been linked to higher prey search efficiency. These results show that in (co-)evolving systems, predator adaptation can occur in traits relevant to offense level without translating into an increased ability of the predator to grow on the ancestral prey type.

Dispersal can strongly influence ecological and evolutionary dynamics. Besides the direct contribution of dispersal to population dynamics, dispersers often differ in their phenotypic attributes from non-dispersers, which leads to dispersal syndromes. The consequences of such dispersal syndromes have been widely explored at the population and community level; however, to date, ecosystem-level effects remain unclear. Here, we examine whether dispersing and resident individuals of two different aquatic keystone invertebrate species have different contributions to detrital processing, a key function in freshwater ecosystems. Using experimental two-patch systems, we found no difference in leaf consumption rates with dispersal status of the common native species Gammarus fossarum . In Dikerogammarus villosus , however, a Ponto-Caspian species now expanding throughout Europe, dispersers consumed leaf litter at roughly three times the rate of non-dispersers. Furthermore, this put the contribution of dispersing D. villosus to leaf litter processing on par with native G. fossarum, after adjusting for differences in organismal size. Given that leaf litter decomposition is a key function in aquatic ecosystems, and the rapid species turnover in freshwater habitats with range expansions of non-native species, this finding suggests that dispersal syndromes may have important consequences for ecosystem functioning.

Environmental change can alter species' abundances within communities consistently; for example, increasing all abundances by the same percentage, or more idiosyncratically. Here, we show how comparing effects of temperature on species grown in isolation and when grown together helps our understanding of how ecological communities more generally respond to environmental change. In particular, we find that the shape of the feasibility domain (the parameter space of carrying capacities compatible with positive species' abundances) helps to explain the composition of experimental microbial communities under changing environmental conditions. First, we introduce a measure to quantify the asymmetry of a community's feasibility domain using the column vectors of the corresponding interaction matrix. These column vectors describe the effects each species has on all other species in the community (hereafter referred to as species' multidimensional effects). We show that as the asymmetry of the feasibility domain increases the relationship between species' abundance when grown together and when grown in isolation weakens. We then show that microbial communities experiencing different temperature environments exhibit patterns consistent with this theory. Specifically, communities at warmer temperatures show relatively more asymmetry; thus, the idiosyncrasy of responses is higher compared with that in communities at cooler temperatures. These results suggest that while species' interactions are typically defined at the pairwise level, multispecies dynamics can be better understood by focusing on the effects of these interactions at the community level.

Assessing individual components of biodiversity, such as local or regional taxon richness, and differences in community composition is a long-standing challenge in ecology. It is especially relevant in spatially structured and diverse ecosystems. Environmental DNA (eDNA) has been suggested as a novel technique to accurately measure biodiversity. However, we do not yet fully understand the comparability of eDNA-based assessments to previously used approaches.We sampled may-, stone-, and caddisfly genera with contemporary eDNA and kicknet methods at 61 sites distributed over a large river network, allowing a comparison of various diversity measures from the catchment to site levels and providing insights into how these measures relate to network properties. We extended our survey data with historical records of total diversity at the catchment level.At the catchment scale, eDNA and kicknet detected similar proportions of the overall and cumulative historically documented species richness (gamma diversity), namely 42% and 46%, respectively. We further found a good overlap (62%) between the two contemporary methods at the regional scale.At the local scale, we found highly congruent values of local taxon richness (alpha diversity) between eDNA and kicknet. Richness of eDNA was positively related with discharge, a descriptor of network position, while kicknet was not.Beta diversity between sites was similar for the two contemporary methods. Contrary to our expectation, however, beta diversity was driven by species replacement and not by nestedness.Although optimization of eDNA approaches is still needed, our results indicate that this novel technique can capture extensive aspects of gamma diversity, proving its potential utility as a new tool for large sampling campaigns across hitherto understudied complete river catchments, requiring less time and becoming more cost-efficient than classical approaches. Overall, the richness estimated with the two contemporary methods is similar at both local and regional scale but community composition is differently assessed with the two methods at individual sites and becomes more similar with higher discharge.

Theoretical models pertaining to feedbacks between ecological and evolutionary processes are prevalent in multiple biological fields. An integrative overview is currently lacking, due to little crosstalk between the fields and the use of different methodological approaches. Here, we review a wide range of models of eco‐evolutionary feedbacks and highlight their underlying assumptions. We discuss models where feedbacks occur both within and between hierarchical levels of ecosystems, including populations, communities and abiotic environments, and consider feedbacks across spatial scales. Identifying the commonalities among feedback models, and the underlying assumptions, helps us better understand the mechanistic basis of eco‐evolutionary feedbacks. Eco‐evolutionary feedbacks can be readily modelled by coupling demographic and evolutionary formalisms. We provide an overview of these approaches and suggest future integrative modelling avenues. Our overview highlights that eco‐evolutionary feedbacks have been incorporated in theoretical work for nearly a century. Yet, this work does not always include the notion of rapid evolution or concurrent ecological and evolutionary time scales. We show the importance of density‐ and frequency‐dependent selection for feedbacks, as well as the importance of dispersal as a central linking trait between ecology and evolution in a spatial context. A plain language summary is available for this article.

International audience; Assessing individual components of biodiversity, such as local or regional taxon richness, and differences in community composition is a long-standing challenge in ecology. It is especially relevant in spatially structured and diverse ecosystems. Environmental DNA (eDNA) has been suggested as a novel technique to detect taxa and therefore may allow to accurately measure biodiversity. However, we do not yet fully understand the comparability of eDNA-based assessments to classical morphological approaches. We assessed may-, stone-, and caddisfly genera with two contemporary methods, namely eDNA sampling followed by molecular identification and kicknet sampling followed by morphological identification. We sampled 61 sites distributed over a large river network, allowing a comparison of various diversity measures from the catchment to site levels and providing insights into how these measures relate to network properties. We extended our data with historical morphological records of total diversity at the catchment level. At the catchment scale, identification based on eDNA and kicknet samples detected similar proportions of the overall and cumulative historically documented richness (gamma diversity), 42% and 46%, respectively. We detected a good overlap (62%) between genera identified from eDNA and kicknet samples at the regional scale. At the local scale, we found highly congruent values of local taxon richness (alpha diversity) between eDNA and kicknet samples. Richness of eDNA was positively related to discharge, a descriptor of network position, while kicknet was not. Beta diversity, a measure of dissimilarity between sites, was comparable for the two contemporary methods and is driven by species replacement and not by nestedness. Although eDNA approaches are still in their infancy and optimization regarding sampling design and laboratory work is still needed, our results indicate that it can capture different components of diversity, proving its potential utility as a new tool for large sampling campaigns across hitherto understudied complete river catchments.

Global analyses of biodiversity consistently reveal recurrent patterns of species distributions worldwide. However, unveiling the specific mechanisms behind those patterns remains logistically challenging, yet necessary for reliable biodiversity forecasts. Here, we combine theory and experiments to investigate the processes underlying spatial biodiversity patterns in dendritic, river-like landscapes, iconic examples of highly threatened ecosystems. We used geometric scaling properties, common to all rivers, to show that the distribution of biodiversity in these landscapes fundamentally depends on how ecological selection is modulated across space: while uniform ecological selection across the network leads to higher diversity in downstream confluences, this pattern can be inverted by disturbances when population turnover (i.e. local mortality) is higher upstream than downstream. Higher turnover in small headwater patches can slow down ecological selection, increasing local diversity in comparison to large downstream confluences. Our results show that disturbance-mediated slowing down of competitive exclusion can generate a specific transient signature in terms of biodiversity distribution when applied over a spatial gradient of disturbance, which is a common feature of many river landscapes.

The logistic growth model is one of the most frequently used formalizations of density dependence affecting population growth, persistence and evolution. Ecological and evolutionary theory and applications to understand population change over time often include this model. However, the assumptions and limitations of this popular model are often not well appreciated.Here, we briefly review past use of the logistic growth model and highlight limitations by deriving population growth models from underlying consumer-resource dynamics. We show that the logistic equation likely is not applicable to many biological systems. Rather, density-regulation functions are usually non-linear and may exhibit convex or both concave and convex curvatures depending on the biology of resources and consumers. In simple cases, the dynamics can be fully described by the continuous-time Beverton-Holt model. More complex consumer dynamics show similarities to a Maynard Smith-Slatkin model.Importantly, we show how population-level parameters, such as intrinsic rates of increase and equilibrium population densities are not independent, as often assumed. Rather, they are functions of the same underlying parameters. The commonly assumed positive relationship between equilibrium population density and competitive ability is typically invalid. As a solution, we propose simple and general relationships between intrinsic rates of increase and equilibrium population densities that capture the essence of different consumer-resource systems.Relating population level models to underlying mechanisms allows us to discuss applications to evolutionary outcomes and how these models depend on environmental conditions, like temperature via metabolic scaling. Finally, we use time-series from microbial food chains to fit population growth models and validate theoretical predictions.Our results show that density-regulation functions need to be chosen carefully as their shapes will depend on the study system’s biology. Importantly, we provide a mechanistic understanding of relationships between model parameters, which has implications for theory and for formulating biologically sound and empirically testable predictions.