Spatiotemporal complexity of patchy invasion in a predator-prey system with the Allee effect

Invasion of an exotic species initiated by its local introduction is considered subject to predator-prey interactions and the Allee effect when the prey growth becomes negative for small values of the prey density. Mathematically, the system dynamics is described by two nonlinear diffusion-reaction equations in two spatial dimensions. Regimes of invasion are studied by means of extensive numerical simulations. We show that, in this system, along with well-known scenarios of species spread via propagation of continuous population fronts, there exists an essentially different invasion regime which we call a patchy invasion. In this regime, the species spreads over space via irregular motion and interaction of separate population patches without formation of any continuous front, the population density between the patches being nearly zero. We show that this type of the system dynamics corresponds to spatiotemporal chaos and calculate the dominant Lyapunov exponent. We then show that, surprisingly, in the regime of patchy invasion the spatially average prey density appears to be below the survival threshold. We also show that a variation of parameters can destroy this regime and either restore the usual invasion scenario via propagation of continuous fronts or brings the species to extinction; thus, the patchy spread can be qualified as the invasion at the edge of extinction. Finally, we discuss the implications of this phenomenon for invasive species management and control.     

Establishing a beachhead: a stochastic population model with an Allee effect applied to species invasion

We formulated a spatially explicit stochastic population model with an Allee effect in order to explore how invasive species may become established. In our model, we varied the degree of migration between local populations and used an Allee effect with variable birth and death rates. Because of the stochastic component, population sizes below the Allee effect threshold may still have a positive probability for successful invasion. The larger the network of populations, the greater the probability of an invasion occurring when initial population sizes are close to or above the Allee threshold. Furthermore, if migration rates are low, one or more than one patch may be successfully invaded, while if migration rates are high all patches are invaded.     

Beyond modules and hubs: the potential of gene coexpression networks for investigating molecular mechanisms of complex brain disorders

In a research environment dominated by reductionist approaches to brain disease mechanisms, gene network analysis provides a complementary framework in which to tackle the complex dysregulations that occur in neuropsychiatric and other neurological disorders. Gene–gene expression correlations are a common source of molecular networks because they can be extracted from high‐dimensional disease data and encapsulate the activity of multiple regulatory systems. However, the analysis of gene coexpression patterns is often treated as a mechanistic black box, in which looming ‘hub genes’ direct cellular networks, and where other features are obscured. By examining the biophysical bases of coexpression and gene regulatory changes that occur in disease, recent studies suggest it is possible to use coexpression networks as a multi‐omic screening procedure to generate novel hypotheses for disease mechanisms. Because technical processing steps can affect the outcome and interpretation of coexpression networks, we examine the assumptions and alternatives to common patterns of coexpression analysis and discuss additional topics such as acceptable datasets for coexpression analysis, the robust identification of modules, disease‐related prioritization of genes and molecular systems and network meta‐analysis. To accelerate coexpression research beyond modules and hubs, we highlight some emerging directions for coexpression network research that are especially relevant to complex brain disease, including the centrality–lethality relationship, integration with machine learning approaches and network pharmacology .     

Connectivity of Caribbean coral populations: complementary insights from empirical and modelled gene flow

Understanding patterns of connectivity among populations of marine organisms is essential for the development of realistic, spatially explicit models of population dynamics. Two approaches, empirical genetic patterns and oceanographic dispersal modelling, have been used to estimate levels of evolutionary connectivity among marine populations but rarely have their potentially complementary insights been combined. Here, a spatially realistic Lagrangian model of larval dispersal and a theoretical genetic model are integrated with the most extensive study of gene flow in a Caribbean marine organism. The 871 genets collected from 26 sites spread over the wider Caribbean subsampled 45.8% of the 1900 potential unique genets in the model. At a coarse scale, significant consensus between modelled estimates of genetic structure and empirical genetic data for populations of the reef-building coral Montastraea annularis is observed. However, modelled and empirical data differ in their estimates of connectivity among northern Mesoamerican reefs indicating that processes other than dispersal may dominate here. Further, the geographic location and porosity of the previously described east-west barrier to gene flow in the Caribbean is refined. A multi-prong approach, integrating genetic data and spatially realistic models of larval dispersal and genetic projection, provides complementary insights into the processes underpinning population connectivity in marine invertebrates on evolutionary timescales.     

Conditions for the invasion of male‐haploidy in diploid populations

Male‐haploidy has independently evolved several times in different phylogenetic groups and has led to various extant lineages in the insects, Arachnida and Rotifera. Although the stability of male‐haploidy as an evolutionary strategy is not well understood, various theories address the invasion of male‐haploidy in diploid populations. Here two of these theories: (i) the maternal transmission hypothesis (MTH) and (ii) the deleterious mutation hypothesis (DMH), are re‐investigated with an agent‐based model to understand the role of genetic drift as a mechanism facilitating the spread of male‐haploidy. These two hypotheses are analysed separately and comparatively, and the results suggest dominance of the MTH. In addition, comparison of the stochastic results to deterministic results using the same model structure shows how genetic drift can enhance the parameter space where male‐haploidy can be expected to invade.     

Comparing the consequences of natural selection,adaptive phenotypic plasticity,and matching habitat choice for phenotype–environment matching,population genetic structure,and reproductive isolation in meta‐populations

Organisms commonly experience significant spatiotemporal variation in their environments. In response to such heterogeneity, different mechanisms may act that enhance ecological performance locally. However, depending on the nature of the mechanism involved, the consequences for populations may differ greatly. Building on a previous model that investigated the conditions under which different adaptive mechanisms (co)evolve, this study compares the ecological and evolutionary population consequences of three very different responses to environmental heterogeneity: matching habitat choice (directed gene flow), adaptive plasticity (associated with random gene flow), and divergent natural selection. Using individual‐based simulations, we show that matching habitat choice can have a greater adaptive potential than plasticity or natural selection: it allows for local adaptation while protecting genetic polymorphism despite global mating or strong environmental changes. Our simulations further reveal that increasing environmental fluctuations and unpredictability generally favor the emergence of specialist genotypes but that matching habitat choice is better at preventing local maladaptation by individuals. This confirms that matching habitat choice can speed up the genetic divergence among populations, cause indirect assortative mating via spatial clustering, and hence even facilitate sympatric speciation. This study highlights the potential importance of directed dispersal in local adaptation and speciation, stresses the difficulty of deriving its operation from nonexperimental observational data alone, and helps define a set of ecological conditions which should favor its emergence and subsequent detection in nature.     

Closing the gaps for animal seed dispersal: Separating the effects of habitat loss on dispersal distances and seed aggregation

Habitat loss can alter animal movements and disrupt animal seed dispersal mutualisms; however, its effects on spatial patterns of seed dispersal are not well understood. To explore the effects of habitat loss on seed dispersal distances and seed dispersion (aggregation), we created a spatially explicit, individual‐based model of an animal dispersing seeds (SEADS—Spatially Explicit Animal Dispersal of Seeds) in a theoretical landscape of 0%–90% habitat loss based on three animal traits: movement distance, gut retention time, and time between movements. Our model design had three objectives: to determine the effects of (1) animal traits and (2) habitat loss on seed dispersal distances and dispersion and (3) determine how animal traits could mitigate the negative effects of habitat loss on these variables. SEADS results revealed a complex interaction involving all animal traits and habitat loss on dispersal distances and dispersion, driven by a novel underlying mechanism of fragment entrapment. Unexpectedly, intermediate habitat loss could increase dispersal distances and dispersion relative to low and high habitat loss for some combinations of animal traits. At intermediate habitat loss, movement between patches was common, and increased dispersal distances and dispersion compared to continuous habitats because animals did not stop in spaces between fragments. However, movement between patches was reduced at higher habitat loss as animals became trapped in fragments, often near the parent plant, and dispersed seeds in aggregated patterns. As movement distance increased, low time between movements and high gut retention time combinations permitted more movement to adjacent patches than other combinations of animal traits. Because habitat loss affects movement in a nonlinear fashion under some conditions, future empirical tests would benefit from comparisons across landscapes with more than two levels of fragmentation.     

How mechanisms of habitat preference evolve and promote divergence with gene flow

Habitat preference may promote adaptive divergence and speciation, yet the conditions under which this is likely are insufficiently explored. We use individual‐based simulations to study the evolution and consequence of habitat preference during divergence with gene flow, considering four different underlying genetically based behavioural mechanisms: natal habitat imprinting, phenotype‐dependent, competition‐dependent and direct genetic habitat preference. We find that the evolution of habitat preference generally requires initially high dispersal, is facilitated by asymmetry in population sizes between habitats, and is hindered by an increasing number of underlying genetic loci. Moreover, the probability of habitat preference to emerge and promote divergence differs greatly among the underlying mechanisms. Natal habitat imprinting evolves most easily and can allow full divergence in parameter ranges where no divergence is possible in the absence of habitat preference. The reason is that imprinting represents a one‐allele mechanism of assortative mating linking dispersal behaviour very effectively to local selection. At the other extreme, direct genetic habitat preference, a two‐allele mechanism, evolves under restricted conditions only, and even then facilitates divergence weakly. Overall, our results indicate that habitat preference can be a strong reproductive barrier promoting divergence with gene flow, but that this is highly contingent on the underlying preference mechanism.     

Determinants of vertebrate invasion success in Europe and North America

Species that are frequently introduced to an exotic range have a high potential of becoming invasive. Besides propagule pressure, however, no other generally strong determinant of invasion success is known. Although evidence has accumulated that human affiliates (domesticates, pets, human commensals) also have high invasion success, existing studies do not distinguish whether this success can be completely explained by or is partly independent of propagule pressure. Here, we analyze both factors independently, propagule pressure and human affiliation. We also consider a third factor directly related to humans, hunting, and 17 traits on each species' population size and extent, diet, body size, and life history. Our dataset includes all 2362 freshwater fish, mammals, and birds native to Europe or North America. In contrast to most previous studies, we look at the complete invasion process consisting of (1) introduction, (2) establishment, and (3) spread. In this way, we not only consider which of the introduced species became invasive but also which species were introduced. Of the 20 factors tested, propagule pressure and human affiliation were the two strongest determinants of invasion success across all taxa and steps. This was true for multivariate analyses that account for intercorrelations among variables as well as univariate analyses, suggesting that human affiliation influenced invasion success independently of propagule pressure. Some factors affected the different steps of the invasion process antagonistically. For example, game species were much more likely to be introduced to an exotic continent than nonhunted species but tended to be less likely to establish themselves and spread. Such antagonistic effects show the importance of considering the complete invasion process.     

Modeling the emergence of migratory corridors and foraging hot spots of the green sea turtle

Environmental factors shape the spatial distribution and dynamics of populations. Understanding how these factors interact with movement behavior is critical for efficient conservation, in particular for migratory species. Adult female green sea turtles, Chelonia mydas, migrate between foraging and nesting sites that are generally separated by thousands of kilometers. As an emblematic endangered species, green turtles have been intensively studied, with a focus on nesting, migration, and foraging. Nevertheless, few attempts integrated these behaviors and their trade‐offs by considering the spatial configurations of foraging and nesting grounds as well as environmental heterogeneity like oceanic currents and food distribution. We developed an individual‐based model to investigate the impact of local environmental conditions on emerging migratory corridors and reproductive output and to thereby identify conservation priority sites. The model integrates movement, nesting, and foraging behavior. Despite being largely conceptual, the model captured realistic movement patterns which confirm field studies. The spatial distribution of migratory corridors and foraging hot spots was mostly constrained by features of the regional landscape, such as nesting site locations, distribution of feeding patches, and oceanic currents. These constraints also explained the mixing patterns in regional forager communities. By implementing alternative decision strategies of the turtles, we found that foraging site fidelity and nesting investment, two characteristics of green turtles' biology, are favorable strategies under unpredictable environmental conditions affecting their habitats. Based on our results, we propose specific guidelines for the regional conservation of green turtles as well as future research suggestions advancing spatial ecology of sea turtles. Being implemented in an easy to learn open‐source software, our model can coevolve with the collection and analysis of new data on energy budget and movement into a generic tool for sea turtle research and conservation. Our modeling approach could also be useful for supporting the conservation of other migratory marine animals.     

Egg limitation and individual variation in parasitization risk among hosts in host–parasitoid dynamics

Egg limitation is known to destabilize host–parasitoid dynamics. This study reexamines the effect of egg limitation in light of the individual variation in parasitization risk among hosts (e.g., some hosts are more likely to be parasitized than others). Previous studies have considered egg limitation (predicted as a destabilizing factor) and individual variation among hosts (predicted as a stabilizing factor) in isolation; however, their interaction is not known. An individual‐based model was used to examine the effects of each factor and their interaction. The model‐based analysis shows a clear interaction between egg limitation and individual variation in risk among hosts. Egg limitation can both stabilize and destabilize host–parasitioid dynamics depending on the presence and absence of the risk variation. The result suggests that the population‐dynamic consequences of egg limitation are more complex than previously thought and emphasizes the importance of the simultaneous consideration of multiple ecological factors (with individual‐level details) to uncover potential interactions among them.     

Node self‐connections in network metrics

Zamborain‐Mason et al. (Ecol. Lett., 20, 2017, 815–831) state that they have newly proposed network metrics that account for node self‐connections. Network metrics incorporating node self‐connections, also referred to as intranode (intrapatch) connectivity, were however already proposed before and have been widely used in a variety of conservation planning applications.     

Variation in foraging success among predators and its implications for population dynamics

The effects of the expected predation rate on population dynamics have been studied intensively, but little is known about the effects of predation rate variability (i.e., predator individuals having variable foraging success) on population dynamics. In this study, variation in foraging success among predators was quantified by observing the predation of the wolf spider Pardosa pseudoannulata on the cricket Gryllus bimaculatus in the laboratory. A population model was then developed, and the effect of foraging variability on predator–prey dynamics was examined by incorporating levels of variation comparable to those quantified in the experiment. The variability in the foraging success among spiders was greater than would be expected by chance (i.e., the random allocation of prey to predators). The foraging variation was density‐dependent; it became higher as the predator density increased. A population model that incorporates foraging variation shows that the variation influences population dynamics by affecting the numerical response of predators. In particular, the variation induces negative density‐dependent effects among predators and stabilizes predator–prey dynamics.     

Movement and egg laying in Monarchs: To move or not to move,that is the equation

Monarch butterfly (Danaus plexippus) populations are in decline in agricultural landscapes, in which genetically modified crops that are resistant to herbicides (‘Roundup Ready’) have resulted in the decimation of milkweed (Asclepias spp.) hosts over large areas due to the increased use of glyphosate. Movement is the key ecological process linking individual fitness traits to the utilization of sparse resources distributed across landscapes with emergent population level consequences. Often, movement ecology is highly simplified or even abstracted into a simple rate of flow between populations (i.e. a metapopulation) separated by a hostile ‘matrix’. Whereas, we can gain important insights into the population dynamic as a whole if we explore movement as an explicit, complex, behavioural process in which the matrix is not simply a void. We developed a spatially explicit individual‐based model to describe host‐seeking behaviour over the lifetime of a monarch butterfly, which utilizes hosts both aggregated in patches and scattered across the wider landscape as a substrate for laying eggs. We examine the simulated movement distances and spatial population distribution (eggs laid) as a result of different movement rules (directionality), perceptive distance (ability to find) and landscape configuration (how milkweed is distributed). This indicates the potential consequences of cleaning up the matrix (i.e. the obliteration of non‐crop vegetation with Roundup) and changing habitat configurations at a landscape scale on individual movement behaviours and the emergent number of eggs laid, essentially the birth term in any population model. Our model generates movement distances of the order of 12 km commensurate with summer breeding monarchs and suggests that milkweed removal has reduced egg laying by up to 30%. We suggest possible amelioration strategies.     

Movement,colonization, and establishment success of a planthopper of prairie potholes,Delphacodes scolochloa (Hemiptera: Delphacidae)

Abstract 1. Movement, and particularly the colonisation of new habitat patches, remains one of the least known aspects of the life history and ecology of the vast majority of species. Here, a series of experiments was conducted to rectify this problem with Delphacodes scolochloa Cronin & Wilson, a wing‐dimorphic planthopper of the North American Great Plains. 2. The movement of brachypterous and macropterous planthoppers within and among host‐plant patches was quantified. Also, an experiment was conducted to assess whether planthopper propagule size (i.e. number of colonists) influenced the presence of planthopper adults or eggs over time, planthopper population growth rate (R₀), and abundance or impact of an egg parasitoid. 3. Delphacodes scolochloa movement was well described by a simple diffusion model. As expected, brachypters were less dispersive than macropters – mean displacement distances among patches were three times greater for macropters (2.8 m vs. 8.1 m per day). 4. Number of colonists of vacant patches increased with increasing patch size (both wing forms) and decreased with increasing isolation (brachypters only). At the scale of individual potholes (<38 m), brachypters were dispersal limited. 5. Establishment success was strongly influenced by propagule size. An Allee effect constrained the establishment of new populations, but low establishment success was not a result of mate limitations or the presence of natural enemies (i.e. egg parasitoids).6. These movement data reveal important insights regarding the spatial population structure and spread of D. scolochloa.     

The frustrated brain: from dynamics on motifs to communities and networks

Cognitive function depends on an adaptive balance between flexible dynamics and integrative processes in distributed cortical networks. Patterns of zero-lag synchrony likely underpin numerous perceptual and cognitive functions. Synchronization fulfils integration by reducing entropy, while adaptive function mandates that a broad variety of stable states be readily accessible. Here, we elucidate two complementary influences on patterns of zero-lag synchrony that derive from basic properties of brain networks. First, mutually coupled pairs of neuronal subsystems—resonance pairs—promote stable zero-lag synchrony among the small motifs in which they are embedded, and whose effects can propagate along connected chains. Second, frustrated closed-loop motifs disrupt synchronous dynamics, enabling metastable configurations of zero-lag synchrony to coexist. We document these two complementary influences in small motifs and illustrate how these effects underpin stable versus metastable phase-synchronization patterns in prototypical modular networks and in large-scale cortical networks of the macaque (CoCoMac). We find that the variability of synchronization patterns depends on the inter-node time delay, increases with the network size and is maximized for intermediate coupling strengths. We hypothesize that the dialectic influences of resonance versus frustration may form a dynamic substrate for flexible neuronal integration, an essential platform across diverse cognitive processes.     

Combined modelling of distribution and niche in invasion biology: a case study of two invasive Tetramorium ant species

Spatial modelling of species distributions has become an important tool in the study of biological invasions. Here, we examine the utility of combining distribution and ecological niche modelling for retrieving information on invasion processes, based on species occurrence data from native and introduced ranges. Specifically, we discuss questions, concerning (1) the global potential to spread to other ranges, (2) the potential to spread within established invasions, (3) the detectability of niche differences across ranges, and (4) the ability to infer invasion history through data from the introduced range. We apply this approach to two congeneric pavement ants, Tetramorium sp.E (formerly T. caespitum (Linnaeus 1758)) and T. tsushimae Emery 1925, both introduced to North America. We identify (1) the potential of both species to inhabit ranges worldwide, and (2) the potential of T. sp.E and T. tsushimae, to spread to 23 additional US states and to five provinces of Canada, and to 24 additional US states and to one province of Canada, respectively. We confirm that (3) niche modelling can be an effective tool to detect niche shifts, identifying an increased width of T. sp.E and a decreased width of T. tsushimae following introduction, with potential changes in niche position for both species. We make feasible that (4) combined modelling could become an auxiliary tool to reconstruct invasion history, hypothesizing admixture following multiple introductions in North America for T. sp.E, and a single introduction to North America from central Japan, for T. tsushimae. Combined modelling represents a rapid means to formulate testable explanatory hypotheses on invasion patterns and helps approach a standard in predictive invasion research.