Isolation-by-distance and outbreeding depression are sufficient to drive parapatric speciation in the absence of environmental influences

A commonly held view in evolutionary biology is that speciation (the emergence of genetically distinct and reproductively incompatible subpopulations) is driven by external environmental constraints, such as localized barriers to dispersal or habitat-based variation in selection pressures. We have developed a spatially explicit model of a biological population to study the emergence of spatial and temporal patterns of genetic diversity in the absence of predetermined subpopulation boundaries. We propose a 2-D cellular automata model showing that an initially homogeneous population might spontaneously subdivide into reproductively incompatible species through sheer isolation-by-distance when the viability of offspring decreases as the genomes of parental gametes become increasingly different. This simple implementation of the Dobzhansky-Muller model provides the basis for assessing the process and completion of speciation, which is deemed to occur when there is complete postzygotic isolation between two subpopulations. The model shows an inherent tendency toward spatial self-organization, as has been the case with other spatially explicit models of evolution. A well-mixed version of the model exhibits a relatively stable and unimodal distribution of genetic differences as has been shown with previous models. A much more interesting pattern of temporal waves, however, emerges when the dispersal of individuals is limited to short distances. Each wave represents a subset of comparisons between members of emergent subpopulations diverging from one another, and a subset of these divergences proceeds to the point of speciation. The long-term persistence of diverging subpopulations is the essence of speciation in biological populations, so the rhythmic diversity waves that we have observed suggest an inherent disposition for a population experiencing isolation-by-distance to generate new species.     

Multilevel Selection in Models of Prebiotic Evolution II: A Direct Comparison of Compartmentalization and Spatial Self-Organization

Multilevel selection has been indicated as an essential factor for the evolution of complexity in interacting RNA-like replicator systems. There are two types of multilevel selection mechanisms: implicit and explicit. For implicit multilevel selection, spatial self-organization of replicator populations has been suggested, which leads to higher level selection among emergent mesoscopic spatial patterns (traveling waves). For explicit multilevel selection, compartmentalization of replicators by vesicles has been suggested, which leads to higher level evolutionary dynamics among explicitly imposed mesoscopic entities (protocells). Historically, these mechanisms have been given separate consideration for the interests on its own. Here, we make a direct comparison between spatial self-organization and compartmentalization in simulated RNA-like replicator systems. Firstly, we show that both mechanisms achieve the macroscopic stability of a replicator system through the evolutionary dynamics on mesoscopic entities that counteract that of microscopic entities. Secondly, we show that a striking difference exists between the two mechanisms regarding their possible influence on the long-term evolutionary dynamics, which happens under an emergent trade-off situation arising from the multilevel selection. The difference is explained in terms of the difference in the stability between self-organized mesoscopic entities and externally imposed mesoscopic entities. Thirdly, we show that a sharp transition happens in the long-term evolutionary dynamics of the compartmentalized system as a function of replicator mutation rate. Fourthly, the results imply that spatial self-organization can allow the evolution of stable folding in parasitic replicators without any specific functionality in the folding itself. Finally, the results are discussed in relation to the experimental synthesis of chemical Darwinian systems and to the multilevel selection theory of evolutionary biology in general. To conclude, novel evolutionary directions can emerge through interactions between the evolutionary dynamics on multiple levels of organization. Different multilevel selection mechanisms can produce a difference in the long-term evolutionary trend of identical microscopic entities.     

Phenotypic and dynamical transitions in model genetic networks. I. Emergence of patterns and genotype-phenotype relationships

SUMMARY Genotype–phenotype interactions during the evolution of form in multicellular organisms is a complex problem but one that can be aided by computational approaches. We present here a framework within which developmental patterns and their underlying genetic networks can be simulated. Gene networks were chosen to reflect realistic regulatory circuits, including positive and negative feedback control, and the exchange of a subset of gene products between cells, or within a syncytium. Some of these networks generate stable spatial patterns of a subset of their molecular constituents, and can be assigned to categories (e.g., "emergent" or "hierarchic") based on the topology of molecular circuitry. These categories roughly correspond to what has been discussed in the literature as "self-organizing" and "programmed" processes of development. The capability of such networks to form patterns of repeating stripes was studied in network ensembles in which parameters of gene-gene interaction were caused to vary in a manner analogous to genetic mutation. The evolution under mutational change of individual representative networks of each category was also simulated. We have found that patterns with few stripes (≤3) are most likely to originate in the form of a hierarchic network, whereas those with greater numbers of stripes (≥4) originate most readily as emergent networks. However, regardless of how many stripes it contains, once a pattern is established, there appears to be an evolutionary tendency for emergent mechanisms to be replaced by hierarchic mechanisms. These results have potential significance for the understanding of genotype-phenotype relationships in the evolution of metazoan form.     

Bilaterally propagating waves of spontaneous activity arising from discrete pacemakers in the neonatal mouse cerebral cortex

Spontaneous electrical activity that moves in synchronized waves across large populations of neurons plays widespread and important roles in nervous system development. The propagation patterns of such waves can encode the spatial location of neurons to their downstream targets and strengthen synaptic connections in coherent spatial patterns. Such waves can arise as an emergent property of mutually excitatory neural networks, or can be driven by a discrete pacemaker. In the mouse cerebral cortex, spontaneous synchronized activity occurs for approximately 72 h of development centered on the day of birth. It is not known whether this activity is driven by a discrete pacemaker or occurs as an emergent network property. Here we show that this activity propagates as a wave that is initiated at either of two homologous pacemakers in the temporal region, and then propagates rapidly across both sides of the brain. When these regions of origin are surgically isolated, waves do not occur. Therefore, this cortical spontaneous activity is a bilateral wave that originates from a discrete subset of pacemaker neurons. © 2009 Wiley Periodicals, Inc. Develop Neurobiol, 2009     

Spatial processes and evolutionary models: a critical review

Evolution is a fundamentally population level process in which variation, drift and selection produce both temporal and spatial patterns of change. Statistical model fitting is now commonly used to estimate which kind of evolutionary process best explains patterns of change through time using models like Brownian motion, stabilizing selection (Ornstein–Uhlenbeck) and directional selection on traits measured from stratigraphic sequences or on phylogenetic trees. But these models assume that the traits possessed by a species are homogeneous. Spatial processes such as dispersal, gene flow and geographical range changes can produce patterns of trait evolution that do not fit the expectations of standard models, even when evolution at the local‐population level is governed by drift or a typical OU model of selection. The basic properties of population level processes (variation, drift, selection and population size) are reviewed and the relationship between their spatial and temporal dynamics is discussed. Typical evolutionary models used in palaeontology incorporate the temporal component of these dynamics, but not the spatial. Range expansions and contractions introduce rate variability into drift processes, range expansion under a drift model can drive directional change in trait evolution, and spatial selection gradients can create spatial variation in traits that can produce long‐term directional trends and punctuation events depending on the balance between selection strength, gene flow, extirpation probability and model of speciation. Using computational modelling that spatial processes can create evolutionary outcomes that depart from basic population‐level notions from these standard macroevolutionary models.     

Noise driven evolutionary waves

Adaptation in spatially extended populations entails the propagation of evolutionary novelties across habitat ranges. Driven by natural selection, beneficial mutations sweep through the population in a "wave of advance". The standard model for these traveling waves, due to R. Fisher and A. Kolmogorov, plays an important role in many scientific areas besides evolution, such as ecology, epidemiology, chemical kinetics, and recently even in particle physics. Here, we extend the Fisher-Kolmogorov model to account for mutations that confer an increase in the density of the population, for instance as a result of an improved metabolic efficiency. We show that these mutations invade by the action of random genetic drift, even if the mutations are slightly deleterious. The ensuing class of noise-driven waves are characterized by a wave speed that decreases with increasing population sizes, contrary to conventional Fisher-Kolmogorov waves. When a trade-off exists between density and growth rate, an evolutionary optimal population density can be predicted. Our simulations and analytical results show that genetic drift in conjunction with spatial structure promotes the economical use of limited resources. The simplicity of our model, which lacks any complex interactions between individuals, suggests that noise-induced pattern formation may arise in many complex biological systems including evolution.     

A model of spatially evolving herpesvirus epidemics causing mass mortality in Australian pilchard Sardinops sagax

In 1995 mass mortality of pilchards Sardinops sagax occurred along >5000 km of Australian coast; similar events occurred in 1998/99. This mortality was closely associated with a herpesvirus. The pilchard is an important food source for larger animals and supports commercial fisheries. Both epidemics originated in South Australian waters and spread as waves with velocities of 10 to 40 km d(-1). Velocity was constant for a single wave, but varied between the epidemics and between the east- and west-bound waves in each epidemic. The pattern of mortality evolved from recurrent episodes to a single peak with distance from the origin. A 1-dimensional model of these epidemics has been developed. The host population is divided into susceptible, infected and latent, infected and infectious, and removed (recovered and dead) phases; the latent and infectious periods are of fixed duration. This model produces the mortality patterns observed locally and during the spread and evolution of the epidemic. It is consistent with evidence from pathology. The wave velocity is sensitive to diffusion coefficients, viral transmission rates and latent period. These parameters are constrained using the local and large-scale patterns of epidemic spread. The relative roles of these parameters in explaining differences between epidemics and between east- and west-bound waves within epidemics are discussed. The model predicts very high levels of infection, indicating that many surviving pilchards recovered following infection. Control appears impracticable once epidemics are initiated, but impact can be minimised by protecting juvenile stocks.     

Pattern selection in a cooperative biochemical in vitro amplification system: the role of parasites

Previously, numerical simulations have shown that evolving systems can be stabilized against emerging parasites by pattern formation in spatially extended flow reactors. Hence, it can be argued that pattern formation is a prerequisite for any experimental investigation of the biochemical evolution of cooperative function. Here, we study a model of an experimental biochemical system for the cooperative in vitro amplification of DNA strands and show that emerging parasites can induce a complex pattern formation even when no pattern formation occurs without parasites. In an adiabatic approximation where the cooperative amplification reaction is assumed to adapt fast to slowly emerging parasites, the parasite concentration itself acts as a Steuer parameter for the selection of various complex patterns. Without such an adiabatic approximation only transient patterns emerge. As any species can grow for very low concentrations, the parasite is able to infect the entire reactor and the system is finally diluted out. In the experimental biochemical system, however, the species are individual molecules and the growth of spatially separated, non-infected regions becomes feasible. Hence a cutoff threshold for the minimal concentration is applied. In these simulations the otherwise lethal infection by parasites induces the formation of spatiotemporal spirals, and this spatial structure help the host and parasitoid species to survive together. These theoretical results describe an inherent property of cooperative reactions and have an important impact on experimental investigations on the molecular evolution and complex function in spatially extended reactors. Since the formation of the complex pattern is restricted either to a rather large cutoff value or a special choice of the kinetic parameters, we, however, conclude that the persistence of evolving cooperative amplification is not possible in a simple reaction-diffusion reactor. Experimental set-ups with patchy environments, e.g. biomolecular amplification in coupled microstructured flow chambers or in microemulsion, are eligible candidates for the observation of such a self-organized pattern selection.     

Too close for comfort: spatial patterns in acorn barnacle populations

Spatial patterns in aggregations form as a result of the interplay between costs and benefits experienced by individuals. Such self-organisation of aggregations can be explained using a zonal model in which a short-range zone of repulsion and longer-range zone of attraction surrounding individuals leads to emergent pattern properties. The signal of these processes can be detected using spatial pattern analyses. Furthermore, in sessile organisms, post-settlement mortality reveals the relative costs and benefits of positions within the aggregation. Acorn barnacles are known to require contact with conspecifics for reproduction and are therefore believed to aggregate for this purpose; isolated individuals may also be more susceptible to abiotic stress and predation. At short distances, however, competition for space and resources is likely to occur. In this study spatial patterns of barnacles (Semibalanus balanoides L.) were analysed using pair-correlation functions. Individuals were dispersed at distances below 0.30 cm, but peak relative density occurred at a distance of 0.36 cm from conspecifics. This is much closer than required for reproductive access, implying a strong aggregative drive, up to the point of physical contact with neighbours. Nevertheless, analysis of dead barnacles illustrated that such proximity carries a cost as barnacles with many neighbours were more likely to have died. The inferences obtained from these patterns are that barnacles aggregate as closely as they can, and that local neighbourhood competition is a powerful determinant of mortality. These processes give rise to the observed pattern properties.     

Spiral wave dynamics in neocortex

Although spiral waves are ubiquitous features of nature and have been observed in many biological systems, their existence and potential function in mammalian cerebral cortex remain uncertain. Using voltage-sensitive dye imaging, we found that spiral waves occur frequently in the neocortex in?vivo, both during pharmacologically induced oscillations and during sleep-like states. While their life span is limited, spiral waves can modify ongoing cortical activity by influencing oscillation frequencies and spatial coherence and by reducing amplitude in the area surrounding the spiral phase singularity. During sleep-like states, the rate of occurrence of spiral waves varies greatly depending on brain states. These results support the hypothesis that spiral waves, as an emergent activity pattern, can organize and modulate cortical population activity on the mesoscopic scale and may contribute to both normal cortical processing and to pathological patterns of activity such as those found in epilepsy.     

A Dendritic Mechanism for Decoding Traveling Waves: Principles and Applications to Motor Cortex

Traveling waves of neuronal oscillations have been observed in many cortical regions, including the motor and sensory cortex. Such waves are often modulated in a task-dependent fashion although their precise functional role remains a matter of debate. Here we conjecture that the cortex can utilize the direction and wavelength of traveling waves to encode information. We present a novel neural mechanism by which such information may be decoded by the spatial arrangement of receptors within the dendritic receptor field. In particular, we show how the density distributions of excitatory and inhibitory receptors can combine to act as a spatial filter of wave patterns. The proposed dendritic mechanism ensures that the neuron selectively responds to specific wave patterns, thus constituting a neural basis of pattern decoding. We validate this proposal in the descending motor system, where we model the large receptor fields of the pyramidal tract neurons — the principle outputs of the motor cortex — decoding motor commands encoded in the direction of traveling wave patterns in motor cortex. We use an existing model of field oscillations in motor cortex to investigate how the topology of the pyramidal cell receptor field acts to tune the cells responses to specific oscillatory wave patterns, even when those patterns are highly degraded. The model replicates key findings of the descending motor system during simple motor tasks, including variable interspike intervals and weak corticospinal coherence. By additionally showing how the nature of the wave patterns can be controlled by modulating the topology of local intra-cortical connections, we hence propose a novel integrated neuronal model of encoding and decoding motor commands.     

Refinement and Pattern Formation in Neural Circuits by the Interaction of Traveling Waves with Spike-Timing Dependent Plasticity

Traveling waves in the developing brain are a prominent source of highly correlated spiking activity that may instruct the refinement of neural circuits. A candidate mechanism for mediating such refinement is spike-timing dependent plasticity (STDP), which translates correlated activity patterns into changes in synaptic strength. To assess the potential of these phenomena to build useful structure in developing neural circuits, we examined the interaction of wave activity with STDP rules in simple, biologically plausible models of spiking neurons. We derive an expression for the synaptic strength dynamics showing that, by mapping the time dependence of STDP into spatial interactions, traveling waves can build periodic synaptic connectivity patterns into feedforward circuits with a broad class of experimentally observed STDP rules. The spatial scale of the connectivity patterns increases with wave speed and STDP time constants. We verify these results with simulations and demonstrate their robustness to likely sources of noise. We show how this pattern formation ability, which is analogous to solutions of reaction-diffusion systems that have been widely applied to biological pattern formation, can be harnessed to instruct the refinement of postsynaptic receptive fields. Our results hold for rich, complex wave patterns in two dimensions and over several orders of magnitude in wave speeds and STDP time constants, and they provide predictions that can be tested under existing experimental paradigms. Our model generalizes across brain areas and STDP rules, allowing broad application to the ubiquitous occurrence of traveling waves and to wave-like activity patterns induced by moving stimuli.     

From infanticide to parental care: why spatial structure can help adults be good parents

We investigate the evolution of parental care and cannibalism in a spatially structured population where adults can either help or kill juveniles in their neighborhood. We show that spatial structure can reverse the selective pressures on adult behavior, leading to the evolution of parental care, whereas the nonspatial model predicts that cannibalism is the sole evolutionary outcome. Our analysis emphasizes that evolution of such spatially structured populations is best understood at the level of the cluster of invading mutants, and we define invasion fitness as the growth rate of that cluster. We derive an analytical expression for the selective pressures on the trait and show that relatedness and Hamilton's rule are recovered as emergent properties of the spatial ecological dynamics. When adults can also help other adults, the benefits to each class of recipients are weighted by the class reproductive value, a result consistent with that of other models of kin selection. Finally, we advocate a different approach to moment equations and argue that even though the development of moment closure approximations is a necessary line of research, much-needed ecological and evolutionary insight can be gained by studying the unclosed moment equations.     

The evolution of static allometry in sexually selected traits

Although it has been the subject of verbal theory since Darwin, the evolution of morphological trait allometries remains poorly understood, especially in the context of sexual selection. Here we present an allocation trade-off model that predicts the optimal pattern of allometry under different selective regimes. We derive a general solution that has a simple and intuitive interpretation and use it to investigate several examples of fitness functions. Verbal arguments have suggested cost or benefit scenarios under which sexual selection on signal or weapon traits may favor larger individuals with disproportionately larger traits (i.e., positive allometry). However, our results suggest that this is necessarily true only under a precisely specified set of conditions: positive allometry will evolve when the marginal fitness gains from an increase in relative trait size are greater for large individuals than for small ones. Thus, the optimal allometric pattern depends on the precise nature of net selection, and simple examples readily yield isometry, positive or negative allometry, or polymorphisms corresponding to sigmoidal scaling. The variety of allometric patterns predicted by our model is consistent with the diversity of patterns observed in empirical studies on the allometries of sexually selected traits. More generally, our findings highlight the difficulty of inferring complex underlying processes from simple emergent patterns.     

Decelerating spread of West Nile virus by percolation in a heterogeneous urban landscape

Vector-borne diseases are emerging and re-emerging in urban environments throughout the world, presenting an increasing challenge to human health and a major obstacle to development. Currently, more than half of the global population is concentrated in urban environments, which are highly heterogeneous in the extent, degree, and distribution of environmental modifications. Because the prevalence of vector-borne pathogens is so closely coupled to the ecologies of vector and host species, this heterogeneity has the potential to significantly alter the dynamical systems through which pathogens propagate, and also thereby affect the epidemiological patterns of disease at multiple spatial scales. One such pattern is the speed of spread. Whereas standard models hold that pathogens spread as waves with constant or increasing speed, we hypothesized that heterogeneity in urban environments would cause decelerating travelling waves in incipient epidemics. To test this hypothesis, we analysed data on the spread of West Nile virus (WNV) in New York City (NYC), the 1999 epicentre of the North American pandemic, during annual epizootics from 2000-2008. These data show evidence of deceleration in all years studied, consistent with our hypothesis. To further explain these patterns, we developed a spatial model for vector-borne disease transmission in a heterogeneous environment. An emergent property of this model is that deceleration occurs only in the vicinity of a critical point. Geostatistical analysis suggests that NYC may be on the edge of this criticality. Together, these analyses provide the first evidence for the endogenous generation of decelerating travelling waves in an emerging infectious disease. Since the reported deceleration results from the heterogeneity of the environment through which the pathogen percolates, our findings suggest that targeting control at key sites could efficiently prevent pathogen spread to remote susceptible areas or even halt epidemics.     

Spatial pattern as an adaptive phenotype

Spatial patterns are common in nature across a broad range of scales, from body coloration patterns of animals to clustering of vegetation. The ultimate causes of these patterns are viewed very differently depending on whether they are traits of individuals or properties of aggregations. Traits of individuals are usually considered to be shaped directly by selection, while patterns of aggregation are typically viewed as incidental side effects of some other underlying processes or environmental heterogeneity. However, given the powerful influence that spatial structure can have on the susceptibility of a population to a dispersal-limited predator or pathogen, it may be useful to consider the possibility that spatial structure per se could serve as an anti-enemy adaptive phenotype. This group-level trait could evolve only if selection at the individual level does not overwhelm higher-level selection. To explore the plausibility of spatial structure as an adaptive phenotype, I consider the specific case of a spatially-explicit, evolutionary host–pathogen model. This model demonstrates the evolution of reproductive restraint, resulting in a low-density, poorly-connected landscape of host clusters that is resistant to the spread of the pathogen. Reimagining spatial structure as an adaptive phenotype may generate new insights of both theoretical and practical significance.     

SCALE AND HIERARCHY IN MACROEVOLUTION

Abstract: Scale and hierarchy must be incorporated into any conceptual framework for the study of macroevolution, i.e. evolution above the species level. Expansion of temporal and spatial scales reveals evolutionary patterns and processes that are virtually inaccessible to, and unpredictable from, short‐term, localized observations. These larger‐scale phenomena range from evolutionary stasis at the species level and the mosaic assembly of complex morphologies in ancestral forms to the non‐random distribution in time and space of the origin of major evolutionary novelties, as exemplified by the Cambrian explosion and post‐extinction recoveries of metazoans, and the preferential origin of major marine groups in onshore environments and tropical waters. Virtually all of these phenomena probably involve both ecological and developmental factors, but the integration of these components with macroevolutionary theory has only just begun. Differential survival and reproduction of units can occur at several levels within a biological hierarchy that includes DNA sequences, organisms, species and clades. Evolution by natural selection can occur at any level where there is heritable variation that affects birth and death of units by virtue of interaction with the environment. This dynamic can occur when selfish DNA sequences replicate disproportionately within genomes, when organisms enjoy fitness advantages within populations (classical Darwinian selection), when differential speciation or extinction occurs within clades owing to organismic properties (effect macroevolution), and when differential speciation or extinction occurs within clades owing to emergent, species‐level properties (in the strict sense species selection). Operationally, emergent species‐level properties such as geographical range can be recognized by testing whether their macroevolutionary effects are similar regardless of the different lower‐level factors that produce them. Large‐scale evolutionary trends can be driven by transformation of species, preferential production of species in a given direction, differential origination or extinction, or any combination of these; the potential for organismic traits to hitch‐hike on other factors that promote speciation or damp extinction is high. Additional key attributes of macroevolutionary dynamics within biological hierarchies are that (1) hierarchical levels are linked by upward and downward causation, so that emergent properties at a focal level do not impart complete independence; (2) hierarchical effects are asymmetrical, so that dynamics at a given focal level need not propagate upwards, but will always cascade downwards; and (3) rates are generally, although not always, faster at lower hierarchical levels. Temporal and spatial patterns in the origin of major novelties and higher taxa are significantly discordant from those at the species and genus levels, suggesting complex hierarchical effects that remain poorly understood. Not only are many of the features promoting survivorship during background times ineffective during mass extinctions, but also they are replaced in at least some cases by higher‐level, irreducible attributes such as clade‐level geographical range. The incorporation of processes that operate across hierarchical levels and a range of temporal and spatial scales has expanded and enriched our understanding of evolution.     

Reinfection induced disease in a spatial SIRI model

Spatial models are widely used in epidemiology to investigate persistence and extinction of disease as well as their spatial patterns. One of the most important issues in studying epidemic models is the role of infection on the persistence and extinction of the disease. In this paper, we investigate a spatial susceptible–infected–recovered–infected model using cellular automata. We show that, in the regime where disease disappears in the susceptible–infected–recovered–susceptible model, spiral and target waves will emerge in the two-dimensional space due to the reinfection. The obtained results may point out that reinfection has great influence on the epidemic spreading, which enriches the findings of spatiotemporal dynamics in epidemic models.     

Scale-dependent feedback and regular spatial patterns in young mussel beds

In the past decade, theoretical ecologists have emphasized that local interactions between predators and prey may invoke emergent spatial patterning at larger spatial scales. However, empirical evidence for the occurrence of emergent spatial patterning is scarce, which questions the relevance of the proposed mechanisms to ecological theory. We report on regular spatial patterns in young mussel beds on soft sediments in the Wadden Sea. We propose that scale-dependent feedback, resulting from short-range facilitation by mutual protection from waves and currents and long-range competition for algae, induces spatial self-organization, thereby providing a possible explanation for the observed patterning. The emergent self-organization affects the functioning of mussel bed ecosystems by enhancing productivity and resilience against disturbance. Moreover, self-organization allows mussels to persist at algal concentrations that would not permit survival of mussels in a homogeneous bed. Our results emphasize the importance of self-organization in affecting the emergent properties of natural systems at larger spatial scales.