Indirect effects shape species fitness in coevolved mutualistic networks.

Ecological interactions are one of the main forces that sustain Earth's biodiversity. A major challenge for studies of ecology and evolution is to determine how these interactions affect the fitness of species when we expand from studying isolated, pairwise interactions to include networks of interacting species1-4. In networks, chains of effects caused by a range of species have an indirect effect on other species they do not interact with directly, potentially affecting the fitness outcomes of a variety of ecological interactions (such as mutualism)5-7. Here we apply analytical techniques and numerical simulations to 186 empirical mutualistic networks and show how both direct and indirect effects alter the fitness of species coevolving in these networks. Although the fitness of species usually increased with the number of mutualistic partners, most of the fitness variation across species was driven by indirect effects. We found that these indirect effects prevent coevolving species from adapting to their mutualistic partners and to other sources of selection pressure in the environment, thereby decreasing their fitness. Such decreases are distributed in a predictable way within networks: peripheral species receive more indirect effects and experience higher reductions in fitness than central species. This topological effect was also evident when we analysed an empirical study of an invasion of pollination networks by honeybees. As honeybees became integrated as a central species within networks, they increased the contribution of indirect effects on several other species, reducing their fitness. Our study shows how and why indirect effects can govern the adaptive landscape of species-rich mutualistic assemblages.

Modeling Mito-nuclear Compatibility and Its Role in Species Identification.

Mitochondrial genetic material (mtDNA) is widely used for phylogenetic reconstruction and as a barcode for species identification. The utility of mtDNA in these contexts derives from its particular molecular properties, including its high evolutionary rate, uniparental inheritance, and small size. But mtDNA may also play a fundamental role in speciation-as suggested by recent observations of coevolution with the nuclear DNA, along with the fact that respiration depends on coordination of genes from both sources. Here, we study how mito-nuclear interactions affect the accuracy of species identification by mtDNA, as well as the speciation process itself. We simulate the evolution of a population of individuals who carry a recombining nuclear genome and a mitochondrial genome inherited maternally. We compare a null model fitness landscape that lacks any mito-nuclear interaction against a scenario in which interactions influence fitness. Fitness is assigned to individuals according to their mito-nuclear compatibility, which drives the coevolution of the nuclear and mitochondrial genomes. Depending on the model parameters, the population breaks into distinct species and the model output then allows us to analyze the accuracy of mtDNA barcode for species identification. Remarkably, we find that species identification by mtDNA is equally accurate in the presence or absence of mito-nuclear coupling and that the success of the DNA barcode derives mainly from population geographical isolation during speciation. Nevertheless, selection imposed by mito-nuclear compatibility influences the diversification process and leaves signatures in the genetic content and spatial distribution of the populations, in three ways. First, speciation is delayed and the resulting phylogenetic trees are more balanced. Second, clades in the resulting phylogenetic tree correlate more strongly with the spatial distribution of species and clusters of more similar mtDNA's. Third, there is a substantial increase in the intraspecies mtDNA similarity, decreasing the number of alleles substitutions per locus and promoting the conservation of genetic information. We compare the evolutionary patterns observed in our model to empirical data from copepods (Tigriopus californicus). We find good qualitative agreement in the geographic patterns and the topology of the phylogenetic tree, provided the model includes selection based on mito-nuclear interactions. These results highlight the role of mito-nuclear compatibility in the speciation process and its reconstruction from genetic data.[Mito-nuclear coevolution; mtDNA barcode; parapatry; phylogeny.].

Matrix coupling and generalized frustration in Kuramoto oscillators.

The Kuramoto model describes the synchronization of coupled oscillators that have different natural frequencies. Among the many generalizations of the original model, Kuramoto and Sakaguchi (KS) proposed a frustrated version that resulted in dynamic behavior of the order parameter, even when the average natural frequency of the oscillators is zero. Here, we consider a generalization of the frustrated KS model that exhibits new transitions to synchronization. The model is identical in form to the original Kuramoto model but written in terms of unit vectors and with the coupling constant replaced by a coupling matrix. The matrix breaks the rotational symmetry and forces the order parameter to point in the direction of the eigenvector with the highest eigenvalue, when the eigenvalues are real. For complex eigenvalues, the module of order parameter oscillates while it rotates around the unit circle, creating active states. We derive the complete phase diagram for the Lorentzian distribution of frequencies using the Ott-Antonsen ansatz. We also show that changing the average value of the natural frequencies leads to further phase transitions where the module of the order parameter goes from oscillatory to static.

Ott-Antonsen ansatz for the D-dimensional Kuramoto model: A constructive approach.

Kuramoto's original model describes the dynamics and synchronization behavior of a set of interacting oscillators represented by their phases. The system can also be pictured as a set of particles moving on a circle in two dimensions, which allows a direct generalization to particles moving on the surface of higher dimensional spheres. One of the key features of the 2D system is the presence of a continuous phase transition to synchronization as the coupling intensity increases. Ott and Antonsen proposed an ansatz for the distribution of oscillators that allowed them to describe the dynamics of the order parameter with a single differential equation. A similar ansatz was later proposed for the D-dimensional model by using the same functional form of the 2D ansatz and adjusting its parameters. In this article, we develop a constructive method to find the ansatz, similarly to the procedure used in 2D. The method is based on our previous work for the 3D Kuramoto model where the ansatz was constructed using the spherical harmonics decomposition of the distribution function. In the case of motion in a D-dimensional sphere, the ansatz is based on the hyperspherical harmonics decomposition. Our result differs from the previously proposed ansatz and provides a simpler and more direct connection between the order parameter and the ansatz.

Signatures of Microevolutionary Processes in Phylogenetic Patterns.

Phylogenetic trees are representations of evolutionary relationships among species and contain signatures of the processes responsible for the speciation events they display. Inferring processes from tree properties, however, is challenging. To address this problem, we analyzed a spatially-explicit model of speciation where genome size and mating range can be controlled. We simulated parapatric and sympatric (narrow and wide mating range, respectively) radiations and constructed their phylogenetic trees, computing structural properties such as tree balance and speed of diversification. We showed that parapatric and sympatric speciation are well separated by these structural tree properties. Balanced trees with constant rates of diversification only originate in sympatry and genome size affected both the balance and the speed of diversification of the simulated trees. Comparison with empirical data showed that most of the evolutionary radiations considered to have developed in parapatry or sympatry are in good agreement with model predictions. Even though additional forces other than spatial restriction of gene flow, genome size, and genetic incompatibilities, do play a role in the evolution of species formation, the microevolutionary processes modeled here capture signatures of the diversification pattern of evolutionary radiations, regarding the symmetry and speed of diversification of lineages.

Synchronization and spatial patterns in forced swarmalators.

Swarmalators are particles that exhibit coordinated motion and, at the same time, synchronize their intrinsic behavior, represented by internal phases. Here, we study the effects produced by an external periodic stimulus over a system of swarmalators that move in two dimensions. The system represents, for example, a swarm of fireflies in the presence of an external light source that flashes at a fixed frequency. If the spatial movement is ignored, the dynamics of the internal variables are equivalent to those of Kuramoto oscillators. In this case, the phases tend to synchronize and lock to the external stimulus if its intensity is sufficiently large. Here, we show that in a system of swarmalators, the force also shifts the phases and angular velocities leading to synchronization with the external frequency. However, the correlation between phase and spatial location decreases with the intensity of the force, going to zero at a critical intensity that depends on the model parameters. In the regime of zero correlation, the particles form a static symmetric circular distribution, following a simple model of aggregation. Interestingly, for intermediate values of the force intensity, different patterns emerge, with the particles spiraling or splitting in two clusters centered at opposite sides of the stimulus' location. The spiral and two-cluster patterns are stable and active. The two clusters slowly rotate around the source while exchanging particles, or separate and collide repeatedly, depending on the parameters.

Quantifying the effects of quarantine using an IBM SEIR model on scalefree networks.

The COVID-19 pandemic led several countries to resort to social distancing, the only known way to slow down the spread of the virus and keep the health system under control. Here we use an individual based model (IBM) to study how the duration, start date and intensity of quarantine affect the height and position of the peak of the infection curve. We show that stochastic effects, inherent to the model dynamics, lead to variable outcomes for the same set of parameters, making it crucial to compute the probability of each result. To simplify the analysis we divide the outcomes in only two categories, that we call best and worst scenarios. Although long and intense quarantine is the best way to end the epidemic, it is very hard to implement in practice. Here we show that relatively short and intense quarantine periods can also be very effective in flattening the infection curve and even killing the virus, but the likelihood of such outcomes are low. Long quarantines of relatively low intensity, on the other hand, can delay the infection peak and reduce its size considerably with more than 50% probability, being a more effective policy than complete lockdown for short periods.

Coevolution Creates Complex Mosaics across Large Landscapes.

The spatial distribution of populations can influence the evolutionary outcome of species interactions. The variation in direction and strength of selection across local communities creates geographic selection mosaics that, when combined with gene flow and genomic processes such as genome duplication or hybridization, can fuel ongoing coevolution. A fundamental problem to solve is how coevolution proceeds when many populations that vary in their ecological outcomes are connected across large landscapes. Here we use a lattice model to explore this problem. Our results show that the complex interrelationships among the elements of the geographic mosaic of coevolution can lead to the formation of clusters of populations with similar phenotypes that are larger than expected by local selection. Our results indicate that neither the spatial distribution of phenotypes nor the spatial differences in magnitude and direction of selection alone dictate coevolutionary dynamics: the geographic mosaic of coevolution affects formation of phenotypic clusters, which in turn affect the spatial and temporal dynamics of coevolution. Because the formation of large phenotypic clusters depends on gene flow, we predict that current habitat fragmentation will change the outcomes of geographic mosaics, coupling spatial patterns in selection and phenotypes.

A genetic approach to the rock-paper-scissors game.

Polymorphisms are usually associated with defenses and mating strategies, affecting the individual's fitness. Coexistence of different morphs is, therefore, not expected, since the fittest morph should outcompete the others. Nevertheless, coexistence is observed in many natural systems. For instance, males of the side-blotched lizards (Uta stansburiana) present three morphs with throat colors orange, yellow and blue, which are associated with mating strategies and territorial behavior. The three male morphs compete for females in a system that is well described by the rock-paper-scissors dynamics of game theory. Previous studies have modeled the lizards as hermaphroditic populations whose individual's behavior were determined only by their phenotypes. Here we consider an extension of this dynamical system where diploidy and sexual reproduction are explicitly taken into account. Similarly to the lizards we represent the genetic system by a single locus with three alleles, o, y, and b in a diploid chromosome with dominance of o over y and of y over b. We show that this genotypic description of the dynamics results in the same equilibrium phenotype frequencies as the phenotypic models, but affects the stability of the system, changing the parameter region where coexistence of the three morphs is possible in a rock-paper-scissors game.

The mutation-drift balance in spatially structured populations.

In finite populations the action of neutral mutations is balanced by genetic drift, leading to a stationary distribution of alleles that displays a transition between two different behaviors. For small mutation rates most individuals will carry the same allele at equilibrium, whereas for high mutation rates of the alleles will be randomly distributed with frequencies close to one half for a biallelic gene. For well-mixed haploid populations the mutation threshold is µc=1/2N, where N is the population size. In this paper we study how spatial structure affects this mutation threshold. Specifically, we study the stationary allele distribution for populations placed on regular networks where connected nodes represent potential mating partners. We show that the mutation threshold is sensitive to spatial structure only if the number of potential mates is very small. In this limit, the mutation threshold decreases substantially, increasing the diversity of the population at considerably low mutation rates. Defining kc as the degree of the network for which the mutation threshold drops to half of its value in well-mixed populations we show that kc grows slowly as a function of the population size, following a power law. Our calculations and simulations are based on the Moran model and on a mapping between the Moran model with mutations and the voter model with opinion makers.

Multilevel and kin selection in a connected world.

Wild et al. argue that the evolution of reduced virulence can be understood from the perspective of inclusive fitness, obviating the need to evoke group selection as a contributing causal factor. Although they acknowledge the mathematical equivalence of the inclusive fitness and multilevel selection approaches, they conclude that reduced virulence can be viewed entirely as an individual-level adaptation by the parasite. Here we show that their model is a well-known special case of the more general theory of multilevel selection, and that the cause of reduced virulence resides in the opposition of two processes: within-group and among-group selection. This distinction is important in light of the current controversy among evolutionary biologists in which some continue to affirm that natural selection centres only and always at the level of the individual organism or gene, despite mathematical demonstrations that evolutionary dynamics must be described by selection at various levels in the hierarchy of biological organization.

Multiconfigurational quantum propagation with trajectory-guided generalized coherent states.

A generalized version of the coupled coherent states method for coherent states of arbitrary Lie groups is developed. In contrast to the original formulation, which is restricted to frozen-Gaussian basis sets, the extended method is suitable for propagating quantum states of systems featuring diversified physical properties, such as spin degrees of freedom or particle indistinguishability. The approach is illustrated with simple models for interacting bosons trapped in double- and triple-well potentials, most adequately described in terms of SU(2) and SU(3) bosonic coherent states, respectively.

Evolution and stability of ring species.

Neutral models, in which genetic change arises through random variation without fitness differences, have proven remarkably successful in describing observed patterns of biodiversity, despite the manifest role of selection in evolution. Here we investigate the effect of barriers on biodiversity by simulating the expansion of a population around a barrier to form a ring species, in which the two ends of the population are reproductively isolated despite ongoing gene flow around the ring. We compare the spatial and genetic properties of a neutral agent-based population model to the greenish warblers' complex, a well-documented example of an actual ring species in nature. Our results match the distribution of subspecies, the principal components of genetic diversity, and the linear spatial-genetic correlation of the observed data, even though selection is expected to be important for traits of this species. We find that ring species are often unstable to speciation or mixing but can persist for extended times depending on species and landscape features. For the greenish warblers, our analysis implies that the expanded area near the point of secondary contact is important for extending the duration of the ring, and thus, for the opportunity to observe this ring species. Nevertheless it also suggests the ring will break up into multiple species in 10,000 to 50,000 y. These results imply that simulations can be used to accurately describe empirical data for complex spatial-genetic traits of an individual species.

Diploid versus haploid models of neutral speciation.

Neutral models of speciation based on isolation by distance and assortative mating, termed topopatric, have shown to be successful in describing abundance distributions and species-area relationships. Previous works have considered this type of process in the context of haploid genomes. Here we discuss the implementation of two schemes of dominance to analyze the effects of diploidy: a complete dominance model in which one allele dominates over the other and a perfect codominant model in which heterozygous genotypes give rise to a third phenotype. In the case of complete dominance, we observe that speciation requires stronger spatial inbreeding in comparison to the haploid model. For perfect codominance, instead, speciation demands stronger genetic assortativeness. Nevertheless, once speciation is established, the three models predict the same abundance distributions even at the quantitative level, revealing the robustness of the original mechanism to describe biodiversity features.

Pleistocene megafaunal interaction networks became more vulnerable after human arrival.

The end of the Pleistocene was marked by the extinction of almost all large land mammals worldwide except in Africa. Although the debate on Pleistocene extinctions has focused on the roles of climate change and humans, the impact of perturbations depends on properties of ecological communities, such as species composition and the organization of ecological interactions. Here, we combined palaeoecological and ecological data, food-web models and community stability analysis to investigate if differences between Pleistocene and modern mammalian assemblages help us understand why the megafauna died out in the Americas while persisting in Africa. We show Pleistocene and modern assemblages share similar network topology, but differences in richness and body size distributions made Pleistocene communities significantly more vulnerable to the effects of human arrival. The structural changes promoted by humans in Pleistocene networks would have increased the likelihood of unstable dynamics, which may favour extinction cascades in communities facing extrinsic perturbations. Our findings suggest that the basic aspects of the organization of ecological communities may have played an important role in major extinction events in the past. Knowledge of community-level properties and their consequences to dynamics may be critical to understand past and future extinctions.

Error catastrophe in populations under similarity-essential recombination.

Organisms are often more likely to exchange genetic information with others that are similar to themselves. One of the most widely accepted mechanisms of RNA virus recombination requires substantial sequence similarity between the parental RNAs and is termed similarity-essential recombination. This mechanism may be considered analogous to assortative mating, an important form of non-random mating that can be found in animals and plants. Here we study the dynamics of haplotype frequencies in populations evolving under similarity-essential recombination. Haplotypes are represented by a genome of B biallelic loci and the Hamming distance between individuals is used as a criterion for recombination. We derive the evolution equations for the haplotype frequencies assuming that recombination does not occur if the genetic distance is larger than a critical value G and that mutation occurs at a rate µ per locus. Additionally, uniform crossover is considered. Although no fitness is directly associated to the haplotypes, we show that frequency-dependent selection emerges dynamically and governs the haplotype distribution. A critical mutation rate µc can be identified as the error threshold transition, beyond which this selective information cannot be stored. For µ<µc the distribution consists of a dominant sequence surrounded by a cloud of closely related sequences, characterizing a quasispecies. For µ>µc the distribution becomes uniform, with all haplotypes having the same frequency. In the case of extreme assortativeness, where individuals only recombine with others identical to themselves (G=0), the error threshold results µc=1/4, independently of the genome size. For weak assortativity (G=B-1)µc=2(-(B+1)) and for the case of no assortativity (G=B) µc=0. We compute the mutation threshold for 0

Order, chaos, and dimensionality transition in a system of swarmalators.

Similarly to sperm, where individuals self-organize in space while also striving for coherence in their tail swinging, several natural and engineered systems exhibit the emergence of swarming and synchronization. The arising and interplay of these phenomena have been captured by collectives of hypothetical particles named swarmalators, each possessing a position and a phase whose dynamics are affected reciprocally and also by the space-phase states of their neighbors. In this work, we introduce a solvable model of swarmalators able to move in two-dimensional spaces. We show that several static and active collective states can emerge and derive necessary conditions for each to show up as the model parameters are varied. These conditions elucidate, in some cases, the displaying of multistability among states. Notably, in the active regime, the system exhibits hyperchaos, maintaining spatial correlation under certain conditions and breaking it under others on what we interpret as a dimensionality transition.

Intermittent migration can induce pulses of speciation in a two-island system.

Geographic barriers can come and go depending on natural conditions. These fluctuations cause population cycles of expansion and contraction, introducing intermittent migrations that may not hinder speciation but rather promote diversification. Here, we study a neutral 2-island speciation model with intermittent migration driven by sea-level fluctuations. Seabed depth modulates isolation and connection periods between the islands, with migration occurring during connection periods with a certain probability. Mating is restricted to genetically compatible individuals on the same island and offspring inherit genomes from both parents through recombination. We observe speciation pulses that would not occur under strict isolation or continuous migration, with infrequent, temporary increases in species richness happening at different times depending on the combination of geographic settings and migration probability. The resulting dynamic patterns of richness exhibit contrasting behavior between connected and isolated scenarios, often including species that do not persist. Prolonged isolation can reduce richness to 1 species per island, resembling patterns commonly associated with archipelagos under sea-level fluctuations. Together with other studies, our results in out-of-equilibrium populations support the relevance of investigating the impact of variable migration on diversification, particularly in regions of high diversity.

Conditions for neutral speciation via isolation by distance.

The branching of new species from an ancestral population requires the evolution of reproductive isolation between groups of individuals. Geographic separation of sub-populations by natural barriers, if sustained for sufficiently long times, may lead to the accumulation of independent genetic changes in each group and to mating incompatibilities (Mayr, 2001; Fitzpatrick et al., 2009). A similar phenomenon may occur in the absence of barriers via isolation by distance if the population is distributed over large areas (de Aguiar et al., 2009; Etienne and Haegeman, 2011; Gavrilets et al., 2000). The first demonstration of this process was based on computer simulations employing agent-based models. Recently, analytical results were derived combining network theory, to model the spatial structure of the population, and an ansatz that accounts for the effect of forbidding mating between individuals that are too different genetically (de Aguiar and Bar-Yam, 2011). The main result obtained with this approach is an expression that indicates when speciation is possible as a function of the parameters describing the population. The aim of this work is to test this analytical result by comparing it with numerical simulations for a hermaphroditic population (de Aguiar et al., 2009) and for a population whose individuals are explicitly separated into males and females (Baptestini et al., 2013). We show that the analytical formula is indeed a very good overall description of the simulations and that the exponents describing dependence of the critical threshold of speciation with the parameters are in good agreement with the simulations.

Generalized frustration in the multidimensional Kuramoto model.

The Kuramoto model describes how coupled oscillators synchronize their phases as the intensity of the coupling increases past a threshold. The model was recently extended by reinterpreting the oscillators as particles moving on the surface of unit spheres in a D-dimensional space. Each particle is then represented by a D-dimensional unit vector; for D=2 the particles move on the unit circle and the vectors can be described by a single phase, recovering the original Kuramoto model. This multidimensional description can be further extended by promoting the coupling constant between the particles to a matrix K that acts on the unit vectors. As the coupling matrix changes the direction of the vectors, it can be interpreted as a generalized frustration that tends to hinder synchronization. In a recent paper we studied in detail the role of the coupling matrix for D=2. Here we extend this analysis to arbitrary dimensions. We show that, for identical particles, when the natural frequencies are set to zero, the system converges either to a stationary synchronized state, given by one of the real eigenvectors of K, or to an effective two-dimensional rotation, defined by one of the complex eigenvectors of K. The stability of these states depends on the set eigenvalues and eigenvectors of the coupling matrix, which controls the asymptotic behavior of the system, and therefore, can be used to manipulate these states. When the natural frequencies are not zero, synchronization depends on whether D is even or odd. In even dimensions the transition to synchronization is continuous and rotating states are replaced by active states, where the module of the order parameter oscillates while it rotates. If D is odd the phase transition is discontinuous and active states can be suppressed for some distributions of natural frequencies.