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.

Synchronization of Sakaguchi swarmalators.

Swarmalators are phase oscillators that cluster in space, like fireflies flashing in a swarm to attract mates. Interactions between particles, which tend to synchronize their phases and align their motion, decrease with the distance and phase difference between them, coupling the spatial and phase dynamics. In this work, we explore the effects of inducing phase frustration on a system of swarmalators that move on a one-dimensional ring. Our model is inspired by the well-known Kuramoto-Sakaguchi equations. We find, numerically and analytically, the ordered and disordered states that emerge in the system. The active states, not present in the model without frustration, resemble states found previously in numerical studies for the two-dimensional swarmalators system. One of these states, in particular, shows similarities to turbulence generated in a flattened media. We show that all ordered states can be generated for any values of the coupling constants by tuning the phase frustration parameters only. Moreover, many of these combinations display multistability.

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.

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.

Mito-nuclear selection induces a trade-off between species ecological dominance and evolutionary lifespan.

Mitochondrial and nuclear genomes must be co-adapted to ensure proper cellular respiration and energy production. Mito-nuclear incompatibility reduces individual fitness and induces hybrid infertility, which can drive reproductive barriers and speciation. Here, we develop a birth-death model for evolution in spatially extended populations under selection for mito-nuclear co-adaptation. Mating is constrained by physical and genetic proximity, and offspring inherit nuclear genomes from both parents, with recombination. The model predicts macroscopic patterns including a community's species diversity, species abundance distribution, speciation and extinction rates, as well as intraspecific and interspecific genetic variation. We explore how these long-term outcomes depend upon the parameters of reproduction: individual fitness governed by mito-nuclear compatibility, constraints on mating compatibility and ecological carrying capacity. We find that strong selection for mito-nuclear compatibility reduces the equilibrium number of species after a radiation, increasing species' abundances and simultaneously increasing both speciation and extinction rates. The negative correlation between species diversity and diversification rates in our model agrees with the broad empirical pattern of lower diversity and higher speciation/extinction rates in temperate regions, compared to the tropics. We conclude that these empirical patterns may be caused in part by latitudinal variation in metabolic demands and corresponding variation in selection for mito-nuclear function.

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.

Diversity patterns and speciation processes in a two-island system with continuous migration.

Geographic isolation is a central mechanism of speciation, but perfect isolation of populations is rare. Although speciation can be hindered if gene flow is large, intermediate levels of migration can enhance speciation by introducing genetic novelty in the semi-isolated populations or founding small communities of migrants. Here, we consider a two-island neutral model of speciation with continuous migration and study diversity patterns as a function of the migration probability, population size, and number of genes involved in reproductive isolation (dubbed as genome size). For small genomes, low levels of migration induce speciation on the islands that otherwise would not occur. Diversity, however, drops sharply to a single species inhabiting both islands as the migration probability increases. For large genomes, sympatric speciation occurs even when the islands are strictly isolated. Then species richness per island increases with the probability of migration, but the total number of species decreases as they become cosmopolitan. For each genome size, there is an optimal migration intensity for each population size that maximizes the number of species. We discuss the observed modes of speciation induced by migration and how they increase species richness in the insular system while promoting asymmetry between the islands and hindering endemism.

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.

Modeling neutral viral mutations in the spread of SARS-CoV-2 epidemics.

Although traditional models of epidemic spreading focus on the number of infected, susceptible and recovered individuals, a lot of attention has been devoted to integrate epidemic models with population genetics. Here we develop an individual-based model for epidemic spreading on networks in which viruses are explicitly represented by finite chains of nucleotides that can mutate inside the host. Under the hypothesis of neutral evolution we compute analytically the average pairwise genetic distance between all infecting viruses over time. We also derive a mean-field version of this equation that can be added directly to compartmental models such as SIR or SEIR to estimate the genetic evolution. We compare our results with the inferred genetic evolution of SARS-CoV-2 at the beginning of the epidemic in China and found good agreement with the analytical solution of our model. Finally, using genetic distance as a proxy for different strains, we use numerical simulations to show that the lower the connectivity between communities, e.g., cities, the higher the probability of reinfection.

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.].

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.

Diverse interactions and ecosystem engineering can stabilize community assembly.

The complexity of an ecological community can be distilled into a network, where diverse interactions connect species in a web of dependencies. Species interact directly with each other and indirectly through environmental effects, however to our knowledge the role of these ecosystem engineers has not been considered in ecological network models. Here we explore the dynamics of ecosystem assembly, where species colonization and extinction depends on the constraints imposed by trophic, service, and engineering dependencies. We show that our assembly model reproduces many key features of ecological systems, such as the role of generalists during assembly, realistic maximum trophic levels, and increased nestedness with mutualistic interactions. We find that ecosystem engineering has large and nonlinear effects on extinction rates. While small numbers of engineers reduce stability by increasing primary extinctions, larger numbers of engineers increase stability by reducing primary extinctions and extinction cascade magnitude. Our results suggest that ecological engineers may enhance community diversity while increasing persistence by facilitating colonization and limiting competitive exclusion.

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.

The indirect paths to cascading effects of extinctions in mutualistic networks.

Biodiversity loss is a hallmark of our times, but predicting its consequences is challenging. Ecological interactions form complex networks with multiple direct and indirect paths through which the impacts of an extinction may propagate. Here we show that accounting for these multiple paths connecting species is necessary to predict how extinctions affect the integrity of ecological networks. Using an approach initially developed for the study of information flow, we estimate indirect effects in plant-pollinator networks and find that even those species with several direct interactions may have much of their influence over others through long indirect paths. Next, we perform extinction simulations in those networks and show that although traditional connectivity metrics fail in the prediction of coextinction patterns, accounting for indirect interaction paths allows predicting species' vulnerability to the cascading effects of an extinction event. Embracing the structural complexity of ecological systems contributes towards a more predictive ecology, which is of paramount importance amid the current biodiversity crisis.

Revealing biases in the sampling of ecological interaction networks.

The structure of ecological interactions is commonly understood through analyses of interaction networks. However, these analyses may be sensitive to sampling biases with respect to both the interactors (the nodes of the network) and interactions (the links between nodes), because the detectability of species and their interactions is highly heterogeneous. These ecological and statistical issues directly affect ecologists' abilities to accurately construct ecological networks. However, statistical biases introduced by sampling are difficult to quantify in the absence of full knowledge of the underlying ecological network's structure. To explore properties of large-scale ecological networks, we developed the software EcoNetGen, which constructs and samples networks with predetermined topologies. These networks may represent a wide variety of communities that vary in size and types of ecological interactions. We sampled these networks with different mathematical sampling designs that correspond to methods used in field observations. The observed networks generated by each sampling process were then analyzed with respect to the number of components, size of components and other network metrics. We show that the sampling effort needed to estimate underlying network properties depends strongly both on the sampling design and on the underlying network topology. In particular, networks with random or scale-free modules require more complete sampling to reveal their structure, compared to networks whose modules are nested or bipartite. Overall, modules with nested structure were the easiest to detect, regardless of the sampling design used. Sampling a network starting with any species that had a high degree (e.g., abundant generalist species) was consistently found to be the most accurate strategy to estimate network structure. Because high-degree species tend to be generalists, abundant in natural communities relative to specialists, and connected to each other, sampling by degree may therefore be common but unintentional in empirical sampling of networks. Conversely, sampling according to module (representing different interaction types or taxa) results in a rather complete view of certain modules, but fails to provide a complete picture of the underlying network. To reduce biases introduced by sampling methods, we recommend that these findings be incorporated into field design considerations for projects aiming to characterize large species interaction networks.

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.

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.

Gene flow and metacommunity arrangement affects coevolutionary dynamics at the mutualism-antagonism interface.

Interspecific interactions are affected by community context and, as a consequence, show spatial variation in magnitude and sign. The selective forces imposed by interactions at the mutualism-antagonism interface are a consequence of the traits involved and their matching between species. If mutualistic and antagonistic communities are linked by gene flow, coevolution between a pair of interacting species is influenced by how selection varies in space. Here we investigate the effects of metacommunity arrangement, i.e. patterns of connection between communities and the number of communities, on the coevolutionary dynamics between two species for which the sign and magnitude of the interaction varies across the landscape. We quantify coevolutionary outcome as an index that can be decomposed into the contribution of intraspecific genetic diversity and interspecific interaction. We show that polymorphisms and mismatches are an expected outcome, which is influenced by spatial structure, interaction strength and the degree of gene flow. The index describes how variation is distributed within and between species, and provides information on the directionality of the mismatches and polymorphisms. Finally, we argue that depending on metacommunity arrangement, some communities have disproportionate roles in maintaining genetic diversity, with implications for the coevolution of interacting species in a fragmented landscape.

Voting contagion: Modeling and analysis of a century of U.S. presidential elections.

Social influence plays an important role in human behavior and decisions. Sources of influence can be divided as external, which are independent of social context, or as originating from peers, such as family and friends. An important question is how to disentangle the social contagion by peers from external influences. While a variety of experimental and observational studies provided insight into this problem, identifying the extent of contagion based on large-scale observational data with an unknown network structure remains largely unexplored. By bridging the gap between the large-scale complex systems perspective of collective human dynamics and the detailed approach of social sciences, we present a parsimonious model of social influence, and apply it to a central topic in political science-elections and voting behavior. We provide an analytical expression of the county vote-share distribution, which is in excellent agreement with almost a century of observed U.S. presidential election data. Analyzing the social influence topography over this period reveals an abrupt phase transition from low to high levels of social contagion, and robust differences among regions. These results suggest that social contagion effects are becoming more instrumental in shaping large-scale collective political behavior, with implications on democratic electoral processes and policies.