Synchronous dynamics and rates of extinction in spatially structured populations

We explore extinction rates using a spatially arranged set of subpopulations obeying Ricker dynamics. The population system is subjected to dispersal of individuals among the subpopulations as well as to local and global disturbances. We observe a tight positive correlation between global extinction rate and the level of synchrony in dynamics among thesubpopulations. Global disturbances and to a lesser extent, migration, are capable of synchronizing the temporal dynamics of the subpopulations over a rather wide span of the population growth rate r. Local noise decreases synchrony, as does increasing distance among the subpopulations. Synchrony also levels off with increasing r: in the chaotic region, subpopulations almost invariably behave asynchronously. We conclude that it is asynchrony that reduces the probability of global extinctions, not chaos as such: chaos is a special case only. The relationship between global extinction rate, synchronous dynamics and population growth rate is robust to changes in dispersal rates and ranges.     

Maximization principles and daisyworld

We investigate whether the equilibrium time-averaged state of a self-organizing system with many internal degrees of freedom, 2D-daisyworld, can be described by optimizing a single quantity. Unlike physical systems where a principle of maximum energy production has been observed, daisyworld follows evolutionary dynamics rather than Hamiltonian dynamics. We find that this is sufficient to invalidate the maximum entropy production principle, finding instead a different principle, that the system self-organizes to a state which maximizes the amount of life.     

A Synaptic Mechanism for Temporal Filtering of Visual Signals

The visual system transmits information about fast and slow changes in light intensity through separate neural pathways. We used in vivo imaging to investigate how bipolar cells transmit these signals to the inner retina. We found that the volume of the synaptic terminal is an intrinsic property that contributes to different temporal filters. Individual cells transmit through multiple terminals varying in size, but smaller terminals generate faster and larger calcium transients to trigger vesicle release with higher initial gain, followed by more profound adaptation. Smaller terminals transmitted higher stimulus frequencies more effectively. Modeling global calcium dynamics triggering vesicle release indicated that variations in the volume of presynaptic compartments contribute directly to all these differences in response dynamics. These results indicate how one neuron can transmit different temporal components in the visual signal through synaptic terminals of varying geometries with different adaptational properties.     

Winner-take-all selection in a neural system with delayed feedback

We consider the effects of temporal delay in a neural feedback system with excitation and inhibition. The topology of our model system reflects the anatomy of the avian isthmic circuitry, a feedback structure found in all classes of vertebrates. We show that the system is capable of performing a 'winner-take-all' selection rule for certain combinations of excitatory and inhibitory feedback. In particular, we show that when the time delays are sufficiently large a system with local inhibition and global excitation can function as a 'winner-take-all' network and exhibit oscillatory dynamics. We demonstrate how the origin of the oscillations can be attributed to the finite delays through a linear stability analysis.     

Competition and species coexistence in a metapopulation model: Can fast asymmetric migration reverse the outcome of competition in a homogeneous environment?

We investigate whether asymmetric fast migration can modify the predictions of classical competition theory and, in particular revert species dominance. We consider a model of two species competing for an implicit resource on a habitat divided into two patches. Both patches are connected through constant migration rates and in each patch local dynamics are driven by a Lotka-Volterra competition system.Local competition is asymmetric with the same superior competitor in both patches. Migration is asymmetric, species dependent and fast in comparison to local competitive interactions. The species and patches are taken to be otherwise similar: in both patches we assume the same carrying capacities for both species, and the same growth rates and pair-wise competition coefficients for each species.We show that global dynamics can be described by a classical Lotka-Volterra competition model. We found that by modifying the ratio of intraspecific migration rates for both species all possible combinations of global species relative dominance can be achieved. We find specific conditions for which the local superior competitor is globally excluded. This is to our knowledge the first study showing that fast asymmetric migration can lead to inferior competitor dominance in a homogeneous environment. We conclude that disparity of temporal scales between migration and local dynamics may have important consequences for the maintenance of biodiversity in spatially structured populations.     

Complex dynamics of mass-closed coupled autocatalytic systems in response to minute asymmetric perturbations

The role of kinetic coupling in catering to a remote-control mechanism for the onset and regulation of self-organization phenomena in a multicompartmental biochemical system has been examined. Using two cyclic autocatalytic reaction networks operating in two chambers separated by a membrane and coupled through a common cofactor, it has been demonstrated that (i) in response to asymmetric perturbations, the coupled reaction networks exhibit a variety of temporal self-organization phenomena such as bistability, multiple periodicity, hard excitation and coexistence of aperiodic oscillation with limit cycle even in mass-closed conditions; (ii) without disturbing a network directly, its dynamic behaviour can be regulated by perturbing some other network kinetically coupled to it and (iii) the dynamics of two coupled networks can be made to flip-flop between oscillatory and steady-states simply by modulating the time of application of external perturbations. The extreme sensitivity of this model to minute asymmetric fluctuations in the environment can predict how the impact of local changes in physico-chemical conditions can be transmitted from one compartment to another through coupled biochemical pathways in a living cell.     

Stabilization through spatial pattern formation in metapopulations with long-range dispersal

Many studies of metapopulation models assume that spatially extended populations occupy a network of identical habitat patches, each coupled to its nearest neighbouring patches by density-independent dispersal. Much previous work has focused on the temporal stability of spatially homogeneous equilibrium states of the metapopulation, and one of the main predictions of such models is that the stability of equilibrium states in the local patches in the absence of migration determines the stability of spatially homogeneous equilibrium states of the whole metapopulation when migration is added. Here, we present classes of examples in which deviations from the usual assumptions lead to different predictions. In particular, heterogeneity in local habitat quality in combination with long-range dispersal can induce a stable equilibrium for the metapopulation dynamics, even when within-patch processes would produce very complex behaviour in each patch in the absence of migration. Thus, when spatially homogeneous equilibria become unstable, the system can often shift to a different, spatially inhomogeneous steady state. This new global equilibrium is characterized by a standing spatial wave of population abundances. Such standing spatial waves can also be observed in metapopulations consisting of identical habitat patches, i.e. without heterogeneity in patch quality, provided that dispersal is density dependent. Spatial pattern formation after destabilization of spatially homogeneous equilibrium states is well known in reaction–diffusion systems and has been observed in various ecological models. However, these models typically require the presence of at least two species, e.g. a predator and a prey. Our results imply that stabilization through spatial pattern formation can also occur in single-species models. However, the opposite effect of destabilization can also occur: if dispersal is short range, and if there is heterogeneity in patch quality, then the metapopulation dynamics can be chaotic despite the patches having stable equilibrium dynamics when isolated. We conclude that more general metapopulation models than those commonly studied are necessary to fully understand how spatial structure can affect spatial and temporal variation in population abundance.     

Nutrient flows between ecosystems can destabilize simple food chains

Dispersal of organisms has large effects on the dynamics and stability of populations and communities. However, current metacommunity theory largely ignores how the flows of limiting nutrients across ecosystems can influence communities. We studied a meta-ecosystem model where two autotroph-consumer communities are spatially coupled through the diffusion of the limiting nutrient. We analyzed regional and local stability, as well as spatial and temporal synchrony to elucidate the impacts of nutrient recycling and diffusion on trophic dynamics. We show that nutrient diffusion is capable of inducing asynchronous local destabilization of biotic compartments through a diffusion-induced spatiotemporal bifurcation. Nutrient recycling interacts with nutrient diffusion and influences the susceptibility of the meta-ecosystem to diffusion-induced instabilities. This interaction between nutrient recycling and transport is further shown to depend on ecosystem enrichment. It more generally emphasizes the importance of meta-ecosystem theory for predicting species persistence and distribution in managed ecosystems.     

A one-dimensional model of PCP signaling: Polarized cell behavior in the notochord of the ascidian Ciona

Despite its importance in development and physiology the planar cell polarity (PCP) pathway remains one of the most enigmatic signaling mechanisms. The notochord of the ascidian Ciona provides a unique model for investigating the PCP pathway. Interestingly, the notochord appears to be the only embryonic structure in Ciona activating the PCP pathway. Moreover, the Ciona notochord as a single-file array of forty polarized cells is a uniquely tractable system for the study of polarization dynamics and the transmission of the PCP pathway. Here, we test models for propagation of a polarizing signal, interrogating temporal, spatial and signaling requirements. A simple cell–cell relay cascading through the entire length of the notochord is not supported; instead a more complex mechanism is revealed, with interactions influencing polarity between neighboring cells, but not distant ones. Mechanisms coordinating notochord-wide polarity remain elusive, but appear to entrain general (i.e., global) polarity even while local interactions remain important. However, this global polarizer does not appear to act as a localized, spatially-restricted determinant. Coordination of polarity along the long axis of the notochord requires the PCP pathway, a role we demonstrate is temporally distinct from this pathway’s earlier role in convergent extension and intercalation. We also reveal polarity in the notochord to be dynamic: a cell’s polarity state can be changed and then restored, underscoring the Ciona notochord’s amenability for in vivo studies of PCP.     

Coupled map lattice approximations for spatially explicit individual-based models of ecology

Spatially explicit individual-based models are widely used in ecology but they are often difficult to treat analytically. Despite their intractability they often exhibit clear temporal and spatial patterning. We demonstrate how a spatially explicit individual-based model of scramble competition with local dispersal can be approximated by a stochastic coupled map lattice. The approximation disentangles the deterministic and stochastic element of local interaction and dispersal. We are thus able to understand the individual-based model through a simplified set of equations. In particular, we demonstrate that demographic noise leads to increased stability in the dynamics of locally dispersing single-species populations. The coupled map lattice approximation has general application to a range of spatially explicit individual-based models. It provides a new alternative to current approximation techniques, such as the method of moments and reaction-diffusion approximation, that captures both stochastic effects and large-scale patterning arising in individual-based models.     

Mutation of albedo and growth response produces oscillations in a spatial Daisyworld

We extended a two-dimensional cellular automaton (CA) Daisyworld to include mutation of optimal growth temperature as well as mutation of albedo. Thus, the organisms (daisies) can adapt to prevailing environmental conditions or evolve to alter their environment. We find the resulting system oscillates with a period of hundreds of daisy generations. Weaker and less regular oscillations exist in previous daisyworld models, but they become much stronger and more regular here with mutation in the growth response. Despite the existence of a particular combination of mean albedo and optimum individual growth temperature which maximises growth, we find that this global state is unstable with respect to mutations which lower absolute growth rate, but increase marginal growth rate. The resulting system oscillates with a period that is found to decrease with increasing death rate, and to increase with increasing heat diffusion and heat capacity. We speculate that the origin of this oscillation is a Hopf bifurcation, previously predicted in a zero-dimensional system.     

Cyclicity and variability in prey dynamics strengthens predator numerical response: the effects of vole fluctuations on white stork productivity

Theory predicts that optimality of life-long investment in reproduction is, among other factors, driven by the variability and predictability of the resources. Similarly, during the breeding season, single resource pulses characterized by short periods and high amplitudes enable strong numerical responses in their consumers. However, it is less well established how spatio-temporal dynamics in resource supplies influence the spatio-temporal variation of consumer reproduction. We used the common vole (Microtus arvalis)—white stork (Ciconia ciconia) resource—consumer model system to test the effect of increased temporal variation and periodicity of vole population dynamics on the strength of the local numerical response of storks. We estimated variability, cycle amplitude, and periodicity (by means of direct and delayed density dependence) in 13 Czech and Polish vole populations. Cross-correlation between annual stork productivity and vole abundance, characterizing the strength of the local numerical response of storks, increased when the vole population fluctuated more and population cycles were shorter. We further show that the onset of incubation of storks was delayed during the years of higher vole abundance. We demonstrate that high reproductive flexibility of a generalist consumer in tracking the temporal dynamics of its resource is driven by the properties of the local resource dynamics and we discuss possible mechanisms behind these patterns.     

One-dimensional daisyworld: spatial interactions and pattern formation

The zero-dimensional daisyworld model of Watson and Lovelock (1983) demonstrates that life can unconsciously regulate a global environment. Here that model is extended to one dimension, incorporating a distribution of incoming solar radiation and diffusion of heat consistent with a spherical planet. Global regulatory properties of the original model are retained. The daisy populations are initially restricted to hospitable regions of the surface but exert both global and local feedback to increase this habitable area, eventually colonizing the whole surface. The introduction of heat diffusion destabilizes the coexistence equilibrium of the two daisy types. In response, a striped pattern consisting of blocks of all black or all white daisies emerges. There are two mechanisms behind this pattern formation. Both are connected to the stability of the system and an overview of the mathematics involved is presented. Numerical experiments show that this pattern is globally determined. Perturbations in one region have an impact over the whole surface but the regulatory properties of the system are not compromised by transient perturbations. The relevance of these results to the Earth and the wider climate modelling field is discussed.     

Modulating RhoA effectors induces transitions to oscillatory and more wavelike RhoA dynamics in Caenorhabditis elegans zygotes

Pulsatile RhoA dynamics underlie a wide range of cell and tissue behaviors. The circuits that produce these dynamics in different cells share common architectures based on fast positive and delayed negative feedback through F-actin, but they can produce very different spatiotemporal patterns of RhoA activity. However, the underlying causes of this variation remain poorly understood. Here we asked how this variation could arise through modulation of actin network dynamics downstream of active RhoA in early Caenorhabditis elegans embryos. We find that perturbing two RhoA effectors—formin and anillin—induce transitions from nonrecurrent focal pulses to either large noisy oscillatory pulses (formin depletion) or noisy oscillatory waves (anillin depletion). In both cases these transitions could be explained by changes in local F-actin levels and depletion dynamics, leading to changes in spatial and temporal patterns of RhoA inhibition. However, the underlying mechanisms for F-actin depletion are distinct, with different dependencies on myosin II activity. Thus, modulating actomyosin network dynamics could shape the spatiotemporal dynamics of RhoA activity for different physiological or morphogenetic functions.     

Coherent Control of Gap Plasmons of a Complex Nanosystem by Shaping Driving Femtosecond Pulses

Geometry-based control of local field of coupled plasmonic nanostructures is efficient for optimization of the field intensity. However, it provides weak control over spatial and temporal dynamics of the field and thus unsuitable for experimental studies and practical applications where fixed geometries are needed. In this study, we report on pulsed excitation of strongly coupled plasmonic nanosystem comprised of nanorod and split-ring antenna. The near-field intensities are manipulated by controlling time delay, relative phase, and polarization of the ultrafast excitation pulses. We show that the spectral and spatial intensities of the local fields at the gap regions of the coupled nanosystem can be pronounced by using two identical pulses with least time delay and phase difference. The corresponding temporal intensities of electric near-fields for both parallel and orthogonal polarization of the illumination fields are also briefly discussed. These findings might have implications for controlled excitation of complexly coupled plasmonic nanosystems.     

Dynamics of Reciprocal Pulsed Subsidies in Local and Meta-Ecosystems

Temporally variable and reciprocal subsidies between ecosystems are ubiquitous. These spatial flows can generate a suite of direct and indirect effects in local and meta-ecosystems. The focus of most subsidy research, however, has been on the response of consumers in recipient ecosystems to constant subsidies over very short or very long time scales. We derive a meta-ecosystem model to explicitly consider the dynamic feedbacks between local ecosystems coupled through reciprocal pulsed subsidies. We predict oscillating reinforcing and dampening effects of reciprocal pulsed herbivore flows. Maximum reinforcing effects between reciprocal pulsed herbivore flows occur when these flows are in phase with the dynamics of neighboring predators. This prediction is robust to a range of pulse quantities and frequencies. Reciprocal pulsed herbivore subsidies lead to spatial and temporal variability in the strength of trophic cascades in local and meta-ecosystems but these cascading effects are the strongest when reciprocal pulsed subsidies are temporally concentrated. When predators demonstrate a behavioral response to prey abundance, reciprocal pulsed subsidies dampen the strength of local trophic cascades but lead to strong trophic cascades across local ecosystems. The timing of reciprocal pulsed subsidies is a critical component that determines the cascading effects of spatial flows. We show that spatial and temporal variabilities in resources and consumers can have a significant influence on the strength of cascading trophic interactions; therefore, our ability to detect and understand trophic cascades may depend on the scale of inquiry of ecological studies.     

Synchronizing genetic oscillators by signaling molecules

The authors examine collective rhythms in a general multicell system with both linearly diffusive and nondiffusive couplings. The effect of coupling on synchronization through intercellular signaling in a population of Escherichia coli cells is studied. In particular, a synchronization solution is given through the auxiliary individual system for 2 types of couplings. The sufficient conditions for the global synchronization of such a coupled system are derived based on the Lyapunov function method. The authors show that an appropriate design of the coupling and the inner-linking matrix can ensure global synchronization of the coupled synthetic biological system. Moreover, they demonstrate that the dynamics of an individual cell with coupling and without coupling may be qualitatively different; one is oscillatory, and the other is steady state. The change from a nonoscillatory state to an oscillatory one is induced by appropriate coupling, which also entrains all cells to synchronization. These results establish not only a theoretical foundation but also a quantitative basis for understanding the essential cooperative dynamics, such as collective rhythms or synchronization, in a population of cells.     

Clone mixtures and a pacemaker: new facets of Red-Queen theory and ecology

Host-parasite antagonistic interaction has been proposed as a potential agent to promote genetic polymorphism and to favour sex against asex, despite its twofold cost in reproduction. However, the host-parasite gene-for-gene dynamics often produce unstable cycles that tend to destroy genetic diversity. Here, we examine such diversity destroying coevolutionary dynamics of host and parasite, which is coupled through local or global migration, or both, between demes in a metapopulation structure. We show that, with global migration in the island model, peculiar out-of-phase islands spontaneously arise in the cluster of islands converging to a global synchrony. Such asynchrony induced by the 'pacemaker islands' serves to restore genetic variation. With increasing fraction of local migration, spots of asynchrony are converted into loci or foci of spiral and target patterns, whose rotating arms then cover the majority of demes. A multi-locus analogue of the model reproduces the same tendency toward asynchrony, and the condition arises for an advantage of asexual clones over their sexual counterpart when enough genetic diversity is maintained through metapopulation storage-migration serves as a cheap alternative to sex.     

A Model for Cross-Cultural Reciprocal Interactions through Mass Media

We investigate the problem of cross-cultural interactions through mass media in a model where two populations of social agents, each with its own internal dynamics, get information about each other through reciprocal global interactions. As the agent dynamics, we employ Axelrod''s model for social influence. The global interaction fields correspond to the statistical mode of the states of the agents and represent mass media messages on the cultural trend originating in each population. Several phases are found in the collective behavior of either population depending on parameter values: two homogeneous phases, one having the state of the global field acting on that population, and the other consisting of a state different from that reached by the applied global field; and a disordered phase. In addition, the system displays nontrivial effects: (i) the emergence of a largest minority group of appreciable size sharing a state different from that of the applied global field; (ii) the appearance of localized ordered states for some values of parameters when the entire system is observed, consisting of one population in a homogeneous state and the other in a disordered state. This last situation can be considered as a social analogue to a chimera state arising in globally coupled populations of oscillators.     

Local phenotypic variation in amphibian-killing fungus predicts infection dynamics

Environmental factors can limit the distribution of organisms if they are not able to respond through phenotypic plasticity or local adaptation. Batrachochytrium dendrobatidis (Bd) is a broadly distributed pathogen, which shows spatially patterned genotypic and phenotypic variation; however, information on the functional consequences of this variation on disease dynamics in natural hosts is limited. We genotyped and quantified variation in Bd phenotypes across an elevational gradient and quantified host infection dynamics at each site. All Bd strains were members of the global panzootic lineage yet differed in phenotype. We hypothesize that this phenotypic variance results from adaptive processes due to the interaction between pathogen, hosts, and environment. We detected a correlation between zoospore and zoosporangia sizes and a positive association between zoosporangia size and Bd prevalence. Given that Bd phenotype predicted disease status in our wild populations, we developed an index to identify critical environments where the fungus could be more deleterious.