Stochasticity Leads to Coexistence of Generalists and Specialists in Assembling Mutualistic Communities.

AbstractSpecies interaction networks are subject to natural and anthropogenic disturbances that lead to their disassembly, while natural regeneration or restoration efforts facilitate their reassembly. Previous models for assembling ecological networks did not include stochasticity at the level of population dynamics (e.g., demographic noise, environmental noise) and focused mainly on food webs. Here, we present a model for the assembly of mutualistic bipartite networks, such as plant-pollinator networks, and examine the influence of demographic noise on the trajectory of species and strategy diversity, that is, the range of present strategies from specialism to generalism. We find that assembled communities show at intermediate assembly stages a maximum of species diversity and of average generalization. Our model thus provides a mechanism for nonlinear, hump-shaped diversity trajectories at intermediate succession, consistent with the intermediate disturbance hypothesis. Long-term coexistence of specialists and generalists emerges only in the presence of demographic noise and is due to a persistent species turnover. These findings highlight the importance of stochasticity for maintaining long-term diversity.

Master stability functions for metacommunities with two types of habitats.

Current questions in ecology revolve around instabilities in the dynamics on spatial networks and particularly the effect of node heterogeneity. We extend the master stability function formalism to inhomogeneous biregular networks having two types of spatial nodes. Notably, this class of systems also allows the investigation of certain types of dynamics on higher-order networks. Combined with the generalized modeling approach to study the linear stability of steady states, this is a powerful tool to numerically asses the stability of large ensembles of systems. We analyze the stability of ecological metacommunities with two distinct types of habitats analytically and numerically in order to identify several sets of conditions under which the dynamics can become stabilized by dispersal. Our analytical approach allows general insights into stabilizing and destabilizing effects in metapopulations. Specifically, we identify self-regulation and negative feedback loops between source and sink populations as stabilizing mechanisms and we show that maladaptive dispersal may be stable under certain conditions.

Nested versus Independent Sampling: Solving the Mystery of Contradictory Species-Area Relationships.

AbstractSpecies-area relationships (SARs) describe how the number of species increases with the size of the area surveyed. They usually take the form of a power law on regional spatial scales. A metareview of empirical data has shown that the exponent of the power law is larger on average when the areas are sampled in a nested manner, compared with sampling of isolated areas such as islands or nature reserves of different sizes. Because this finding contradicts ecological reasoning, we performed computer simulations of three qualitatively different models that generate species distributions in space and time driven by the mechanisms of speciation, dispersal, and extinction. We find that in all cases and over a wide parameter range the SARs obtained by nested sampling have a smaller slope on the regional scale than those obtained by independent sampling. However, the slopes change considerably with spatial scale and in a different manner for the two sampling methods. By evaluating the spatial scales on which the two types of empirical data were taken, we can explain the discrepancy between simulation results and empirical data.

The concerted emergence of well-known spatial and temporal ecological patterns in an evolutionary food web model in space.

Ecological systems show a variety of characteristic patterns of biodiversity in space and time. It is a challenge for theory to find models that can reproduce and explain the observed patterns. Since the advent of island biogeography these models revolve around speciation, dispersal, and extinction, but they usually neglect trophic structure. Here, we propose and study a spatially extended evolutionary food web model that allows us to study large spatial systems with several trophic layers. Our computer simulations show that the model gives rise simultaneously to several biodiversity patterns in space and time, from species abundance distributions to the waxing and waning of geographic ranges. We find that trophic position in the network plays a crucial role when it comes to the time evolution of range sizes, because the trophic context restricts the occurrence and survival of species especially on higher trophic levels.

A closed form for Jacobian reconstruction from time series and its application as an early warning signal in network dynamics.

The Jacobian matrix of a dynamical system describes its response to perturbations. Conversely, one can estimate the Jacobian matrix by carefully monitoring how the system responds to environmental noise. We present a closed-form analytical solution for the calculation of a system's Jacobian from a time series. Being able to access the Jacobian enables a broad range of mathematical analyses by which deeper insights into the system can be gained. Here we consider in particular the computation of the leading Jacobian eigenvalue as an early warning signal for critical transitions. To illustrate this approach, we apply it to ecological meta-foodweb models, which are strongly nonlinear dynamical multi-layer networks. Our analysis shows that accurate results can be obtained, although the data demand of the method is still high.

Modern models of trophic meta-communities.

Dispersal and foodweb dynamics have long been studied in separate models. However, over the past decades, it has become abundantly clear that there are intricate interactions between local dynamics and spatial patterns. Trophic meta-communities, i.e. meta-foodwebs, are very complex systems that exhibit complex and often counterintuitive dynamics. Over the past decade, a broad range of modelling approaches have been used to study these systems. In this paper, we review these approaches and the insights that they have revealed. We focus particularly on recent papers that study trophic interactions in spatially extensive settings and highlight the common themes that emerged in different models. There is overwhelming evidence that dispersal (and particularly intermediate levels of dispersal) benefits the maintenance of biodiversity in several different ways. Moreover, some insights have been gained into the effect of different habitat topologies, but these results also show that the exact relationships are much more complex than previously thought, highlighting the need for further research in this area. This article is part of the theme issue 'Integrative research perspectives on marine conservation'.

Predicting properties of the stationary probability currents for two-species reaction systems without solving the Fokker-Planck equation.

We derive methods for estimating the topology of the stationary probability current j[over ⃗]_{s} of the two-species Fokker-Planck equation (FPE) without the need to solve the FPE. These methods are chosen such that they become exact in certain limits, such as infinite system size or vanishing coupling between species in the diffusion matrix. The methods make predictions about the fixed points of j[over ⃗]_{s} and their relation to extrema of the stationary probability distribution and to fixed points of the convective field, which is related to the deterministic drift of the system. Furthermore, they predict the rotation sense of j[over ⃗]_{s} around extrema of the stationary probability distribution. Even though these methods cannot be proven to be valid away from extrema, the boundary lines between regions with different rotation senses are obtained with surprising accuracy. We illustrate and test these methods, using simple reaction systems with only one coupling term between the two species as well as a few generic reaction networks taken from the literature. We use it also to investigate the shape of nonphysical probability currents occurring in reaction systems with detailed balance due to the approximations involved in deriving the Fokker-Planck equation.

Far-ranging generalist top predators enhance the stability of meta-foodwebs.

Identifying stabilizing factors in foodwebs is a long standing challenge with wide implications for community ecology and conservation. Here, we investigate the stability of spatially resolved meta-foodwebs with far-ranging super-predators for whom the whole meta-foodwebs appears to be a single habitat. By using a combination of generalized modeling with a master stability function approach, we are able to efficiently explore the asymptotic stability of large classes of realistic many-patch meta-foodwebs. We show that meta-foodwebs with far-ranging top predators are more stable than those with localized top predators. Moreover, adding far-ranging generalist top predators to a system can have a net stabilizing effect. These results highlight the importance of top predator conservation.

A combined experimental and theoretical study of radon solubility in fat and water.

Radon is a radioactive noble gas that can enter the human body, thus increasing the risk of lung cancer. But it is also used for treatment of various ailments, most notably rheumatoid arthritis. The accumulation of radon differs between tissues, with particularly high concentrations in fat tissue. To understand the underlying mechanisms, a combination of γ-spectroscopy and molecular dynamics simulations were performed, to study the accumulation of radon gas in contact with several liquids (water, fatty acids). The solubilities, specific for a defined radon activity concentration, are in good agreement and differ by two orders of magnitude between water and fat, caused by radon disrupting the hydrogen bond network of water. In contrast, the energy cost of introducing radon atoms into fat is low due to the dispersive interaction between radon and fat, which is a non-polar solvent. This correlation was also explicitly demonstrated in our simulations by changing the polarization of the solvent.

Rad54 Phosphorylation Promotes Homologous Recombination by Balancing Rad54 Mobility and DNA Binding.

The repair of DNA double-strand breaks by homologous recombination is of crucial importance for maintaining genomic stability. Two major players during this repair pathway are Rad51 and Rad54. Previously, it was shown that Rad54 exists as a monomer or oligomer when bound to DNA and drives the displacement of Rad51 by translocating along the DNA. Moreover, phosphorylation of Rad54 was reported to stimulate this clearance of Rad51 from DNA. However, it is currently unclear how phosphorylation of Rad54 modulates its molecular-structural function and how it affects the activity of monomeric or oligomeric Rad54 during the removal of Rad51. To examine the impact of Rad54 phosphorylation on a molecular-structural level, we applied molecular dynamics simulations of Rad54 monomers and hexamers in the absence or presence of DNA. Our results suggest that 1) phosphorylation of Rad54 stabilizes the monomeric form by reducing the interlobe movement of Rad54 monomers and might therefore facilitate multimer formation around DNA and 2) phosphorylation of Rad54 in a higher-order hexamer reduces its binding strength to DNA, which is a requirement for efficient mobility on DNA. To further address the relationship between the mobility of Rad54 and its phosphorylation state, we performed fluorescence recovery after photobleaching experiments in living cells, which expressed different versions of the Rad54 protein. Here, we could measure that the phosphomimetic version of Rad54 was highly mobile on DNA, whereas a nonphosphorylatable mutant displayed a mobility defect. Taken together, these data show that the phosphorylation of Rad54 is a critical event in balancing the DNA binding strength and mobility of Rad54 and might therefore provide optimal conditions for DNA translocation and subsequent removal of Rad51 during homologous recombination repair.

PCNA-Mediated Degradation of p21 Coordinates the DNA Damage Response and Cell Cycle Regulation in Individual Cells.

To enable reliable cell fate decisions, mammalian cells need to adjust their responses to dynamically changing internal states by rewiring the corresponding signaling networks. Here, we combine time-lapse microscopy of endogenous fluorescent reporters with computational analysis to understand at the single-cell level how the p53-mediated DNA damage response is adjusted during cell cycle progression. Shape-based clustering revealed that the dynamics of the CDK inhibitor p21 diverges from the dynamics of its transcription factor p53 during S phase. Using mathematical modeling, we predict and experimentally validate that S phase-specific degradation of p21 by PCNA-CRL4cdt2 is sufficient to explain these heterogeneous responses. This highlights how signaling pathways and cell regulatory networks intertwine to adjust the cellular response to the individual needs of a given cell.

Context in synthetic biology: Memory effects of environments with mono-molecular reactions.

Synthetic biology aims at designing modular genetic circuits that can be assembled according to the desired function. When embedded in a cell, a circuit module becomes a small subnetwork within a larger environmental network, and its dynamics is therefore affected by potentially unknown interactions with the environment. It is well-known that the presence of the environment not only causes extrinsic noise but also memory effects, which means that the dynamics of the subnetwork is affected by its past states via a memory function that is characteristic of the environment. We study several generic scenarios for the coupling between a small module and a larger environment, with the environment consisting of a chain of mono-molecular reactions. By mapping the dynamics of this coupled system onto random walks, we are able to give exact analytical expressions for the arising memory functions. Hence, our results give insights into the possible types of memory functions and thereby help to better predict subnetwork dynamics.

AutoFoci, an automated high-throughput foci detection approach for analyzing low-dose DNA double-strand break repair.

Double-strand breaks (DSBs) are the most lethal DNA damages induced by ionising radiation (IR) and their efficient repair is crucial to limit genomic instability. The cellular DSB response after low IR doses is of particular interest but its examination requires the analysis of high cell numbers. Here, we present an automated DSB quantification method based on the analysis of γH2AX and 53BP1 foci as markers for DSBs. We establish a combination of object properties, combined in the object evaluation parameter (OEP), which correlates with manual object classification. Strikingly, OEP histograms show a bi-modal distribution with two maxima and a minimum in between, which correlates with the manually determined transition between background signals and foci. We used algorithms to detect the minimum, thus separating foci from background signals and automatically assessing DSB levels. To demonstrate the validity of this method, we analyzed over 600.000 cells to verify results of previous studies showing that DSBs induced by low doses are less efficiently repaired compared with DSBs induced by higher doses. Thus, the automated foci counting method, called AutoFoci, provides a valuable tool for high-throughput image analysis of thousands of cells which will prove useful for many biological screening approaches.

Master stability functions reveal diffusion-driven pattern formation in networks.

We study diffusion-driven pattern formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing random walks, while they can be created or destroyed by reactions between or within a layer. We show that the stability of homogeneous steady states can be analyzed with a master stability function approach that reveals a deep analogy between pattern formation in networks and pattern formation in continuous space. For illustration, we consider a generalized model of ecological meta-food webs. This fairly complex model describes the dispersal of many different species across a region consisting of a network of individual habitats while subject to realistic, nonlinear predator-prey interactions. In this example, the method reveals the intricate dependence of the dynamics on the spatial structure. The ability of the proposed approach to deal with this fairly complex system highlights it as a promising tool for ecology and other applications.

Analysis of stochastic bifurcations with phase portraits.

We propose a method to obtain phase portraits for stochastic systems. Starting from the Fokker-Planck equation, we separate the dynamics into a convective and a diffusive part. We show that stable and unstable fixed points of the convective field correspond to maxima and minima of the stationary probability distribution if the probability current vanishes at these points. Stochastic phase portraits, which are vector plots of the convective field, therefore indicate the extrema of the stationary distribution and can be used to identify stochastic bifurcations that change the number and stability of these extrema. We show that limit cycles in stochastic phase portraits can indicate ridges of the probability distribution, and we identify a novel type of stochastic bifurcation, where the probability maximum moves to the edge of the system through a gap between the two nullclines of the convective field.

Impact of stochastic migration on species diversity in meta-food webs consisting of several patches.

The structure of space has an appreciable influence on the diversity and stability of ecosystems. So far, there are only few theoretical studies investigating the population dynamics of food webs consisting of many species that can migrate between several patches, and in most of these models migration is a continuous, deterministic process. However, when migration events are rare (for instance because the patches are far apart), migration is a stochastic process and should be modeled accordingly. We present computer simulations of a food web model of many species on a spatial network of several patches, combining deterministic local population dynamics with stochastic migration. We evaluate the influence of the migration rate and other model parameters on local and regional species diversity and on stability. We find that migration increases the number of surviving and coexisting populations by two effects. These are the rescue effect, which restores local populations that have gone extinct, and dynamical coexistence, which sustains local populations that could not persist in the absence of immigration. Both effects occur even when migration events are rare. Species diversity increases on local and regional scales with the frequency of migration events. Furthermore, we investigate the adiabatic limit in which population dynamics always reaches an equilibrium before the next migration event, and we investigate the possible long-term scenarios. While the final state often contains the same food web on all patches, we also find instances where two slightly different food webs coexist on different patches, even when initially each patch contained the same food web.

Habitat heterogeneity hypothesis and edge effects in model metacommunities.

Spatial heterogeneity is an inherent property of any living environment and is expected to favour biodiversity due to a broader niche space. Furthermore, edges between different habitats can provide additional possibilities for species coexistence. Using computer simulations, this study examines metacommunities consisting of several trophic levels in heterogeneous environments in order to explore the above hypotheses on a community level. We model heterogeneous landscapes by using two different sized resource pools and evaluate the combined effect of dispersal and heterogeneity on local and regional species diversity. This diversity is obtained by running population dynamics and evaluating the robustness (i.e., the fraction of surviving species). The main results for regional robustness are in agreement with the habitat heterogeneity hypothesis, as the largest robustness is found in heterogeneous systems with intermediate dispersal rates. This robustness is larger than in homogeneous systems with the same total amount of resources. We study the edge effect by arranging the two types of resources in two homogeneous blocks. Different edge responses in diversity are observed, depending on dispersal strength. Local robustness is highest for edge habitats that contain the smaller amount of resource in combination with intermediate dispersal. The results show that dispersal is relevant to correctly identify edge responses on community level.

Spatial topologies affect local food web structure and diversity in evolutionary metacommunities.

An important challenge in theoretical ecology is to better predict ecological responses to environmental change, and in particular to spatial changes such as habitat fragmentation. Classical food-web models have focused on purely ecological predictions, without taking adaptation or evolution of species traits into account. We address this issue using an eco-evolutionary model, which is based on body masses and diets as the key traits that determine metabolic rates and trophic interactions. The model implements evolution by the introduction of new morphs that are related to the existing ones, so that the network structure itself evolves in a self-organized manner. We consider the coupling and decoupling of habitats in multi-trophic metacommunities consisting of 2 or 4 habitats. Our model thus integrates metacommunity models, which describe ecosystems as networks of networks, with large community evolution models. We find that rescue effects and source-sink effects occur within coupled habitats, which have the potential to change local selection pressures so that the local food web structure shows a fingerprint of its spatial conditions. Within our model system, we observe that habitat coupling increases the lifetimes of top predators and promotes local biodiversity.

A minimal model of burst-noise induced bistability.

We investigate the influence of intrinsic noise on stable states of a one-dimensional dynamical system that shows in its deterministic version a saddle-node bifurcation between monostable and bistable behaviour. The system is a modified version of the Schlögl model, which is a chemical reaction system with only one type of molecule. The strength of the intrinsic noise is varied without changing the deterministic description by introducing bursts in the autocatalytic production step. We study the transitions between monostable and bistable behavior in this system by evaluating the number of maxima of the stationary probability distribution. We find that changing the size of bursts can destroy and even induce saddle-node bifurcations. This means that a bursty production of molecules can qualitatively change the dynamics of a chemical reaction system even when the deterministic description remains unchanged.

Structure and dynamics of a silica melt in neutral confinement.

We analyze the effects of spatial confinement on viscous silica using molecular dynamics simulations. For this purpose, we prepare a silica melt in a cylindrical pore, which is produced by pinning appropriate fractions of silicon and oxygen atoms in a bulk system after an equilibration period. In this way, the structure of the confined silica melt remains unaffected, while the confinement has a strong impact on the dynamics. We find that the structural relaxation of viscous silica is slowed down according to a double exponential law when approaching the pore wall. Moreover, we observe that static density correlations exist in the vicinity of the pore wall. Based on these effects, we determine dynamical and structural length scales of the silica melt. Both length scales show a similar increase upon cooling, with values on the order of the next-neighbor distances in the studied temperature range. Interestingly, we find no evidence that the growth of the length scales is affected by a fragile-to-strong transition of the silica melt. This observation casts serious doubts on the relevance of these length scales for the structural relaxation, at least for the studied glass former.