A theoretical model for the prediction of sequence-dependent nucleosome thermodynamic stability

A theoretical model for predicting nucleosome thermodynamic stability in terms of DNA sequence is advanced. The model is based on a statistical mechanical approach, which allows the calculation of the canonical ensemble free energy involved in the competitive nucleosome reconstitution. It is based on the hypothesis that nucleosome stability mainly depends on the bending and twisting elastic energy to transform the DNA intrinsic superstructure into the nucleosomal structure. The ensemble average free energy is calculated starting from the intrinsic curvature, obtained by integrating the dinucleotide step deviations from the canonical B-DNA and expressed in terms of a Fourier series, in the framework of first-order elasticity. The sequence-dependent DNA flexibility is evaluated from the differential double helix thermodynamic stability. A large number of free-energy experimental data, obtained in different laboratories by competitive nucleosome reconstitution assays, are successfully compared to the theoretical results. They support the hypothesis that the stacking energies are the major factor in DNA rigidity and could be a measure of DNA stiffness. A dual role of DNA intrinsic curvature and flexibility emerges in the determination of nucleosome stability. The difference between the experimental and theoretical (elastic) nucleosome-reconstitution free energy for the whole pool of investigated DNAs suggests a significant role for the curvature-dependent DNA hydration and counterion interactions, which appear to destabilize nucleosomes in highly curved DNAs. This model represents an attempt to clarify the main features of the nucleosome thermodynamic stability in terms of physical-chemical parameters and suggests that in molecular systems with a large degree of complexity, the average molecular properties dominate over the local features, as in a statistical ensemble.     

Increasing community size and connectance can increase stability in competitive communities

The relationship between community complexity and stability has been the subject of an enduring debate in ecology over the last 50 years. Results from early model communities showed that increased complexity is associated with decreased local stability. I demonstrate that increasing both the number of species in a community and the connectance between these species results in an increased probability of local stability in discrete-time competitive communities, when some species would show unstable dynamics in the absence of competition. This is shown analytically for a simple case and across a wider range of community sizes using simulations, where individual species have dynamics that can range from stable point equilibria to periodic or more complex. Increasing the number of competitive links in the community reduces per-capita growth rates through an increase in competitive feedback, stabilising oscillating dynamics. This result was robust to the introduction of a trade-off between competitive ability and intrinsic growth rate and changes in species interaction strengths. This throws new light on the discrepancy between the theoretical view that increased complexity reduces stability and the empirical view that more complex systems are more likely to be stable, giving one explanation for the relative lack of complex dynamics found in natural systems. I examine how these results relate to diversity-biomass stability relationships and show that an analytical solution derived in the region of stable equilibrium dynamics captures many features of the change in biomass fluctuations with community size in communities including species with oscillating dynamics.     

Disentangling the effect of hybrid interactions and of the constant effort hypothesis on ecological community stability

In the last years, a remarkable theoretical effort has been made in order to understand the relation between stability and complexity in ecological communities. Yet, what maintains species diversity in real ecological communities is still an open question. The non‐random structures of ecological interaction networks have been recognized as one key ingredient impacting the maximum number of coexisting species within the ecological community. However most of the earlier theoretical studies have considered communities with only one interaction type (either antagonistic, competitive or mutualistic). Recently, it has been proposed that multiple interaction types might stabilize ecosystems and that, in this hybrid case, increasing complexity increases stability. Here we show that these results depend on ad hoc hypothesis that the authors used in their model and we highlight the need to disentangle the role of multiple interaction types and constant interaction effort allocation on community stability. Indeed, we find that mixing of mutualistic and predator–prey interaction types does not stabilize the community dynamics and we demonstrate that a positive correlation between complexity and stability is observed only if a constant effort allocation is imposed in the ecological interactions. Synthesis In recent years a sparkling research has been devoted to the search of new theoretical mechanisms to explain way ecosystems may persist despite their complexity. Here we show that, contrary to what recently suggested (Mougi et al. 2012), the mismatch between theoretical results and empirical evidences on the stability of ecological community is still there also for communities with both mutualistic and antagonistic interactions, and the ‘complexity‐stability’ paradox is still alive. Indeed, we demonstrate that their results arise as an artifact of the peculiar rescaling of the interaction strengths they imposed. Our study suggests that further theoretical studies and experimental evidences are still needed to better understand the role of interaction strengths in real ecological communities.     

Sequential behavior and stability properties of enzymatic neuron networks

The cycle structure of enzymatic neural networks may be characterized in terms of number of cycles exhibited, size of cycle state sets and cycle lengths. Simulation experiments show that the stability properties of these networks have some unusual features which are not exhibited by networks of two-state switching elements or by randomly constructed ecosystem models. The behavioral and structural stability of these systems decreases with their structural complexity, as measured by the number of components. The behavioral and structural stability of enzymatic neural networks also decreases with structural complexity, as measured by the number of excitase types, but only up to the middle level of excitases per neuron. This is the point of highest potential responsiveness of the system to environmental stimuli. Beyond this point the behavioral and structural stability increase. This is due to the fact that the number of possible states increases up to this point and decreases beyond it. The number of possible states, not the number of components, serves as the useful measure of complexity in these types of systems. The selection circuits learning algorithm has been used to evolve networks whose cycle structures have desired features.     

Competitive processes. II. Stability of random systems

In this work, by employing the concept of vector Lyapunov functions and the theory of random differential inequalities, the stability analysis of random competitive systems is initiated in a systematic and unified way. Furthermore, an attempt has been made to formulate and partially resolve the “deterministic vs. stochastic”, and the “complexity vs. stability” problems in stochastic competitive processes. Finally, the usefulness of the stability analysis of the competitive systems has been demonstrated by exhibiting several well-known examples of competitive processes in biological, medical, physical and social sciences in a coherent way.     

Complexity and stability revisited

Since Robert May's work on random community matrices it has been known that stability tends to decrease with complexity. Recently, it was shown that this is not necessarily true in competitive ecosystems. We investigated the stability of random ecosystems and found that it can largely be predicted by simple matrix statistics such as the mean and the variance of the interaction coefficients. We use this to explain why stability can increase as well as decrease with complexity in ecological communities. We argue that the variance, and to a lesser extent the mean, of the interaction coefficients go a long way in explaining patterns in the stability of ecosystems.     

Complexity does not affect stability in feasible model communities

The complexity-stability relation is a central issue in ecology. In this paper, we show how the sampling method most often used to parameterize an ecological community, can affect the conclusions about whether or not complexity promotes stability and we suggest a sampling algorithm that overcomes the problem. We also illustrate the importance of treating feasibility separately from stability when constructing model communities. Using model Lotka-Volterra competition communities we found that probability of feasibility decreases with increasing interaction strength and number of species in the community. However, for feasible systems we found that local stability probability and resilience do not significantly differ between communities with few or many species, in contrast with earlier studies that, did not account for feasibility and concluded that species-poor communities had higher probability of being locally stable than species-rich communities.     

Food web complexity and stability across habitat connectivity gradients

The effects of habitat connectivity on food webs have been studied both empirically and theoretically, yet the question of whether empirical results support theoretical predictions for any food web metric other than species richness has received little attention. Our synthesis brings together theory and empirical evidence for how habitat connectivity affects both food web stability and complexity. Food web stability is often predicted to be greatest at intermediate levels of connectivity, representing a compromise between the stabilizing effects of dispersal via rescue effects and prey switching, and the destabilizing effects of dispersal via regional synchronization of population dynamics. Empirical studies of food web stability generally support both this pattern and underlying mechanisms. Food chain length has been predicted to have both increasing and unimodal relationships with connectivity as a result of predators being constrained by the patch occupancy of their prey. Although both patterns have been documented empirically, the underlying mechanisms may differ from those predicted by models. In terms of other measures of food web complexity, habitat connectivity has been empirically found to generally increase link density but either reduce or have no effect on connectance, whereas a unimodal relationship is expected. In general, there is growing concordance between empirical patterns and theoretical predictions for some effects of habitat connectivity on food webs, but many predictions remain to be tested over a full connectivity gradient, and empirical metrics of complexity are rarely modeled. Closing these gaps will allow a deeper understanding of how natural and anthropogenic changes in connectivity can affect real food webs.     

New criteria on global exponential stability of bam neural networks with distributed delays and reaction-diffusion terms

This paper presents new theoretical results on global exponential stability of bi-directional associative memory neural networks with distributed delays and reaction-diffusion terms based on the inequality technique, Lyapunov functional, and analysis technique. The results remove the usual assumption that the activation functions are of monotonous or differential character. Exponential converging velocity index is estimated, which depends on the delay kernel functions and system parameters. Finally, two numerical examples are given to show the validity and feasibility of our results.     

Effect of delay in a Lotka-Volterra type predator-prey model with a transmissible disease in the predator species

We consider a system of delay differential equations modeling the predator-prey ecoepidemic dynamics with a transmissible disease in the predator population. The time lag in the delay terms represents the predator gestation period. We analyze essential mathematical features of the proposed model such as local and global stability and in addition study the bifurcations arising in some selected situations. Threshold values for a few parameters determining the feasibility and stability conditions of some equilibria are discovered and similarly a threshold is identified for the disease to die out. The parameter thresholds under which the system admits a Hopf bifurcation are investigated both in the presence of zero and non-zero time lag. Numerical simulations support our theoretical analysis.     

Intra-generic competition among Nothofagus in New Zealand's primary indigenous forests

Competitive interactions between New Zealand's four Nothofagus or southern beech species were analysed using an extensive dataset describing the composition of natural forests, supplemented by environmental estimates describing both climate and landform. Using multiple regression models of progressively increasing complexity, the analysis first accounted for variation in tree abundance attributable to both environment and regional-scale distributional disjunctions of likely historic origin. Intra-generic competition, expressed as variation in tree abundance dependent on the presence or absence of each congener, was then assessed by adding (1) simple terms to assess the magnitude of gross changes in abundance, and (2) interaction terms to assess variation in abundance along the dominant temperature gradient given different competitive contexts. Results indicate the presence of substantial intra-generic interactions, with simple interaction terms giving marginal increases in explained deviance equal to that explained by initial regressions using environment alone. Addition of interaction terms brought about smaller improvements in model fit, but confirm that variation in abundance along the dominant annual temperature gradient is strongly influenced by the competitive context provided by the remaining congeners. Such results are consistent with current understanding of the niche concept, and underline the difficulty inherent in using current species limits to predict likely changes in species distributions consequent on global warming.     

Size and complexity among multicellular organisms

The diversity of specialized cell types ('complexity') is estimated for a wide range of multicellular organisms. Complexity increases with size, independently of phylogeny. This is interpreted in economic terms as the consequence of a greater degree of cooperative division of labour within larger entities. The rate of increase of complexity with size is less in the case of a cooperative division of labour (cell types within bodies) than in the analogous case of a competitive division of labour (species within communities). This is atttributed to the inutility of single specialized cells whose goods must be shared among all the many cells of a large organism. Major groups of organisms differ in complexity at given size: animals are more complex than plants, and phaeophytes are simpler than either.     

Conundrums of competitive ability in plants: what to measure?

A survey of recent literature indicates that competitive ability in plants has been measured, in most studies, only in terms of the relative intensity of size suppression experienced by competitors within one growing season. Far fewer studies have recorded relative success in terms of survival and even fewer studies have recorded fecundity under competition. Differences in size suppression are usually assumed to reflect differences in relative abilities to deny resources to competitors. However, most previous studies have failed to control or account for other sources of variation in the size suppression that plants experience under competition, i.e. variation between mixtures in the resource supply/demand ratio (approach to carrying capacity), or variation in the degree of niche overlap between competitors, or variation in the intensity of concurrent facilitative interactions between competitors. For future studies, much greater caution is required in recognizing these inherent limitations of traditional measures of competitive ability and, hence, guarding against unfounded conclusions or predictions about potential for competitive success that are based on these measures. There is also a significant challenge for future studies to adopt empirical approaches for minimizing these limitations. Some initial recommendations are considered here based on an emerging view of competitive ability measured in terms of traits associated with all three conventional components of Darwinian fitness, i.e. not just growth (plant size) but also survival and fecundity allocation (offspring production per unit plant size per unit time). According to this model, differences in competitive ability imply differences in the ability, despite intense competition (i.e. low resource supply/demand ratio), to recruit offspring into the next generation and thereby limit offspring recruitment by other plants. The important traits of competitive ability, therefore, are not only those that allow a plant to deny resources to competitors, suppress their sizes and hence, maximize the plant's own size, but also those traits that allow the plant to withstand suppression from competition enough to persist, both as an individual (through survival) and across generations (through descendants).     

Qualitative stability and ambiguity in model ecosystems

Qualitative analysis of stability in model ecosystems has previously been limited to determining whether a community matrix is sign stable or not with little analytical means to assess the impact of complexity on system stability. Systems are seen as either unconditionally or conditionally stable with little distinction and therefore much ambiguity in the likelihood of stability. First, we reexamine Hurwitz's principal theorem for stability and propose two "Hurwitz criteria" that address different aspects of instability: positive feedback and insufficient lower-level feedback. Second, we derive two qualitative metrics based on these criteria: weighted feedback (wF(n)) and weighted determinants (wDelta(n)). Third, we test the utility of these qualitative metrics through quantitative simulations in a random and evenly distributed parameter space in models of various sizes and complexities. Taken together they provide a practical means to assess the relative degree to which ambiguity has entered into calculations of stability as a result of system structure and complexity. From these metrics we identify two classes of models that may have significant relevance to system research and management. This work helps to resolve some of the impasse between theoretical and empirical discussions on the complexity and stability of natural communities.     

More plant biomass results in more offspring production in annuals,or does it?

Competitive ability in plants has been previously measured almost exclusively in terms of traits related to growth (biomass) or plant size. In this study, however, we used a multi‐species competition experiment with six annuals to measure relative competitive ability in terms of reproductive output, i.e. the number of offspring produced for the next generation. Under greenhouse conditions, plants of each species were started in pots from germinating seeds and were grown singly (free of competition) and at high density in both monocultures and in mixtures with all study species. Several traits traditionally regarded as determinants of competitive ability in plants were recorded for each species grown singly, including: seed mass, germination time, early growth rate and potential plant size (biomass and height). Under competition, several traits were recorded as indicators of relative performance in both monocultures and mixtures, including: biomass of survivors, total number of survivors, number of reproductive survivors, and reproductive output (total seed production) of the survivors. As expected, species that grew to a larger biomass in isolation had higher seed production in isolation. However, none of the traditional plant growth/size‐related traits, measured either in isolation or under competition, could predict between species variation in reproductive output under competition in either monocultures or mixtures. In mixtures, 97% of this variation in reproductive output could be explained by between‐species variation in the number of reproductive survivors. The results indicate that traits measured on plants grown singly may be poor predictors of reproductive output under competition, and that species’ rank order of competitive ability in terms of the biomass of survivors may bear no relationship to their rank order in terms of the number of offspring produced by these survivors. This has important implications for the interpretation of mechanisms of species coexistence and community assembly within vegetation.     

Stability of large systems

We use the May-Wigner Stability Theorem (Geman (1984) preprint, Brown University; Hastings (1984) preprint, Hofstra University), to study the Lyapunov and structural stability of "real" large systems. Here are our new main results. For large systems which satisfy certain natural scaling relations (Harrison, Am. Natur., 113 (1979) 659; May (1979) Blackwell Scientific, Oxford), Lyapunov stability tends to increase with increasing complexity. However, at least one aspect of structural stability decreases: both competitive and cooperative effects can rapidly destabilize such a system. Finally, we observe that random matrices which satisfy the hypotheses and stability criterion of the May-Wigner theorem are asymptotically of the form 'rotation followed by multiplication by lambda,lambda less than 1'. This allows an easy analysis of the effects of noise in these systems. We conclude by briefly discussing applications to analysis of stability of systems such as the world economy, power networks, and the immune system.     

Nested species interactions promote feasibility over stability during the assembly of a pollinator community

The foundational concepts behind the persistence of ecological communities have been based on two ecological properties: dynamical stability and feasibility. The former is typically regarded as the capacity of a community to return to an original equilibrium state after a perturbation in species abundances and is usually linked to the strength of interspecific interactions. The latter is the capacity to sustain positive abundances on all its constituent species and is linked to both interspecific interactions and species demographic characteristics. Over the last 40 years, theoretical research in ecology has emphasized the search for conditions leading to the dynamical stability of ecological communities, while the conditions leading to feasibility have been overlooked. However, thus far, we have no evidence of whether species interactions are more conditioned by the community''s need to be stable or feasible. Here, we introduce novel quantitative methods and use empirical data to investigate the consequences of species interactions on the dynamical stability and feasibility of mutualistic communities. First, we demonstrate that the more nested the species interactions in a community are, the lower the mutualistic strength that the community can tolerate without losing dynamical stability. Second, we show that high feasibility in a community can be reached either with high mutualistic strength or with highly nested species interactions. Third, we find that during the assembly process of a seasonal pollinator community located at The Zackenberg Research Station (northeastern Greenland), a high feasibility is reached through the nested species interactions established between newcomer and resident species. Our findings imply that nested mutualistic communities promote feasibility over stability, which may suggest that the former can be key for community persistence.