Over the last decade, several studies have shown the importance of trait diversity in natural populations. Theoretical ecological studies are beginning to incorporate trait variations in models but they continue to be largely ignored in the context of ecosystems that exhibit alternative stable states. Here, we begin with a mean-field model of bistable savanna-woodland system and then introduce trait variation in functional and demographic traits of savanna trees and saplings in the model. Our study reveals that higher trait variation reduces the extent of bistability in the system, such that the woodland state is favoured; that is, woodland occurs over a wider range of driver values compared to the grassland state. We find that the shift from one state to another can become less or more drastic, depending on the trait which exhibits variation. Interestingly, we find that even if the overall tree and grass cover remain insensitive to different initial conditions, the steady-state population trait distribution exhibits sensitivity to initial conditions. Our model findings suggest that in dryland ecosystems, and potentially in a broader class of bistable ecosystems, historical contingency has a stronger impact at the population level rather than at the ecosystem level when trait diversity is considered.

In this article, we model cultural knowledge as a capital in which individuals invest at a cost. To this end, following other models of cultural evolution, we explicitly consider the investments made by individuals in culture as life history decisions. Our aim is to understand what then determines the dynamics of cultural accumulation. We show that culture can accumulate provided it improves the efficiency of people's lives in such a way as to increase their productivity or, said differently, provided the knowledge created by previous generations improves the ability of subsequent generations to invest in new knowledge. Our central message is that this positive feedback allowing cultural accumulation can occur for many different reasons. It can occur if cultural knowledge increases people's productivity, including in domains that have no connection with knowledge, because it frees up time that people can then spend learning and/or innovating. We also show that it can occur if cultural knowledge, and thus the higher level of resources that results from increased productivity, leads individuals to modify their life history decisions through phenotypic plasticity. Finally, we show that it can occur if technical knowledge reduces the effective cost of its own acquisition via division of labour. These results suggest that culture should not be defined only as a set of knowledge and skills but, more generally, as all the capital that has been produced by previous generations and that continues to affect current generations.

Mitochondria are one of the most important organelles determining Ca2+regulatory pathway in the cell. Recent experiments suggested the existence of cytosolicmicrodomains with locally elevated calcium concentration (CMDs) in the nearest vicinity ofthe outer mitochondrial membrane (OMM). These intermediate physical connections betweenendoplasmic reticulum (ER) and mitochodria are called MAM (mitochondria-associated ERmembrane) complexes.

The aim of this paper is to take into account the direct calcium flowfrom ER to mitochondria implied by the existence of MAMs and perform detailed numericalanalysis of the influence of this flow on the type and shape of calcium oscillations.Depending on the permeability of MAMs interface and ER channels, different patterns ofoscillations appear (simple, bursting and chaotic). For some parameters the oscillatorypattern disappear and the system tends to a steady state with extremely high calcium levelin mitochondria, which can be interpreted as a crucial point at the beginning of anapoptotic pathway.

Unveiling the mechanisms through which the somitogenesis regulatory network exertsspatiotemporal control of the somitic patterning has required a combination ofexperimental and mathematical modeling strategies. Significant progress has been made forthe zebrafish clockwork. However, due to its complexity, the clockwork of the amniotesegmentation regulatory network has not been fully elucidated. Here, we address thequestion of how oscillations are arrested in the amniote segmentation clock. We do this byconstructing a minimal model of the regulatory network, which privileges architecturalinformation over molecular details. With a suitable choice of parameters, our model isable to reproduce the oscillatory behavior of the Wnt, Notch and FGF signaling pathways inpresomitic mesoderm (PSM) cells. By introducing positional information via a single Wnt3agradient, we show that oscillations are arrested following an infinite-period bifurcation.Notably: the oscillations increase their amplitude as cells approach the anterior PSM andremain in an upregulated state when arrested; the transition from the oscillatory regimeto the upregulated state exhibits hysteresis; and opposing Fgf8 and RA gradients along thePSM naturally arise in our simulations. We hypothesize that the interaction between alimit cycle (originated by the Notch delayed-negative feedback loop) and a bistable switch(originated by the Wnt-Notch positive cross-regulation) is responsible for the observedsegmentation patterning. Our results agree with previously unexplained experimentalobservations and suggest a simple plausible mechanism for spatiotemporal control ofsomitogenesis in amniotes.

Computational models for human decision making are typically based on the properties of bistable dynamical systems where each attractor represents a different decision. A limitation of these models is that they do not readily account for the fragilities of human decision making, such as “choking under pressure”, indecisiveness and the role of past experiences on current decision making. Here we examine the dynamics of a model of two interacting neural populations with mutual time–delayed inhibition. When the input to each population is sufficiently high, there is bistability and the dynamics is determined by the relationship of the initial function to the separatrix (the stable manifold of a saddle point) that separates the basins of attraction of two co–existing attractors. The consequences for decision making include long periods of indecisiveness in which trajectories are confined in the neighborhood of the separatrix and wrong decision making, particularly when the effects of past history and irrelevant information (“noise”) are included. Since the effects of delay, past history and noise on bistable dynamical systems are generic, we anticipate that similar phenomena will arise in the setting of other physical, chemical and neural time–delayed systems which exhibit bistability.

We study the role of interactions between habitats in rotifer dynamics. For this purpose we use a modified version of the Consensus model. The Consensus model has been shown to be realistic enough to reproduce distinguishing features of the rotifer species dynamics. Being uncoupled, intrinsically bistable rotifer populations, which inhabit the regions under different environmental conditions, do not impact each other. We show that migration of the rotifers between the habitats leads to the transformation of bistability to oscillatory dynamics. The coupling-induced oscillations of the rotifer biomass are shown to be either regular or irregular depending on the value of the model parameters, which describe environmental conditions and the biomass exchange between the habitats. We show that the irregular oscillations are characterized by positive values of the Lyapunov exponent, which means that they are chaotic.