Mutualistic networks emerging from adaptive niche-based interactions.

Mutualistic networks are vital ecological and social systems shaped by adaptation and evolution. They involve bipartite cooperation via the exchange of goods or services between actors of different types. Empirical observations of mutualistic networks across genres and geographic conditions reveal correlated nested and modular patterns. Yet, the underlying mechanism for the network assembly remains unclear. We propose a niche-based adaptive mechanism where both nestedness and modularity emerge simultaneously as complementary facets of an optimal niche structure. Key dynamical properties are revealed at different timescales. Foremost, mutualism can either enhance or reduce the network stability, depending on competition intensity. Moreover, structural adaptations are asymmetric, exhibiting strong hysteresis in response to environmental change. Finally, at the evolutionary timescale we show that the adaptive mechanism plays a crucial role in preserving the distinctive patterns of mutualism under species invasions and extinctions.

Phase transitions in cooperative coinfections: Simulation results for networks and lattices.

We study the spreading of two mutually cooperative diseases on different network topologies, and with two microscopic realizations, both of which are stochastic versions of a susceptible-infected-removed type model studied by us recently in mean field approximation. There it had been found that cooperativity can lead to first order transitions from spreading to extinction. However, due to the rapid mixing implied by the mean field assumption, first order transitions required nonzero initial densities of sick individuals. For the stochastic model studied here the results depend strongly on the underlying network. First order transitions are found when there are few short but many long loops: (i) No first order transitions exist on trees and on 2-d lattices with local contacts. (ii) They do exist on Erdos-Rényi (ER) networks, on d-dimensional lattices with d≥4, and on 2-d lattices with sufficiently long-ranged contacts. (iii) On 3-d lattices with local contacts the results depend on the microscopic details of the implementation. (iv) While single infected seeds can always lead to infinite epidemics on regular lattices, on ER networks one sometimes needs finite initial densities of infected nodes. (v) In all cases the first order transitions are actually "hybrid"; i.e., they display also power law scaling usually associated with second order transitions. On regular lattices, our model can also be interpreted as the growth of an interface due to cooperative attachment of two species of particles. Critically pinned interfaces in this model seem to be in different universality classes than standard critically pinned interfaces in models with forbidden overhangs. Finally, the detailed results mentioned above hold only when both diseases propagate along the same network of links. If they use different links, results can be rather different in detail, but are similar overall.

Neuronal synapse as a memristor: modeling pair- and triplet-based STDP rule.

We propose a new memristive model for the neuronal synapse based on the spike-timing-dependent plasticity (STDP) protocol, considering both long-term and short-term plasticity in the synapse. Higher-order behavior is modeled by a memristor with adaptive thresholds, which realizes the well-established suppression principle of Froemke. We assume a mechanism of variable thresholds adapting to synaptic potentiation (LTP) and depression (LTD), which reproduces the refractory time in the weight modification. The corresponding dynamical process is governed by a set of ordinary differential equations. Interestingly, the Froemke's model and our memristive model, based on two completely different mechanisms, are found to be quantitatively equivalent for the 'pre-post-pre' case and 'post-pre-post' case. A relation of the adaptive thresholds to short-term plasticity is addressed.