SummaryMicrobial communities are increasingly utilized in biotechnology. Efficiency and productivity in many of these applications depends on the presence of cooperative interactions between members of the community. Two key processes underlying these interactions are the production of public goods and metabolic cross‐feeding, which can be understood in the general framework of ecological and evolutionary (eco‐evo) dynamics. In this review, we illustrate the relevance of cooperative interactions in microbial biotechnological processes, discuss their mechanistic origins and analyse their evolutionary resilience. Cooperative behaviours can be damaged by the emergence of ‘cheating’ cells that benefit from the cooperative interactions but do not contribute to them. Despite this, cooperative interactions can be stabilized by spatial segregation, by the presence of feedbacks between the evolutionary dynamics and the ecology of the community, by the role of regulatory systems coupled to the environmental conditions and by the action of horizontal gene transfer. Cooperative interactions enrich microbial communities with a higher degree of robustness against environmental stress and can facilitate the evolution of more complex traits. Therefore, the evolutionary resilience of microbial communities and their ability to constraint detrimental mutants should be considered to design robust biotechnological applications.

We consider here spiking neural P systems with a non-synchronized (i.e., asynchronous) use of rules: in any step, a neuron can apply or not apply its rules which are enabled by the number of spikes it contains (further spikes can come, thus changing the rules enabled in the next step). Because the time between two firings of the output neuron is now irrelevant, the result of a computation is the number of spikes sent out by the system, not the distance between certain spikes leaving the system. The additional non-determinism introduced in the functioning of the system by the nonsynchronization is proved not to decrease the computing power in the case of using extended rules (several spikes can be produced by a rule). That is, we obtain again the equivalence with Turing machines (interpreted as generators of sets of (vectors of) numbers). However, this problem remains open for the case of restricted spiking neural P systems, whose rules can only produce one spike. On the other hand we prove that asynchronous systems, with extended rules, and where each neuron is either bounded or unbounded, are not computationally complete. For these systems, the configuration reachability, membership (in terms of generated vectors), emptiness, infiniteness, and disjointness problems are shown to be decidable. However, containment and equivalence are undecidable. In short, an SN P system consists of a set of neurons placed in the nodes of a directed graph and sending signals (spikes, denoted in what follows by the symbol a) along the arcs of the graph (they are called synapses). Thus, the architecture is that of a tissue-like P system, with only one kind of object present in the cells (the reader is referred to [18] for an introduction to membrane computing and to [23] for the up-to-date information about this research area). The objects evolve by means of standard spiking rules, which are of the form E/a c → a; d, where E is a regular expression over {a} and c, d are natural numbers, c ≥ 1, d ≥ 0. The meaning is that a neuron containing k spikes such that a k ∈ L(E), k ≥ c, can consume c spikes and produce one spike, after a delay of d steps. This spike is sent to all neurons connected by an outgoing synapse from the neuron where the rule was applied. There also are forgetting rules, of the form a s → λ, with the meaning that s ≥ 1 spikes are removed, provided that the neuron contains exactly s spikes. Extended rules were considered in [4], [17]: these rules are of the form E/a c → a p ; d, with the meaning that when using the rule, c spikes are consumed and p spikes are produced. Because p can be 0 or greater than 0, we obtain a generalization of both standard spiking and forgetting rules. In this paper we consider extended spiking rules with restrictions on the type of the regular expressions used. In particular, we consider two types of rules. The first type are called bounded rules and are of the form a i /a c → a p ; d, where 1 ≤ c ≤ i, p ≥ 0, and d ≥ 0. We also consider unbounded rules of the form a i (a j) * /a c → a p ; d...

Social, biological and economic networks grow and decline with occasional fragmentation and re-formation, often explained in terms of external perturbations. We show that these phenomena can be a direct consequence of simple imitation and internal conflicts between ‘cooperators’ and ‘defectors’. We employ a game-theoretic model of dynamic network formation where successful individuals are more likely to be imitated by newcomers who adopt their strategies and copy their social network. We find that, despite using the same mechanism, cooperators promote well-connected highly prosperous networks and defectors cause the network to fragment and lose its prosperity; defectors are unable to maintain the highly connected networks they invade. Once the network is fragmented it can be reconstructed by a new invasion of cooperators, leading to the cycle of formation and fragmentation seen, for example, in bacterial communities and socio-economic networks. In this endless struggle between cooperators and defectors we observe that cooperation leads to prosperity, but prosperity is associated with instability. Cooperation is prosperous when the network has frequent formation and fragmentation.