The Concept of Additivity of Drug Combinations in the Case of Quantal Response

The concept of additivity of drug combinations is widely accepted in pharmacology and toxicology. Up to now, no general statistical methods to test that property are available. The present paper gives a mathematical formulation of additivity, a method to fit dose response surfaces under additivity assumption and a statistical test.     

Game Theory of Mind

This paper introduces a model of ‘theory of mind’, namely, how we represent the intentions and goals of others to optimise our mutual interactions. We draw on ideas from optimum control and game theory to provide a ‘game theory of mind’. First, we consider the representations of goals in terms of value functions that are prescribed by utility or rewards. Critically, the joint value functions and ensuing behaviour are optimised recursively, under the assumption that I represent your value function, your representation of mine, your representation of my representation of yours, and so on ad infinitum. However, if we assume that the degree of recursion is bounded, then players need to estimate the opponent's degree of recursion (i.e., sophistication) to respond optimally. This induces a problem of inferring the opponent's sophistication, given behavioural exchanges. We show it is possible to deduce whether players make inferences about each other and quantify their sophistication on the basis of choices in sequential games. This rests on comparing generative models of choices with, and without, inference. Model comparison is demonstrated using simulated and real data from a ‘stag-hunt’. Finally, we note that exactly the same sophisticated behaviour can be achieved by optimising the utility function itself (through prosocial utility), producing unsophisticated but apparently altruistic agents. This may be relevant ethologically in hierarchal game theory and coevolution.     

Local Replicator Dynamics: A Simple Link Between Deterministic and Stochastic Models of Evolutionary Game Theory

Classical replicator dynamics assumes that individuals play their games and adopt new strategies on a global level: Each player interacts with a representative sample of the population and if a strategy yields a payoff above the average, then it is expected to spread. In this article, we connect evolutionary models for infinite and finite populations: While the population itself is infinite, interactions and reproduction occurs in random groups of size N. Surprisingly, the resulting dynamics simplifies to the traditional replicator system with a slightly modified payoff matrix. The qualitative results, however, mirror the findings for finite populations, in which strategies are selected according to a probabilistic Moran process. In particular, we derive a one-third law that holds for any population size. In this way, we show that the deterministic replicator equation in an infinite population can be used to study the Moran process in a finite population and vice versa. We apply the results to three examples to shed light on the evolution of cooperation in the iterated prisoner’s dilemma, on risk aversion in coordination games and on the maintenance of dominated strategies.     

Evolutionary Game Dynamics in Populations with Heterogenous Structures

Evolutionary graph theory is a well established framework for modelling the evolution of social behaviours in structured populations. An emerging consensus in this field is that graphs that exhibit heterogeneity in the number of connections between individuals are more conducive to the spread of cooperative behaviours. In this article we show that such a conclusion largely depends on the individual-level interactions that take place. In particular, averaging payoffs garnered through game interactions rather than accumulating the payoffs can altogether remove the cooperative advantage of heterogeneous graphs while such a difference does not affect the outcome on homogeneous structures. In addition, the rate at which game interactions occur can alter the evolutionary outcome. Less interactions allow heterogeneous graphs to support more cooperation than homogeneous graphs, while higher rates of interactions make homogeneous and heterogeneous graphs virtually indistinguishable in their ability to support cooperation. Most importantly, we show that common measures of evolutionary advantage used in homogeneous populations, such as a comparison of the fixation probability of a rare mutant to that of the resident type, are no longer valid in heterogeneous populations. Heterogeneity causes a bias in where mutations occur in the population which affects the mutant''s fixation probability. We derive the appropriate measures for heterogeneous populations that account for this bias.     

The Use of the Gompertz Function in the Treatment of – Quantal Response Data

In this paper it is shown that the Gompertz function can be used in the treatment of quantal response data. It is argued that the fitting of this function is particularly indicated when the ordinate of the inflection point is smaller than 0.5. An example where the Gompertz function leads to the best fitting is provided.     

A Guide to Bivariate Ideas of Quantal Response Analysis,as Applied in Biometrics and Econometrics

A review is provided of the several bivariate generalisations of quantal response analysis that have appeared in the biometric and econometric literatures. There are three main types: (i) where a binary outcome is the result of two stimulants, and thus the bivariate distribution of the thresholds for response is relevant; (ii) where three or more alternative outcomes may arise from a single stimulant; and (iii) where the response itself is bivariate (i.e., two types of response may simultaneously be observed).     

Stochastic Fluctuations Through Intrinsic Noise in Evolutionary Game Dynamics

A one-step (birth–death) process is used to investigate stochastic noise in an elementary two-phenotype evolutionary game model based on a payoff matrix. In this model, we assume that the population size is finite but not fixed and that all individuals have, in addition to the frequency-dependent fitness given by the evolutionary game, the same background fitness that decreases linearly in the total population size. Although this assumption guarantees population extinction is a globally attracting absorbing barrier of the Markov process, sample trajectories do not illustrate this result even for relatively small carrying capacities. Instead, the observed persistent transient behavior can be analyzed using the steady-state statistics (i.e., mean and variance) of a stochastic model for intrinsic noise that assumes the population does not go extinct. It is shown that there is good agreement between the theory of these statistics and the simulation results. Furthermore, the ESS of the evolutionary game can be used to predict the mean steady state.     

Continuous Probabilistic Analysis to Evolutionary Game Dynamics in Finite Populations

Evolutionary game dynamics of two strategies in finite population is studied by continuous probabilistic approach. Besides frequency dependent selection, mutation was also included in this study. The equilibrium probability density functions of abundance, expected time to extinction or fixation were derived and their numerical solutions are calculated as illustrations. Meanwhile, individual-based computer simulations are also done. A comparison reveals the consistency between theoretical analysis and simulations.     

Game Dynamics with Learning and Evolution of Universal Grammar

We investigate a model of language evolution, based on population game dynamics with learning. First, we examine the case of two genetic variants of universal grammar (UG), the heart of the human language faculty, assuming each admits two possible grammars. The dynamics are driven by a communication game. We prove using dynamical systems techniques that if the payoff matrix obeys certain constraints, then the two UGs are stable against invasion by each other, that is, they are evolutionarily stable. Then, we prove a similar theorem for an arbitrary number of disjoint UGs. In both theorems, the constraints are independent of the learning process. Intuitively, if a mutation in UG results in grammars that are incompatible with the established languages, then the mutation will die out because mutants will be unable to communicate and therefore unable to realize any potential benefit of the mutation. An example for which these theorems do not apply shows that compatible mutations may or may not be able to invade, depending on the population's history and the learning process. These results suggest that the genetic history of language is constrained by the need for compatibility and that mutations in the language faculty may have died out or taken over due more to historical accident than to any straightforward notion of relative fitness. MSC 1991: 37N25 · 92D15 · 91F20     

Strategy Selection in Evolutionary Game Dynamics on Group Interaction Networks

Evolutionary game theory provides an appropriate tool for investigating the competition and diffusion of behavioral traits in biological or social populations. A core challenge in evolutionary game theory is the strategy selection problem: Given two strategies, which one is favored by the population? Recent studies suggest that the answer depends not only on the payoff functions of strategies but also on the interaction structure of the population. Group interactions are one of the fundamental interactive modes within populations. This work aims to investigate the strategy selection problem in evolutionary game dynamics on group interaction networks. In detail, the strategy selection conditions are obtained for some typical networks with group interactions. Furthermore, the obtained conditions are applied to investigate selection between cooperation and defection in populations. The conditions for evolution of cooperation are derived for both the public goods game and volunteer’s dilemma game. Numerical experiments validate the above analytical results.     

Quantal release of ATP in mouse cortex

Transient currents occur at rest in cortical neurones that reflect the quantal release of transmitters such as glutamate and gamma-aminobutyric acid (GABA). We found a bimodal amplitude distribution for spontaneously occurring inward currents recorded from mouse pyramidal neurones in situ, in acutely isolated brain slices superfused with picrotoxin. Larger events were blocked by glutamate receptor (AMPA, kainate) antagonists; smaller events were partially inhibited by P2X receptor antagonists suramin and PPADS. The decay of the larger events was selectively prolonged by cyclothiazide. Stimulation of single intracortical axons elicited quantal glutamate-mediated currents and also quantal currents with amplitudes corresponding to the smaller spontaneous inward currents. It is likely that the lower amplitude spontaneous events reflect packaged ATP release. This occurs with a lower probability than that of glutamate, and evokes unitary currents about half the amplitude of those mediated through AMPA receptors. Furthermore, the packets of ATP appear to be released from vesicle in a subset of glutamate-containing terminals.     

Quantal analysis of synaptic processes in the neocortex

The application of fluctuation analysis to studies of synaptic function in the neocortex is discussed. Analysis of failures of transmission has been valuable in indicating whether a presynaptic or a postsynaptic site is responsible for a change in synaptic efficacy. When combined with detailed ultrastructural verification of all synapses involved in an individual cell to cell connection, a reasonable estimate of quantal size and release probability under conditions of low frequency activity can be obtained. However, both the number of available release sites in functional terms and the probability that an action potential (AP) will release transmitter from any given site can vary from AP to AP at higher frequencies. A variety of presynaptic mechanisms that modulate release are now apparent. For example, one mechanism dominates release patterns at one class of connection which is insensitive to absolute firing frequency, but responsive to changes in frequency. At another class of connection, a different mechanism dominates, resulting in high sensitivity to frequency.     

Dynamin-2 Regulates Fusion Pore Expansion and Quantal Release through a Mechanism that Involves Actin Dynamics in Neuroendocrine Chromaffin Cells

Over the past years, dynamin has been implicated in tuning the amount and nature of transmitter released during exocytosis. However, the mechanism involved remains poorly understood. Here, using bovine adrenal chromaffin cells, we investigated whether this mechanism rely on dynamin’s ability to remodel actin cytoskeleton. According to this idea, inhibition of dynamin GTPase activity suppressed the calcium-dependent de novo cortical actin and altered the cortical actin network. Similarly, expression of a small interfering RNA directed against dynamin-2, an isoform highly expressed in chromaffin cells, changed the cortical actin network pattern. Disruption of dynamin-2 function, as well as the pharmacological inhibition of actin polymerization with cytochalasine-D, slowed down fusion pore expansion and increased the quantal size of individual exocytotic events. The effects of cytochalasine-D and dynamin-2 disruption were not additive indicating that dynamin-2 and F-actin regulate the late steps of exocytosis by a common mechanism. Together our data support a model in which dynamin-2 directs actin polymerization at the exocytosis site where both, in concert, adjust the hormone quantal release to efficiently respond to physiological demands.     

Dynamics of the Microbiota in Response to Host Infection

Longitudinal studies of the microbiota are important for discovering changes in microbial communities that affect the host. The complexity of these ecosystems requires rigorous integrated experimental and computational methods to identify temporal signatures that promote physiologic or pathophysiologic responses in vivo. Employing a murine model of infectious colitis with the pathogen Citrobacter rodentium, we generated a 2-month time-series of 16S rDNA gene profiles, and quantitatively cultured commensals, from multiple intestinal sites in infected and uninfected mice. We developed a computational framework to discover time-varying signatures for individual taxa, and to automatically group signatures to identify microbial sub-communities within the larger gut ecosystem that demonstrate common behaviors. Application of this model to the 16S rDNA dataset revealed dynamic alterations in the microbiota at multiple levels of resolution, from effects on systems-level metrics to changes across anatomic sites for individual taxa and species. These analyses revealed unique, time-dependent microbial signatures associated with host responses at different stages of colitis. Signatures included a Mucispirillum OTU associated with early disruption of the colonic surface mucus layer, prior to the onset of symptomatic colitis, and members of the Clostridiales and Lactobacillales that increased with successful resolution of inflammation, after clearance of the pathogen. Quantitative culture data validated findings for predominant species, further refining and strengthening model predictions. These findings provide new insights into the complex behaviors found within host ecosystems, and define several time-dependent microbial signatures that may be leveraged in studies of other infectious or inflammatory conditions.