7,107 research outputs found
Every which way? On predicting tumor evolution using cancer progression models
Successful prediction of the likely paths of tumor progression is valuable for diagnostic,
prognostic, and treatment purposes. Cancer progression models (CPMs) use cross-sectional samples to identify restrictions in the order of accumulation of driver mutations and
thus CPMs encode the paths of tumor progression. Here we analyze the performance of
four CPMs to examine whether they can be used to predict the true distribution of paths of
tumor progression and to estimate evolutionary unpredictability. Employing simulations we
show that if fitness landscapes are single peaked (have a single fitness maximum) there is
good agreement between true and predicted distributions of paths of tumor progression
when sample sizes are large, but performance is poor with the currently common much
smaller sample sizes. Under multi-peaked fitness landscapes (i.e., those with multiple fitness maxima), performance is poor and improves only slightly with sample size. In all
cases, detection regime (when tumors are sampled) is a key determinant of performance.
Estimates of evolutionary unpredictability from the best performing CPM, among the four
examined, tend to overestimate the true unpredictability and the bias is affected by detection
regime; CPMs could be useful for estimating upper bounds to the true evolutionary unpredictability. Analysis of twenty-two cancer data sets shows low evolutionary unpredictability
for several of the data sets. But most of the predictions of paths of tumor progression are
very unreliable, and unreliability increases with the number of features analyzed. Our results
indicate that CPMs could be valuable tools for predicting cancer progression but that, currently, obtaining useful predictions of paths of tumor progression from CPMs is dubious, and
emphasize the need for methodological work that can account for the probably multi-peaked
fitness landscapes in cancerWork partially supported by BFU2015-
67302-R (MINECO/FEDER, EU) to RDU. CV
supported by PEJD-2016-BMD-2116 from
Comunidad de Madrid to RD
A Model of Evolutionay Drift
Drift appears to be crucial to study the stability properties of Nash equilibria in a component specifying different out-of-equilibrium behaviour. We propose a new microeconomic model of drift to be added to the learning process by which agents find their way to equilibrium. A key feature of the model is the sensitivity of the noisy agent to the proportion of agents in his player population playing the same strategy as his current one. We show that, 1. Perturbed Payoff-Positive and PayoffMonotone selection dynamics are capable of stabilizing pure non strict Nash equilibria in either singleton or nonsingleton component of equilibria; 2. The model is relevant to understand the role of drift in the behaviour observed in the laboratory for the Ultimatum Game and for predicting outcomes that can be experimentally tested. Hence, the selection dynamics model perturbed with the proposed drift may be seen as well as a new learning tool to understand observed behaviour.drift, Nash equilibrium, similarity relations, replicator dynam, learning
Doubts and equilibria
In real life strategic interactions decision-makers are likely to entertain doubts about the
degree of optimality of their play. To capture this feature of real choice-making, we present here
a model based on the doubts felt by an agent about how well is playing a game. The doubts are
coupled with (and mutually reinforced by) imperfect discrimination capacity, which we model
here by means of similarity relations. We assume that each agent builds procedural preferences
defined on the space of expected payoffsstrategy frequencies attached to his current strategy.
These preferences, together with an adaptive learning process lead to doubt-based selection
dynamic systems. We introduce the concepts of Mixed Strategy Doubt Equilibria, Mixed
Strategy Doubt-Full Equilibria and Mixed Strategy Doubtless Equilibria and show the
theoretical and the empirical relevance of these concept
A Behavioral Foundation for Models of Evolutionary Drift
Binmore and Samuelson (1999) have shown that perturbations (drift) are crucial to study the stability properties of Nash equilibria. We contribute to this literature by providing a behavioural foundation for models of evolutionary drift. In particular, this article introduces a microeconomic model of drift based on the similarity theory developed by Tversky (1977), Kahneman and Tversky (1979) and Rubinstein (1988),(1998). An innovation with respect to those works is that we deal with similarity relations that are derived from the perception that each agent has about how well he is playing the game. In addition, the similarity relations are adapted to a dynamic setting. We obtain different models of drift depending on how we model the agent´s assessment of his behaviour in the game. The examples of the ultimatum game and the chain-store game are used to show the conditions for each model to stabilize elements in the component of Nash equilibria that are not subgame- perfect. It is also shown how some models approximate the laboratory data about those games while others match the data.similarity relations, drift, Nash equilibrium, selection dynamics, learning
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