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PubMed2003

Application of quantitative models from population biology and evolutionary game theory to tumor therapeutic strategies.

Quantitative models from population biology and evolutionary game theory frame the tumor-host interface as a dynamical microenvironment of competing tumor and normal populations. Through this approach, critical parameters that control the outcome of this competition are identified and the conditions necessary for formation of an invasive cancer are defined. Perturbations in these key parameters that destabilize the cancer solution of the state equations and produce tumor regression can be predicted. The mathematical models demonstrate significant theoretical limitations in therapies based solely on cytotoxic drugs. Because these approaches do not alter critical parameters controlling system dynamics, the tumor population growth term will remain positive as long as any individual cells are present so that the tumor will invariably recur unless all proliferative cells are killed. The models demonstrate that such total effectiveness is rendered unlikely by the genotypic heterogeneity of tumor populations (and, therefore, the variability of their response to such drugs) and the ability of tumor cells to adapt to these proliferation constraints by evolving resistant phenotypes. The mathematical models support therapeutic strategies that simultaneously alter several of the key parameters in the state equations. Furthermore, the models demonstrate that administration of cytotoxic therapies will, by reducing the tumor population density, create system dynamics more conducive to perturbations by biological modifiers.

Biological Evolution↗
PubMed2006

Application of game theory for a groundwater conflict in Mexico.

Exploitation of scarce water resources, particularly in areas of high demand, inevitably produces conflict among disparate stakeholders, each of whom may have their own set of priorities. In order to arrive at a socially acceptable compromise, the decision-makers should seek an optimal trade-off between conflicting objectives that reflect the priorities of the various stakeholders. In this study, game theory was applied to a multiobjective conflict problem for the Alto Rio Lerma Irrigation District, located in the state of Guanajuato in Mexico, where economic benefits from agricultural production should be balanced with associated negative environmental impacts. The short period of rainfall in this area, combined with high groundwater withdrawals from irrigation wells, has produced severe aquifer overdraft. In addition, current agricultural practices of applying high loads of fertilizers and pesticides have contaminated regions of the aquifer. The net economic benefit to this agricultural region in the short-term lies with increasing crop yields, which requires large pumping extractions for irrigation as well as high chemical loading. In the longer term, this can produce economic loss due to higher pumping costs (i.e., higher lift requirements), or even loss of the aquifer as a viable source of water. Negative environmental impacts include continued diminishment of groundwater quality, and declining groundwater levels in the basin, which can damage surface water systems that support environmental habitats. The two primary stakeholders or players, the farmers in the irrigation district and the community at large, must find an optimal balance between positive economic benefits and negative environmental impacts. In this paper, game theory was applied to find the optimal solution between the two conflicting objectives among 12 alternative groundwater extraction scenarios. Different attributes were used to quantify the benefits and costs of the two objectives, and, following generation of the Pareto frontier or trade-off curve, four conflict resolution methods were then applied.

Agriculture↗
PubMed1987

Rectangular game theory and metabolic response to random changes in environmental states.

Rectangular game theory is applied to the response of organisms to random environmental changes: A hypothetical example of the response of a facultative algae to random changes in illumination is analyzed. Two strategies are discussed: Bayes' risk and maximin. It is shown how to detect such strategies in populations. The analysis does not require assumptions about the form of the relationship between metabolic activities and selective advantage, but assumptions about evolutionary optimization are required. The maximin strategy is shown to be related to metabolic homeostasis.

Animals↗
PubMed1997

Discrete time spatial models arising in genetics, evolutionary game theory, and branching processes.

A saddle point method is used to obtain the speed of first spread of new genotypes in genetic models and of new strategies in game theoretic models. It is also used to obtain the speed of the forward tail of the distribution of farthest spread for branching process models. The technique is applicable to a wide range of models. They include multiple allele and sex-linked models in genetics, multistrategy and bimatrix evolutionary games, and multitype and demographic branching processes. The speed of propagation has been obtained for genetics models (in simple cases only) by Weinberger and Lui, using exact analytical methods. The exact results were obtained only for two-allele, single-locus genetic models. The saddle point method agrees in these very simple cases with the results obtained by using the exact analytic methods. Of course, it can also be used in much more general situations far less tractable to exact analysis. The connection between genetic and game theoretic models is also briefly considered, as is the extent to which the exact analytic methods yield results for simple models in game theory.

Alleles↗
PubMed2004

Resistance is useless?--Extensions to the game theory of kleptoparasitism.

We extend the game theoretic model of kleptoparasitism introduced by Broom and Ruxton (1998, Behav. Ecol. 9, 397-403) in two ways: we allow for asymmetric contests, where the probability alpha of the challenger winning can take any value from 0 to 1; and we allow the handler to choose not to resist the challenge, but to immediately concede and relinquish its food to the challenger. We find, in general, three possible evolutionarily stable strategies--challenge-and-resist (Hawk), challenge-but-do-not-resist (Marauder) and do-not-challenge-but-resist (Retaliator). When alpha = 1/2, we find that Hawk and Marauder are the only ESS's, in contrast to the result of the original model; we also find an overlap region, in parameter space, where two different ESS's are possible, depending on initial conditions. For general alpha, we see that all three ESS are possible, depending on different values of the environmental parameters; however, as the average time of a contest over food becomes long, then the Marauder strategy becomes more and more prevalent. The model makes a potentially significant prediction about animal behaviour in the area of kleptoparasitism, that a searcher, when it meets a handler, will only decline to attack that handler when alpha < 1/2 i.e. when the defender is more likely to win. One possible converse of this statement, that a handler whose probability of success is greater than 1/2 should always resist a challenge, is not true.

Animals↗
PubMed2001

Game theory in the operating room environment.

To optimize the functioning of an operating room the interactions of the staff (physicians and nurses) and other stakeholders (administrators) must be understood. Game theory provides a representation of the interactions that typically take place in the operating room environment. By understanding the types of games/interactions that occur the participants can better predict outcome and adapt their own behavior to optimize that outcome. Types of games seen in the operating room include fixed-sum, zero-sum, and non-zero-sum games. The Prisoner's Dilemma game and some of its variations are used to illustrate common interactions in the operating room. Examples of strategies for typical scenarios are discussed as well as ways to improve the outcome of the games. A better understanding of human behavior can improve the functioning of complex systems such as that found in the operating room.

Game Theory↗
PubMed2005

Evolutionary game theory in an agent-based brain tumor model: exploring the 'Genotype-Phenotype' link.

To investigate the genotype-phenotype link in a polyclonal cancer cell population, here we introduce evolutionary game theory into our previously developed agent-based brain tumor model. We model the heterogeneous cell population as a mixture of two distinct genotypes: the more proliferative Type A and the more migratory Type B. Our agent-based simulations reveal a phase transition in the tumor's velocity of spatial expansion linking the tumor fitness to genotypic composition. Specifically, velocity initially falls as rising payoffs reward the interactions among the more stationary Type A cells, but unexpectedly accelerates again when these A-A payoffs increase even further. At this latter accelerating stage, fewer migratory Type B cells appear to confer a competitive advantage in terms of the tumor's spatial aggression over the overall numerically dominating Type A cells, which in turn leads to an acceleration of the overall tumor dynamics while its surface roughness declines. We discuss potential implications of our findings for cancer research.

Brain Neoplasms↗
PubMed1998

Self-organized criticality in spatial evolutionary game theory.

Self-organized criticality is an important framework for understanding the emergence of scale-free natural phenomena. Cellular automata provide simple interesting models in which to study self-organized criticality. We consider the dynamics of a new class of cellular automata which are constructed as natural spatial extensions of evolutionary game theory. This construction yields a discrete one-parameter family of cellular automata. We show that there is a range of parameter values for which this system exhibits complex dynamics with long range correlations between states in both time and space. In this region the dynamics evolve to a self-organized critical state in which structures exist on all time and length scales, and the relevant statistical measures have power law behaviour.

Animals↗
PubMed1997

Game-theory models of interactions between tumour cells.

The population of cells that comprises a tumour may consist of genetically different individuals. Often, such polymorphisms result from the expansion of a new, advantageous clone. The hypothesis is presented that sometimes tumour cells may adopt genetically-determined strategies to boost their own replication at the expense of other cells in the tumour. Simple game-theory models have been used to study this hypothesis, taking as an example the hypothetical advantage gained by tumour cells which produce a cytotoxin to harm other tumour cells. The models show that genotypes which cause cells to produce cytotoxic substances can spread through the tumour cell population, as can genotypes for resistance to the cytotoxin; in other circumstances, stable polymorphisms between these strategies can occur. The path of the tumour cell population to internal or external equilibrium is often complex, with large fluctuations in genotype frequencies. Flexible strategies are usually superior to fixed strategies. As in populations of whole organisms, 'social' interactions between tumour cells can act in favour of the individual cell at the expense of the tumour as a whole: strategies that retard the growth of the tumour can be selected and tumour regression is theoretically possible. Many mutations in tumours, especially in large or late-stage lesions, may play a role in relations between tumour cells rather than providing those cells with a simple replicative advantage.

Cell Communication↗
PubMed2003

Matchmaking and species marriage: a game-theory model of community assembly.

Theories developed to explain the processes that govern the assembly and composition of natural plant communities can be divided into two broad categories. Niche-based theories propose that coevolutionary changes among species lead to character divergence (displacement), which allows for coexistence by partitioning resources among species. In contrast, ecological-drift theories propose that species diversity results from a balance of migration, speciation, and extinction, with little microevolutionary change. We use a game-theory model to reconcile drift and niche perspectives by developing a theory of species "marriage." Initially, ecological drift may determine which species encounter each other in a competitive arena. Once species come into contact, historical niche development as a result of prior coevolutionary molding of competitive ability determines which species may coexist. The model shows that only species that display the well-known tradeoff between seed size and competitive ability as a result of past competitive histories comply with the requisite for mutual evolutionary stability. Mutual evolutionary stability of competitive ability tends to make reproductive outputs more similar between species, increasing the chances of ecological equilibrium, i.e., the coexistence of species competing for a single resource. Moreover, mutual evolutionary stability guarantees that such an ecological equilibrium will be stable. The species-marriage model predicts that two or more plant species will coexist indefinitely (i.e., "marry") when their difference in seed size, their densities, and the resource availability obey a specific quantitative relation. For example, when resource availability is high, married species should be characterized by a greater asymmetry in seed size than when resource availability is low. Thus, in the species-marriage model, competition can shape the detailed properties of communities without violating the postulates of ecological-drift theory.

Ecology↗
PubMed1997

Spatial and density effects in evolutionary game theory.

Two models are considered for the study of game dynamics in a spatial domain. Both models are continuous in space and time and give rise to reaction-diffusion equations. The spatial domain is homogeneous but the mobility of the individuals is allowed to depend upon the strategy. The models are analysed for spatial patterns (via a Turing instability) and also for the direction of the travelling wave that replaces one strategy by another. It is shown that the qualitative behaviour of the two models is quite different. When considering the existence of spatial patterns and deciding whether increased mobility is helpful or not, it is shown that the answers depend crucially upon the model equations. Since both models (in the absence of spatial variation) are quite standard, it is clear that considerable care has to be exercised in the formulation of spatial models and in their interpretation.

Animals↗
PubMed2005

Game theory provides no explanation for seed size variation in grasslands.

Game theoretical models have been suggested to explain the maintenance of a remarkable variation in seed size across species in most types of vegetation. According to these models, which are based on the existence of a trade-off between seed size and seed number; smaller-seeded species can invade any species mixture due to their numerical advantage, and larger-seeded species can invade any species mixture due to their competitive superiority over smaller-seeded species during recruitment. However, till now, there is very limited evidence for seed size effects on recruitment interactions among different species. An experiment was designed using 16 species in Swedish grasslands, varying 384-fold in seed size. Species were sown pairwise and alone in disturbed versus undisturbed small plots in grazed versus ungrazed grassland, and the resulting recruitment was recorded. Seedling densities in the experimental plots were within the natural range. Both disturbance and grazing had a positive effect on recruitment. Seed size did not affect recruitment except from a tendency that increasing seed size made recruitment less dependent on disturbance. Recruitment of smaller-seeded species was not affected by the presence of larger-seeded species. Larger-seeded species did not generally win in direct contest. These results suggest that game theoretical models do not explain maintenance of seed size variation across species in these grasslands. Alternative explanations for seed size variation are that either small-scale heterogeneity provide conditions favouring a range of different seed sizes or other attributes than seed size effectively determine recruitment.

Ecosystem↗