Coclustering of human cancer microarrays using Minimum Sum-Squared Residue coclustering

It is a consensus in microarray analysis that identifying potential local patterns, characterized by coherent groups of genes and conditions, may shed light on the discovery of previously undetectable biological cellular processes of genes as well as macroscopic phenotypes of related samples. In order to simultaneously cluster genes and conditions, we have previously developed a fast co-clustering algorithm, Minimum Sum-Squared Residue Co-clustering (MSSRCC), which employs an alternating minimization scheme and generates what we call co-clusters in a checkerboard structure. In this paper, we propose specific strategies that enable MSSRCC to escape poor local minima and resolve the degeneracy problem in partitional clustering algorithms. The strategies include binormalization, deterministic spectral initialization, and incremental local search. We assess the effects of various strategies on both synthetic gene expression datasets and real human cancer microarrays and provide empirical evidence that MSSRCC with the proposed strategies performs better than existing co-clustering and clustering algorithms. In particular, the combination of all the three strategies leads to the best performance. Furthermore, we illustrate coherence of the resulting co-clusters in a checkerboard structure, where genes in a co-cluster manifest the phenotype structure of corresponding specific samples, and evaluate the enrichment of functional annotations in Gene Ontology (GO).     

Function-valued adaptive dynamics and optimal control theory

In this article we further develop the theory of adaptive dynamics of function-valued traits. Previous work has concentrated on models for which invasion fitness can be written as an integral in which the integrand for each argument value is a function of the strategy value at that argument value only. For this type of models of direct effect, singular strategies can be found using the calculus of variations, with singular strategies needing to satisfy Euler’s equation with environmental feedback. In a broader, more mechanistically oriented class of models, the function-valued strategy affects a process described by differential equations, and fitness can be expressed as an integral in which the integrand for each argument value depends both on the strategy and on process variables at that argument value. In general, the calculus of variations cannot help analyzing this much broader class of models. Here we explain how to find singular strategies in this class of process-mediated models using optimal control theory. In particular, we show that singular strategies need to satisfy Pontryagin’s maximum principle with environmental feedback. We demonstrate the utility of this approach by studying the evolution of strategies determining seasonal flowering schedules.     

Robustness of optimal mixed strategies

 Mixed strategies, or variable phenotypes, can evolve in fluctuating environments when at the time that a strategy is chosen the consequences of that decision are relatively uncertain. In a previous paper, we have shown several examples of explicit forms of optimal mixed strategies when an environmental distribution and payoff function are given. In many of these examples, the mixed strategy has a continuous distribution. In a recent study, however, Sasaki and Ellner proved that, if the distribution of the environmental parameter is modified in certain ways, the exact ESS distribution becomes discrete rather than continuous. This forces us to take a closer look at the robustness of optimal mixed strategies. In the current paper we prove that such strategies are indeed robust against small perturbations of the environmental distribution and/or the payoff function, in the sense that the optimal strategy distribution for the perturbed system, converges weakly to the optimal strategy distribution for the unperturbed system as the magnitude of the perturbation goes to zero. Furthermore, we show that the fitness difference between the two strategies converges to zero. Thus, although optimal strategies in ‘ideal’ and perturbed systems can be qualitatively different, the difference between the distributions (in a measure theoretic sense) is small. Received: 27 October 1996 / Revised version: 5 March 1997     

Chemotherapy for tumors: an analysis of the dynamics and a study of quadratic and linear optimal controls

We investigate a mathematical model of tumor-immune interactions with chemotherapy, and strategies for optimally administering treatment. In this paper we analyze the dynamics of this model, characterize the optimal controls related to drug therapy, and discuss numerical results of the optimal strategies. The form of the model allows us to test and compare various optimal control strategies, including a quadratic control, a linear control, and a state-constraint. We establish the existence of the optimal control, and solve for the control in both the quadratic and linear case. In the linear control case, we show that we cannot rule out the possibility of a singular control. An interesting aspect of this paper is that we provide a graphical representation of regions on which the singular control is optimal.     

A Performance Comparison of Coscheduling Strategies for Workstation Clusters

Workstation clusters are emerging as a general-purpose computing platform for the execution of workloads comprising parallel and sequential applications. The scalability and flexibility typical of implicit coscheduling strategies makes them a very promising solution to the scheduling needs of workstation clusters. In this paper we present a simulation study that compares, for a variety of workloads (that include both parallel and sequential applications) and operating system schedulers, 12 implicit coscheduling strategies in terms of the performance they are able to deliver to applications. By using a detailed simulator, we evaluate the performance of different coscheduling alternatives for a variety of simulation scenarios, and we identify the set of strategies that deliver the best performance to all the applications composing typical cluster workloads. Moreover, we show that for schedulers providing immediate preemption, the best strategies are also the simplest ones to implement.     

On treatment of tuberculosis in heterogeneous populations

Global eradication of tuberculosis (TB) is an international agenda. Thus understanding effects of treatment of TB in different settings is crucial. In previous work, we introduced the framework for a mathematical model of epidemic TB in demographically distinct, heterogeneous populations. Simulations showed the importance of genetic susceptibility in determining endemic prevalence levels. In the work presented here, we include treatment and investigate different strategies for treatment of latent and active TB disease in heterogeneous populations. We illustrate how the presence of a genetically susceptible subpopulation dramatically alters effects of treatment in the same way a core population does in the setting of sexually transmitted diseases. In addition, we evaluate treatment strategies that focus specifically on this subpopulation, and our results indicate that genetically susceptible subpopulations should be accounted for when designing treatment strategies to achieve the greatest reduction in disease prevalence.     

Optimization and Phenotype Allocation

We study the phenotype allocation problem for the stochastic evolution of a multitype population in a random environment. Our underlying model is a multitype Galton–Watson branching process in a random environment. In the multitype branching model, different types denote different phenotypes of offspring, and offspring distributions denote the allocation strategies. Two possible optimization targets are considered: the long-term growth rate of the population conditioned on nonextinction, and the extinction probability of the lineage. In a simple and biologically motivated case, we derive an explicit formula for the long-term growth rate using the random Perron–Frobenius theorem, and we give an approximation to the extinction probability by a method similar to that developed by Wilkinson. Then we obtain the optimal strategies that maximize the long-term growth rate or minimize the approximate extinction probability, respectively, in a numerical example. It turns out that different optimality criteria can lead to different strategies.     

A comparison of foraging strategies in a patchy environment.

In this paper we compare foraging strategies that might be used by predators seeking prey in a patchy environment. The strategies differ in the extent to which predators aggregate in response to prey density. The approach to the comparison is suggested by the idea of evolutionarily stable strategies. A strategy is said to be evolutionarily stable if it cannot be invaded by another strategy. Thus we examine scenarios where a small number of individuals using one strategy are introduced into a situation where a large number of individuals using the other strategy are already present. However, our foraging models do not explicitly incorporate predator population dynamics, so we use net energy uptake as a surrogate for reproductive fitness. In cases where all of the patches visited by predators sustain prey populations, we find that for any pair of strategies one of them will have a higher net energy uptake than the other whether it is the resident or the introduced strain. However, which one is higher will typically depend on the total predator population, which is determined by the resident strain. If the predators leave prey densities high, the more aggregative strain will have the advantage. If the predators reduce prey densities to low levels the less aggregative strain will have the advantage. In cases where one strain of predators aggregates in response to prey density and the other does not, then there might be patches which do not contain prey but do contain (non-aggregating) predators. In those cases, there is the possibility that whichever strategy is used by the introduced strain will yield a higher energy uptake than that used by the resident strain. This suggests that if some patches are empty of prey then aggregative and non-aggregative strategies may be able to coexist.     

Adaptive Patch Searching Strategies in Fragmented Landscapes

The search strategies dispersers employ to search for new habitat patches affect individuals’ search success and subsequently landscape connectivity and metapopulation viability. Some evidence indicates that individuals within the same species may display a variety of behavioural patch searching strategies rather than one species-specific strategy. This may result from landscape heterogeneity. We modelled the evolution of individual patch searching strategies in different landscapes. Specifically, we analysed whether evolution can favour different, co-existing, behavioural search strategies within one population and to what extent this coexistence of multiple strategies was dependent on landscape configuration. Using an individual-based simulation model, we studied the evolution of patch searching strategies in three different landscape configurations: uniform, random and clumped. We found that landscape configuration strongly influenced the evolved search strategy. In uniform landscapes, one fixed search strategy evolved for the entire spatially structured population, while in random and clumped landscapes, a set of different search strategies emerged. The coexistence of several search strategies also strongly depended on the dispersal mortality. We show that our result can affect landscape connectivity and metapopulation dynamics. Co-ordinating editor: N. Yamamura     

Evolution of Cooperation in Spatially Structured Populations

Using a spatial lattice model of the Iterated Prisoner's Dilemma we studied the evolution of cooperation within the strategy space of all stochastic strategies with a memory of one round. Comparing the spatial model with a randomly mixed model showed that (1) there is more cooperative behaviour in a spatially structured population, (2) PAVLOV and generous variants of it are very successful strategies in the spatial context and (3) in spatially structured populations evolution is much less chaotic than in unstructured populations. In spatially structured populations, generous variants of PAVLOV are found to be very successful strategies in playing the Iterated Prisoner's Dilemma. The main weakness of PAVLOV is that it is exploitable by defective strategies. In a spatial context this disadvantage is much less important than the good error correction of PAVLOV, and especially of generous PAVLOV, because in a spatially structured population successful strategies always build clusters.     

Oscillatory dynamics in evolutionary games are suppressed by heterogeneous adaptation rates of players

Game dynamics in which three or more strategies are cyclically competitive, as represented by the rock-scissors-paper game, have attracted practical and theoretical interests. In evolutionary dynamics, cyclic competition results in oscillatory dynamics of densities of individual strategists. In finite-size populations, it is known that oscillations blow up until all but one strategies are eradicated if without mutation. In the present paper, we formalize replicator dynamics with players who have different adaptation rates. We show analytically and numerically that the heterogeneous adaptation rate suppresses the oscillation amplitude. In social dilemma games with cyclically competing strategies and homogeneous adaptation rates, altruistic strategies are often relatively weak and cannot survive in finite-size populations. In such situations, heterogeneous adaptation rates save coexistence of different strategies and hence promote altruism. When one strategy dominates the others without cyclic competition, fast adaptors earn more than slow adaptors. When not, mixture of fast and slow adaptors stabilizes population dynamics, and slow adaptation does not imply inefficiency for a player.     

The Beverton-Holt model with periodic and conditional harvesting

In this theoretical study, we investigate the effect of different harvesting strategies on the discrete Beverton-Holt model in a deterministic environment. In particular, we make a comparison between the constant, periodic and conditional harvesting strategies. We find that for large initial populations, constant harvest is more beneficial to both the population and the maximum sustainable yield. However, periodic harvest has a short-term advantage when the initial population is low, and conditional harvest has the advantage of lowering the risk of depletion or extinction. Also, we investigate the periodic character under each strategy and show that periodic harvesting drives population cycles to be multiples (period-wise) of the harvesting period.     

The Beverton–Holt model with periodic and conditional harvesting

In this theoretical study, we investigate the effect of different harvesting strategies on the discrete Beverton–Holt model in a deterministic environment. In particular, we make a comparison between the constant, periodic and conditional harvesting strategies. We find that for large initial populations, constant harvest is more beneficial to both the population and the maximum sustainable yield. However, periodic harvest has a short-term advantage when the initial population is low, and conditional harvest has the advantage of lowering the risk of depletion or extinction. Also, we investigate the periodic character under each strategy and show that periodic harvesting drives population cycles to be multiples (period-wise) of the harvesting period.     

Constraint-based strain design using continuous modifications (CosMos) of flux bounds finds new strategies for metabolic engineering

In recent years, a growing number of metabolic engineering strain design techniques have employed constraint-based modeling to determine metabolic and regulatory network changes which are needed to improve chemical production. These methods use systems-level analysis of metabolism to help guide experimental efforts by identifying deletions, additions, downregulations, and upregulations of metabolic genes that will increase biological production of a desired metabolic product. In this work, we propose a new strain design method with continuous modifications (CosMos) that provides strategies for deletions, downregulations, and upregulations of fluxes that will lead to the production of the desired products. The method is conceptually simple and easy to implement, and can provide additional strategies over current approaches. We found that the method was able to find strain design strategies that required fewer modifications and had larger predicted yields than strategies from previous methods in example and genome-scale networks. Using CosMos, we identified modification strategies for producing a variety of metabolic products, compared strategies derived from Escherichia coli and Saccharomyces cerevisiae metabolic models, and examined how imperfect implementation may affect experimental outcomes. This study gives a powerful and flexible technique for strain engineering and examines some of the unexpected outcomes that may arise when strategies are implemented experimentally.     

Optimal Foraging Theory Perspectives on the Strategies of Itinerant Beekeepers in Semiarid Northeast Brazil

Foraging theory has been widely used to understand patterns associated with obtaining resources and the optimal cost-benefit relationship between forager and resource. However, many analytical theoretical models do not consider the influence of social groups on forager strategy. We analyzed strategies for obtaining resources from two perspectives: individual and social. For the first, we tested hypotheses that addressed whether individual strategies followed the predictions of classic models of foraging theory. In the second approach, we investigated potential social influences on resource-obtaining strategies. Our results suggest that regardless of the strategy adopted by the forager (specialist or generalist), environmental factors, such as abundance, regulated success in obtaining resources. However, we observed that specialists had a greater advantage relative to generalists when resources were abundant. We also observed that forager decision-making was related to the social context of the individual forager, which influenced their strategies.     

Burning Prairie to Restore Butterfly Habitat: A Modeling Approach to Management Tradeoffs for the Fender's Blue

Designing strategies to manage rare species' habitats may involve tradeoffs that include negative short-term impacts to achieve positive long-term success. In managing grasslands, fire is a powerful tool to control invasive weeds and stimulate native plant growth, but it may decimate the invertebrate fauna. To rank potential burn strategies for Icaricia icarioides fenderi (Fender's blue butterfly) habitat, we present an empirically based mathematical model. Parameter estimates are based on experiments conducted by Wilson and Clark from 1994 to 1997. Potential strategies include combinations of times between burn (1, 2, 3, 4, or 5 years) and fractions of a habitat to burn in each fire (1/8, 1/4, 1/3, or 1/2), as well as a strategy of never burning. Burning one-third of the habitat every year maximizes the average annual population growth rate, but, based on maximum likelihood parameter estimates, 8 of 21 strategies led to 95% of simulated butterfly populations persisting for 100 years. In simulations based on the parameters' lower confidence limits, however, there were some cases in which no strategies led to populations persisting 100 years. In this uncertainty analysis—the effect of changes in parameters based on our confidence in them—we also investigated the rank order of the strategies. This uncertainty analysis indicated that the rank order of burning strategies is most sensitive to our confidence in rates of habitat change after a burn (number of "good" years after a fire and time for habitat to return to pre-burn conditions). Surprisingly, however, the rank order of strategies changes little over a wide range of butterfly demographic rates. Better knowledge of rates of habitat change after a burn would improve our ability to make management decisions substantially more than better knowledge of the butterfly's vital rates.     

Strategies for analysing missing item response data with an application to lung cancer

Missing data problems persist in many scientific investigations. Although various strategies for analyzing missing data have been proposed, they are mainly limited to data on continuous measurements. In this paper, we focus on implementing some of the available strategies to analyze item response data. In particular, we investigate the effects of popular missing data methods on various missing data mechanisms. We examine large sample behaviors of estimators in a simulation study that evaluates and compares their performance. We use data from a quality of life study with lung cancer patients to illustrate the utility of these methods.     

Mineralocorticoid Receptors Guide Spatial and Stimulus-Response Learning in Mice

Adrenal corticosteroid hormones act via mineralocorticoid (MR) and glucocorticoid receptors (GR) in the brain, influencing learning and memory. MRs have been implicated in the initial behavioral response in novel situations, which includes behavioral strategies in learning tasks. Different strategies can be used to solve navigational tasks, for example hippocampus-dependent spatial or striatum-dependent stimulus-response strategies. Previous studies suggested that MRs are involved in spatial learning and induce a shift between learning strategies when animals are allowed a choice between both strategies. In the present study, we further explored the role of MRs in spatial and stimulus-response learning in two separate circular holeboard tasks using female mice with forebrain-specific MR deficiency and MR overexpression and their wildtype control littermates. In addition, we studied sex-specific effects using male and female MR-deficient mice. First, we found that MR-deficient compared to control littermates and MR-overexpressing mice display altered exploratory and searching behavior indicative of impaired acquisition of novel information. Second, female (but not male) MR-deficient mice were impaired in the spatial task, while MR-overexpressing female mice showed improved performance in the spatial task. Third, MR-deficient mice were also impaired in the stimulus-response task compared to controls and (in the case of females) MR-overexpressing mice. We conclude that MRs are important for coordinating the processing of information relevant for spatial as well as stimulus-response learning.     

One option,two countries,several strategies: subjacent mechanisms of assisted migration implementation in Canada and France

Climate change obliges societies to develop adaptive strategies in order to maintain sustainable management of resources and landscapes. However, the development and implementation of these strategies require dialogue between researchers and policy‐makers about what they understand for adaptation. This dialogue can be hindered by language differences, the hidden agendas, and conflicting concerns of those involved. In this research study, we explored the mechanisms that underlie the implementation process of assisted migration (AM), an adaptation strategy that aims to limit the impact of climate change. We conducted a comparative analysis of 80 semistructured interviews with actors in the forestry sectors in Canada and France. In Canada, our results show a division between the provinces strategies, causing a debate about AM because researchers are wary of the geoengineering and economic arguments that frame AM in areas where the effects of climate change remain unclear. In contrast, we found that the observation of climate impacts is a strong trigger for the application of AM despite an awareness of its associated risks. In France, we explained the absence of AM implementation by a lack of information flow between research and foresters regarding the concept of AM, a cultural attachment of French foresters to their forest landscapes and that climate change effects are not clear yet. Clarity on what implies a true ecological engineering approach in ecological restoration can help maintaining adaptive actions like AM within the general scope of ecosystem management and minimize simplistic applications of adaptation strategies because of climate change.     

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.