Genotype by random environmental interactions gives an advantage to non-favored minor alleles.

Fixation probability, the probability that the frequency of a newly arising mutation in a population will eventually reach unity, is a fundamental quantity in evolutionary genetics. Here we use a number of models (several versions of the Moran model and the haploid Wright-Fisher model) to examine fixation probabilities for a constant size population where the fitness is a random function of both allelic state and spatial position, despite neither allele being favored on average. The concept of fitness varying with respect to both genotype and environment is important in models of cancer initiation and progression, bacterial dynamics, and drug resistance. Under our model spatial heterogeneity redefines the notion of neutrality for a newly arising mutation, as such mutations fix at a higher rate than that predicted under neutrality. The increased fixation probability appears to be due to rare alleles having an advantage. The magnitude of this effect can be large, and is an increasing function of the spatial variance and skew in fitness. The effect is largest when the fitness values of the mutants and wild types are anti-correlated across environments. We discuss results for both a spatial ring geometry of cells (such as that of a colonic crypt), a 2D lattice and a mass-action (complete graph) arrangement.

[Evaluation of compensation abilities of kidneys using radionuclide examination].

The article presents the results of evaluation of compensation abilities of kidney based on the identification of volume of functioning renal tissue according to the single-photon emission scintigraphy (SPECT) and planar scintigraphy. The study included adult patients (65 patients with renal cell carcinoma, 32 patients with renal cysts and 20 patients without renal involvement) and pediatric patients aged 1 to 17 years (57 patients with various non-neoplastic lesions of the kidney). The following parameters were used: volume ratio of functioning tissue and the specific activities of the affected and contralateral kidneys, and the volumetric ratio of volumes estimated to the reference kidney volume depending on anthropomorphic data of patient (age and sex). It was found that the maximum compensatory renal reserve occurs in the case of reducing the volume of functioning tissue of the affected kidney and the simultaneous increase in the volume ofcontralateral kidney.

Spatial invasion dynamics on random and unstructured meshes: implications for heterogeneous tumor populations.

In this work we discuss a spatial evolutionary model for a heterogeneous cancer cell population. We consider the gain-of-function mutations that not only change the fitness potential of the mutant phenotypes against normal background cells but may also increase the relative motility of the mutant cells. The spatial modeling is implemented as a stochastic evolutionary system on a structured grid (a lattice, with random neighborhoods, which is not necessarily bi-directional) or on a two-dimensional unstructured mesh, i.e. a bi-directional graph with random numbers of neighbors. We present a computational approach to investigate the fixation probability of mutants in these spatial models. Additionally, we examine the effect of the migration potential on the spatial dynamics of mutants on unstructured meshes. Our results suggest that the probability of fixation is negatively correlated with the width of the distribution of the neighborhood size. Also, the fixation probability increases given a migration potential for mutants. We find that the fixation probability (of advantaged, disadvantaged and neutral mutants) on unstructured meshes is relatively smaller than the corresponding results on regular grids. More importantly, in the case of neutral mutants the introduction of a migration potential has a critical effect on the fixation probability and increases this by orders of magnitude. Further, we examine the effect of boundaries and as intuitively expected, the fixation probability is smaller on the boundary of regular grids when compared to its value in the bulk. Based on these computational results, we speculate on possible better therapeutic strategies that may delay tumor progression to some extent.

Levels of selection in positive-strand virus dynamics.

Conflicting selection pressures occurring over the life cycle of an organism constitute serious challenges to the robustness of replication. Viruses present a credible model system for analysing problems that arise through evolutionary conflicts of interest. We present a multi-level selection model for the life cycle of positive-strand RNA viruses. The model combines within-cell replication kinetics and protein synthesis, and between-cell population dynamics of virion production and transmission. We show how these two levels of within-host selection interact to produce tradeoffs in the life history strategy of a virus without consideration of host mortality. We find that viruses evolve towards intermediate rather than maximum encapsidation rates. This can be interpreted as selection for intermediate virulence through cellular persistence. We characterize a theoretical persistence threshold arising from the trade-off between genome replication and genetic translation within the cell. We present counter-intuitive relationships whereby increasing genome decay rates and rates of encapsidation lead to increases in the abundance of virus-encoded proteins. Data from poliovirus suggest that viruses might be unable to resolve the vertical conflicts of interests among different levels of selection.

Towards an evolutionary theory of language.

Language is a biological trait that radically changed the performance of one species and the appearance of the planet. Understanding how human language came about is one of the most interesting tasks for evolutionary biology. Here we discuss how natural selection can guide the emergence of some basic features of human language, including arbitrary signs, words, syntactic communication and grammar. We show how natural selection can lead to the duality of patterning of human language: sequences of phonemes form words; sequences of words form sentences. Finally, we present a framework for the population dynamics of grammar acquisition, which allows us to study the cultural evolution of grammar and the biological evolution of universal grammar.

The evolutionary dynamics of the lexical matrix.

The lexical matrix is an integral part of the human language system. It provides the link between word form and word meaning. A simple lexical matrix is also at the center of any animal communication system, where it defines the associations between form and meaning of animal signals. We study the evolution and population dynamics of the lexical matrix. We assume that children learn the lexical matrix of their parents. This learning process is subject to mistakes: (i) children may not acquire all lexical items of their parents (incomplete learning); and (ii) children might acquire associations between word forms and word meanings that differ from their parents' lexical items (incorrect learning). We derive an analytic framework that deals with incomplete learning. We calculate the maximum error rate that is compatible with a population maintaining a coherent lexical matrix of a given size. We calculate the equilibrium distribution of the number of lexical items known to individuals. Our analytic investigations are supplemented by numerical simulations that describe both incomplete and incorrect learning, and other extensions.

Natural selection of the critical period for language acquisition.

The language acquisition period in humans lasts about 13 years. After puberty it becomes increasingly difficult to learn a language. We explain this phenomenon by using an evolutionary framework. We present a dynamical system describing competition between language acquisition devices, which differ in the length of the learning period. There are two selective forces that play a role in determining the critical learning period: (i) having a longer learning period increases the accuracy of language acquisition; (ii) learning is associated with certain costs that affect fitness. As a result, there exists a limited learning period which is evolutionarily stable. This result is obtained analytically by means of a Nash equilibrium analysis of language acquisition devices. Interestingly, the evolutionarily stable learning period does not maximize the average fitness of the population.

The evolutionary dynamics of grammar acquisition.

Grammar is the computational system of language. It is a set of rules that specifies how to construct sentences out of words. Grammar is the basis of the unlimited expressibility of human language. Children acquire the grammar of their native language without formal education simply by hearing a number of sample sentences. Children could not solve this learning task if they did not have some pre-formed expectations. In other words, children have to evaluate the sample sentences and choose one grammar out of a limited set of candidate grammars. The restricted search space and the mechanism which allows to evaluate the sample sentences is called universal grammar. Universal grammar cannot be learned; it must be in place when the learning process starts. In this paper, we design a mathematical theory that places the problem of language acquisition into an evolutionary context. We formulate equations for the population dynamics of communication and grammar learning. We ask how accurate children have to learn the grammar of their parents' language for a population of individuals to evolve and maintain a coherent grammatical system. It turns out that there is a maximum error tolerance for which a predominant grammar is stable. We calculate the maximum size of the search space that is compatible with coherent communication in a population. Thus, we specify the conditions for the evolution of universal grammar.

Evolution of universal grammar.

Universal grammar specifies the mechanism of language acquisition. It determines the range of grammatical hypothesis that children entertain during language learning and the procedure they use for evaluating input sentences. How universal grammar arose is a major challenge for evolutionary biology. We present a mathematical framework for the evolutionary dynamics of grammar learning. The central result is a coherence threshold, which specifies the condition for a universal grammar to induce coherent communication within a population. We study selection of grammars within the same universal grammar and competition between different universal grammars. We calculate the condition under which natural selection favors the emergence of rule-based, generative grammars that underlie complex language.