Person:

Nowak, Martin

We study the origin of evolution. Evolution is based on replication, mutation, and selection. But how does evolution begin? When do chemical kinetics turn into evolutionary dynamics? We propose “prelife” and “prevolution” as the logical precursors of life and evolution. Prelife generates sequences of variable length. Prelife is a generative chemistry that proliferates information and produces diversity without replication. The resulting “prevolutionary dynamics” have mutation and selection. We propose an equation that allows us to investigate the origin of evolution. In one limit, this “originator equation” gives the classical selection equation. In the other limit, we obtain “prelife.” There is competition between life and prelife and there can be selection for or against replication. Simple prelife equations with uniform rate constants have the property that longer sequences are exponentially less frequent than shorter ones. But replication can reverse such an ordering. As the replication rate increases, some longer sequences can become more frequent than shorter ones. Thus, replication can lead to “reversals” in the equilibrium portraits. We study these reversals, which mark the transition from prelife to life in our model. If the replication potential exceeds a critical value, then life replicates into existence.

We investigate the cooperation dynamics attributed to the interplay between the evolution of individual strategies and evolution of individual partnerships. We focus on the effect of reputation on an individual’s partner-switching process. We assume that individuals can either change their strategies by imitating their partners or adjust their partnerships based on local information about reputations. We manipulate the partner switching in two ways; that is, individuals can switch from the lowest reputation partners, either to their partners’ partners who have the highest reputation (i.e., ordering in partnership) or to others randomly chosen from the entire population (i.e., randomness in partnership). We show that when individuals are able to alter their behavioral strategies and their social interaction partnerships on the basis of reputation, cooperation can prevail. We find that the larger temptation to defect and the denser the partner network, the more frequently individuals need to shift their partnerships in order for cooperation to thrive. Furthermore, an increasing tendency of switching to partners’ partners is more likely to lead to a higher level of cooperation. We show that when reputation is absent in such partner-switching processes, cooperation is much less favored than that of the reputation involved. Moreover, we investigate the effect of discounting an individual’s reputation on the evolution of cooperation. Our results highlight the importance of the consideration of reputation (indirect reciprocity) on the promotion of cooperation when individuals can adjust their partnerships.

We show that the times separating the birth of benign, invasive, and metastatic tumor cells can be determined by analysis of the mutations they have in common. When combined with prior clinical observations, these analyses suggest the following general conclusions about colorectal tumorigenesis: (i) It takes ≈17 years for a large benign tumor to evolve into an advanced cancer but <2 years for cells within that cancer to acquire the ability to metastasize; (ii) it requires few, if any, selective events to transform a highly invasive cancer cell into one with the capacity to metastasize; (iii) the process of cell culture ex vivo does not introduce new clonal mutations into colorectal tumor cell populations; and (iv) the rates at which point mutations develop in advanced cancers are similar to those of normal cells. These results have important implications for understanding human tumor pathogenesis, particularly those associated with metastasis.

Background: The basic idea of tag-based models for cooperation is that individuals recognize each other via arbitrary signals, so-called tags. If there are tags of different colors, then cooperators can always establish new signals of recognition. The resulting “chromodynamics” is a mechanism for the evolution of cooperation. Cooperators use a secret tag until they are discovered by defectors who then destroy cooperation based on this tag. Subsequently, a fraction of the population manages to establish cooperation based on a new tag. Methodology/Principal Findings: We derive a mathematical description of stochastic evolutionary dynamics of tag-based cooperation in populations of finite size. Benefit and cost of cooperation are given by b and c. We find that cooperators are more abundant than defectors if (b/c > 1+2u/v), where (u) is the mutation rate changing only the strategy and v is the mutation rate changing strategy and tag. We study specific assumptions for (u) and (v) in two genetic models and one cultural model. Conclusions/Significance: In a genetic model, tag-based cooperation only evolves if a gene encodes both strategy and tag. In a cultural model with equal mutation rates between all possible phenotypes (tags and behaviors), the crucial condition is (b/c > (K+1)/(K-1)), where (K) is the number of tags. A larger number of tags requires a smaller benefit-to-cost ratio. In the limit of many different tags, the condition for cooperators to have a higher average abundance than defectors becomes (b > c).

The idea of evolutionary game theory is to relate the payoff of a game to reproductive success (= fitness). An underlying assumption in most models is that fitness is a linear function of the payoff. For stochastic evolutionary dynamics in finite populations, this leads to analytical results in the limit of weak selection, where the game has a small effect on overall fitness. But this linear function makes the analysis of strong selection difficult. Here, we show that analytical results can be obtained for any intensity of selection, if fitness is defined as an exponential function of payoff. This approach also works for group selection (= multi-level selection). We discuss the difference between our approach and that of inclusive fitness theory.

Evolutionary game dynamics in finite populations provide a new framework for studying selection of traits with frequency-dependent fitness. Recently, a “one-third law” of evolutionary dynamics has been described, which states that strategy A fixates in a B-population with selective advantage if the fitness of A is greater than that of B when A has a frequency View the MathML source. This relationship holds for all evolutionary processes examined so far, from the Moran process to games on graphs. However, the origin of the “number” View the MathML source is not understood. In this paper we provide an intuitive explanation by studying the underlying stochastic processes. We find that in one invasion attempt, an individual interacts on average with B-players twice as often as with A-players, which yields the one-third law. We also show that the one-third law implies that the average Malthusian fitness of A is positive.

How does natural selection lead to cooperation between competing individuals? The Prisoner's Dilemma captures the essence of this problem. Two players can either cooperate or defect. The payoff for mutual cooperation, R, is greater than the payoff for mutual defection, P. But a defector versus a cooperator receives the highest payoff, T, where as the cooperator obtains the lowest payoff, S. Hence, the Prisoner's Dilemma is defined by the payoff ranking T > R > P > S . In a well-mixed population, defectors always have a higher expected payoff than cooperators, and therefore natural selection favors defectors. The evolution of cooperation requires specific mechanisms. Here we discuss five mechanisms for the evolution of cooperation: direct reciprocity, indirect reciprocity, kin selection, group selection, and network reciprocity (or graph selection). Each mechanism leads to a transformation of the Prisoner's Dilemma payoff matrix. From the transformed matrices, we derive the fundamental conditions for the evolution of cooperation. The transformed matrices can be used in standard frameworks of evolutionary dynamics such as the replicator equation or stochastic processes of game dynamics in finite populations.

Cancer cells are generally viewed as a problem innate to their host, but evidence is mounting that they can evolve to become infectious agents and be transmitted between individuals.

The current view of cancer development is that normal cells are transformed into tumour cells by sequential mutations that activate cancer-promoting 'oncogenes', or inhibit genes that would otherwise suppress tumours, or trigger genetic instabilities. As a consequence, every tumour is the result of a unique evolutionary process as the cancer cells adapt to out-compete their neighbours.

The evolution of genotypic mutation rates has been investigated in numerous theoretical and experimental studies. Mutations, however, occur not only when copying DNA, but also when building the phenotype, especially when translating and transcribing DNA to RNA and protein. Here we study the effect of such phenotypic mutations. We find a maximum phenotypic mutation rate, umax, that is compatible with maintaining a certain function of the organism. This may be called a phenotypic error threshold. In particular, we find a minimum phenotypic mutation rate, umin, with the property that there is (nearly) no selection pressure to reduce the rate of phenotypic mutations below this value. If there is a cost for lowering the phenotypic mutation rate, then umin is close to the optimum phenotypic mutation rate that maximizes the fitness of the organism. In our model, there is selective pressure to decrease the rate of genotypic mutations to zero, but to decrease the rate of phenotypic mutations only to a positive value. Despite its simplicity, our model can explain part of the huge difference between genotypic and phenotypic mutation rates that is observed in nature. The relevant data are summarize