Stochastic slowdown in evolutionary processes

We examine birth--death processes with state dependent transition probabilities and at least one absorbing boundary. In evolution, this describes selection acting on two different types in a finite population where reproductive events occur successively. If the two types have equal fitness the system performs a random walk. If one type has a fitness advantage it is favored by selection, which introduces a bias (asymmetry) in the transition probabilities. How long does it take until advantageous mutants have invaded and taken over? Surprisingly, we find that the average time of such a process can increase, even if the mutant type always has a fitness advantage. We discuss this finding for the Moran process and develop a simplified model which allows a more intuitive understanding. We show that this effect can occur for weak but non--vanishing bias (selection) in the state dependent transition rates and infer the scaling with system size. We also address the Wright-Fisher model commonly used in population genetics, which shows that this stochastic slowdown is not restricted to birth-death processes.Comment: 8 pages, 3 figures, accepted for publicatio

From discrete to continuous evolution models: a unifying approach to drift-diffusion and replicator dynamics

We study the large population limit of the Moran process, assuming weak-selection, and for different scalings. Depending on the particular choice of scalings, we obtain a continuous model that may highlight the genetic-drift (neutral evolution) or natural selection; for one precise scaling, both effects are present. For the scalings that take the genetic-drift into account, the continuous model is given by a singular diffusion equation, together with two conservation laws that are already present at the discrete level. For scalings that take into account only natural selection, we obtain a hyperbolic singular equation that embeds the Replicator Dynamics and satisfies only one conservation law. The derivation is made in two steps: a formal one, where the candidate limit model is obtained, and a rigorous one, where convergence of the probability density is proved. Additional results on the fixation probabilities are also presented.Comment: 18 pages, 3 figure

Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution

A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with $n$ current particles, a new particle is born with instantaneous rate $\lambda_n$ and a particle dies with instantaneous rate $\mu_n$. Currently no robust and efficient method exists to evaluate the finite-time transition probabilities in a general birth-death process with arbitrary birth and death rates. In this paper, we first revisit the theory of continued fractions to obtain expressions for the Laplace transforms of these transition probabilities and make explicit an important derivation connecting transition probabilities and continued fractions. We then develop an efficient algorithm for computing these probabilities that analyzes the error associated with approximations in the method. We demonstrate that this error-controlled method agrees with known solutions and outperforms previous approaches to computing these probabilities. Finally, we apply our novel method to several important problems in ecology, evolution, and genetics

The early phase of a bacterial insertion sequence infection

Bacterial insertion sequences are the simplest form of autonomous mobile DNA. It is unknown whether they need to have beneficial effects to infect and persist in bacterial populations, or whether horizontal gene transfer suffices for their persistence. We address this question by using branching process models to investigate the critical, early phase of an insertion sequence infection. We find that the probability of a successful infection is low and depends linearly on the difference between the rate of horizontal gene transfer and the fitness cost of the insertion sequences. Our models show that the median time to extinction of an insertion sequence that dies out is very short, while the median time for a successful infection to reach a modest population size is very long. We conclude that horizontal gene transfer is strong enough to allow the persistence of insertion sequences, although infection is an erratic and slow process

Temperature controls on aquatic bacterial production and community dynamics in arctic lakes and streams

The impact of temperature on bacterial activity and community composition was investigated in arctic lakes and streams in northern Alaska. Aquatic bacterial communities incubated at different temperatures had different rates of production, as measured by 14 C-leucine uptake, indicating that populations within the communities had different temperature optima. Samples from Toolik Lake inlet and outlet were collected at water temperatures of 14.2°C and 15.9°C, respectively, and subsamples incubated at temperatures ranging from 6°C to 20°C. After 5 days, productivity rates varied from 0.5 to ∼13.7 µg C l −1 day −1 and two distinct activity optima appeared at 12°C and 20°C. At these optima, activity was 2- to 11-fold higher than at other incubation temperatures. The presence of two temperature optima indicates psychrophilic and psychrotolerant bacteria dominate under different conditions. Community fingerprinting via denaturant gradient gel electrophoresis (DGGE) of 16S rRNA genes showed strong shifts in the composition of communities driven more by temperature than by differences in dissolved organic matter source; e.g. four and seven unique operational taxonomic units (OTUs) were found only at 2°C and 25°C, respectively, and not found at other incubation temperatures after 5 days. The impact of temperature on bacteria is complex, influencing both bacterial productivity and community composition. Path analysis of measurements of 24 streams and lakes sampled across a catchment 12 times in 4 years indicates variable timing and strength of correlation between temperature and bacterial production, possibly due to bacterial community differences between sites. As indicated by both field and laboratory experiments, shifts in dominant community members can occur on ecologically relevant time scales (days), and have important implications for understanding the relationship of bacterial diversity and function.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/79247/1/j.1462-2920.2010.02176.x.pd

The Ascorbate-glutathione-α-tocopherol Triad in Abiotic Stress Response

The life of any living organism can be defined as a hurdle due to different kind of stresses. As with all living organisms, plants are exposed to various abiotic stresses, such as drought, salinity, extreme temperatures and chemical toxicity. These primary stresses are often interconnected, and lead to the overproduction of reactive oxygen species (ROS) in plants, which are highly reactive and toxic and cause damage to proteins, lipids, carbohydrates and DNA, which ultimately results in oxidative stress. Stress-induced ROS accumulation is counteracted by enzymatic antioxidant systems and non-enzymatic low molecular weight metabolites, such as ascorbate, glutathione and α-tocopherol. The above mentioned low molecular weight antioxidants are also capable of chelating metal ions, reducing thus their catalytic activity to form ROS and also scavenge them. Hence, in plant cells, this triad of low molecular weight antioxidants (ascorbate, glutathione and α-tocopherol) form an important part of abiotic stress response. In this work we are presenting a review of abiotic stress responses connected to these antioxidants