Gravimetric Radar: Gravity-Based Detection of a Point-Mass Moving in a Static Background

This paper discusses a novel approach for detecting moving massive objects based on the time variation that these objects produce in the local gravitational field measured by several detectors. Such an approach may provide a viable method for detecting stealth aircraft, UAVs, cruise, and ballistic missiles. By inverting a set of nonlinear algebraic equations, it is possible to use the time variation in the gravitational fields to compute the mass, position, and velocity of one or more moving objects. The approach is essentially a gravity-based form of triangulation. Based on order-of-magnitude calculations, we estimate that under realistic scenarios, this approach will be feasible if it is possible to design gravimetric devices that are four to five order of magnitude more sensitive than current devices. To achieve such a level of sensitivity, we suggest designing detectors that exploit a quantum-mechanical effect known as gravity-induced quantum interference. Furthermore, even if we have a perfect detector, it will be necessary to determine the magnitude of various atmospheric disturbances and other sources of noise.

Second-Order Catalytic Quasispecies Yields First-Order Phase Transition

The quasispecies model describes processes related to the origin of life and viral evolutionary dynamics. We discuss how the error catastrophe that reflects the transition from localized to delocalized quasispecies population is affected by catalytic replication of different reaction orders. Specifically, we find that 2nd order mechanisms lead to 1st order discontinuous phase transitions in the viable population fraction, and conclude that the higher the interaction the lower the transition. We discuss potential implications for understanding the replication of highly mutating RNA viruses.

Semiconservative quasispecies equations for polysomic genomes: The general case

This paper develops a formulation of the quasispecies equations appropriate for polysomic, semiconservatively replicating genomes. This paper is an extension of previous work on the subject, which considered the case of haploid genomes. Here, we develop a more general formulation of the quasispecies equations that is applicable to diploid and even polyploid genomes. Interestingly, with an appropriate classification of population fractions, we obtain a system of equations that is formally identical to the haploid case. As with the work for haploid genomes, we consider both random and immortal DNA strand chromosome segregation mechanisms. However, in contrast to the haploid case, we have found that an analytical solution for the mean fitness is considerably more difficult to obtain for the polyploid case. Accordingly, whereas for the haploid case we obtained expressions for the mean fitness for the case of an analogue of the single-fitness-peak landscape for arbitrary lesion repair probabilities (thereby allowing for non-complementary genomes), here we solve for the mean fitness for the restricted case of perfect lesion repair.

The influence of horizontal gene transfer on the mean fitness of unicellular populations in static environments

This paper develops a mathematical model describing the influence that conjugation-mediated Horizontal Gene Transfer (HGT) has on the mutation-selection balance in an asexually reproducing population of unicellular, prokaryotic organisms. It is assumed that mutation-selection balance is reached in the presence of a fixed background concentration of antibiotic, to which the population must become resistant in order to survive. We analyze the behavior of the model in the limit of low and high antibiotic-induced first-order death rate constants, and find that the highest mean fitness is obtained at low rates of bacterial conjugation. As the rate of conjugation crosses a threshold, the mean fitness decreases to a minimum, and then rises asymptotically to a limiting value as the rate of conjugation becomes infinitely large. However, this limiting value is smaller than the mean fitness obtained in the limit of low conjugation rate. This dependence of the mean fitness on the conjugation rate is fairly small for the parameter ranges we have considered, and disappears as the first-order death rate constant due to the presence of antibiotic approaches zero. For large values of the antibiotic death rate constant, we have obtained an analytical solution for the behavior of the mean fitness that agrees well with the results of simulations. The results of this paper suggest that conjugation-mediated HGT has a slightly deleterious effect on the mean fitness of a population at mutation-selection balance. Therefore, we argue that HGT confers a selective advantage by allowing for faster adaptation to a new or changing environment. The results of this paper are consistent with the observation that HGT can be promoted by environmental stresses on a population.

Diploidy and the selective advantage for sexual reproduction in unicellular organisms

This paper develops mathematical models describing the evolutionary dynamics of both asexually and sexually reproducing populations of diploid unicellular organisms. We consider two forms of genome organization. In one case, we assume that the genome consists of two multi-gene chromosomes, while in the second case we assume that each gene defines a separate chromosome. If the organism has $ l $ homologous pairs that lack a functional copy of the given gene, then the fitness of the organism is $ kappa_l $. The $ kappa_l $ are assumed to be monotonically decreasing, so that $ kappa_0 = 1 > kappa_1 > kappa_2 > ... > kappa_{infty} = 0 $. For nearly all of the reproduction strategies we consider, we find, in the limit of large $ N $, that the mean fitness at mutation-selection balance is $ max{2 e^{-mu} - 1, 0} $, where $ N $ is the number of genes in the haploid set of the genome, $ epsilon $ is the probability that a given DNA template strand of a given gene produces a mutated daughter during replication, and $ mu = N epsilon $. The only exception is the sexual reproduction pathway for the multi-chromosomed genome. Assuming a multiplicative fitness landscape where $ kappa_l = alpha^{l} $ for $ alpha in (0, 1) $, this strategy is found to have a mean fitness that exceeds the mean fitness of all of the other strategies. Furthermore, while the other reproduction strategies experience a total loss of viability due to the steady accumulation of deleterious mutations once $ mu $ exceeds $ ln 2 $, no such transition occurs in the sexual pathway. The results of this paper demonstrate a selective advantage for sexual reproduction with fewer and much less restrictive assumptions than previous work.

A Dual Role for Sex?

The two classic theories for the existence of sexual replication are that sex purges deleterious mutations from a population, and that sex allows a population to adapt more rapidly to changing environments. These two theories have often been presented as opposing explanations for the existence of sex. Here, we develop and analyze evolutionary models based on the asexual and sexual replication pathways in Saccharomyces cerevisiae (Bakers yeast), and show that sexual replication can both purge deleterious mutations in a static environment, as well as lead to faster adaptation in a dynamic environment. This implies that sex can serve a dual role, which is in sharp contrast to previous theories.

The effect of the SOS response on the mean fitness of unicellular populations: A quasispecies approach

This paper develops a quasispecies model that incorporates the SOS response. We consider a unicellular, asexually replicating population of organisms, whose genomes consist of a single, double-stranded DNA molecule, i.e. one chromosome. We assume that repair of post-replication mismatched base-pairs occurs with probability $ lambda $, and that the SOS response is triggered when the total number of mismatched base-pairs exceeds $ l_S $. We further assume that the per-mismatch SOS elimination rate is characterized by a first-order rate constant $ kappa_{SOS} $. For a single fitness peak landscape where the master genome can sustain up to $ l $ mismatches and remain viable, this model is analytically solvable in the limit of infinite sequence length. The results, which are confirmed by stochastic simulations, indicate that the SOS response does indeed confer a fitness advantage to a population, provided that it is only activated when DNA damage is so extensive that a cell will die if it does not attempt to repair its DNA.

The Effect of Mutators on Adaptability in Time-Varying Fitness Landscapes

This Letter studies the quasispecies dynamics of a population capable of genetic repair evolving on a time-dependent fitness landscape. We develop a model that considers an asexual population of single-stranded, conservatively replicating genomes, whose only source of genetic variation is due to copying errors during replication. We consider a time-dependent, single-fitness-peak landscape where the master sequence changes by a single point mutation every time $ tau $. We are able to analytically solve for the evolutionary dynamics of the population in the point-mutation limit. In particular, our model provides an analytical expression for the fraction of mutators in the dynamic fitness landscape that agrees well with results from stochastic simulations.

A comparison of sexual and asexual replication strategies in a simplified model based on the yeast life cycle

This paper develops simplified mathematical models describing the mutation-selection balance for the asexual and sexual replication pathways in {it Saccharomyces cerevisiae}. We assume diploid genomes consisting of two chromosomes, and we assume that each chromosome is functional if and only if its base sequence is identical to some master sequence. The growth and replication of the yeast cells is modeled as a first-order process, with first-order growth rate constants that are determined by whether a given genome consists of zero, one, or two functional chromosomes. In the asexual pathway, we assume that a given diploid cell divides into two diploids. In the sexual pathway, we assume that a given diploid cell divides into two diploids, each of which then divide into two haploids. The resulting four haploids enter a haploid pool, where they grow and replicate until they meet another haploid with which to fuse. When the cost for sex is low, we find that the selective mating strategy leads to the highest mean fitness of the population, when compared to all of the other strategies. We also show that, at low to intermediate replication fidelities, sexual replication with random mating has a higher mean fitness than asexual replication, as long as the cost for sex is low. This is consistent with previous work suggesting that sexual replication is advantageous at high population densities, low replication rates, and intermediate replication fidelities. The results of this paper also suggest that {it S. cerevisiae} switches from asexual to sexual replication when stressed, because stressful growth conditions provide an opportunity for the yeast to clear out deleterious mutations from their genomes.

Selective advantage for sexual reproduction with random haploid fusion

This paper develops a simplified set of models describing asexual and sexual replication in unicel- lular diploid organisms. The models assume organisms whose genomes consist of two chromosomes, where each chromosome is assumed to be functional if it is equal to some master sequence $ sigma_0 $, and non-functional otherwise. The first-order growth rate constant, or fitness, of an organism, is determined by whether it has zero, one, or two functional chromosomes in its genome. For a population replicating asexually, a given cell replicates both of its chromosomes, and splits its genetic material evenly between the two cells. For a population replicating sexually, a given cell first divides into two haploids, which enter a haploid pool, fuse into diploids, and then divide via the normal mitotic process. Haploid fusion is modeled as a second-order rate process. When the cost for sex is small, as measured by the ratio of the characteristic haploid fusion time to the characteristic growth time, we find that sexual replication with random haploid fusion leads to a greater mean fitness for the population than a purely asexual strategy. However, independently of the cost for sex, we find that sexual replication with a selective mating strategy leads to a higher mean fitness than the random mating strategy. This result is based on the assumption that a selective mating strategy does not have any additional time or energy costs over the random mating strategy, an assumption that is discussed in the paper. The results of this paper are consistent with previous studies suggesting that sex is favored at intermediate mutation rates, for slowly replicating organisms, and at high population densities.