Detection of Patient Subgroups with Differential Expression in Omics Data: A Comprehensive Comparison of Univariate Measures

Detection of yet unknown subgroups showing differential gene or protein expression is a frequent goal in the analysis of modern molecular data. Applications range from cancer biology over developmental biology to toxicology. Often a control and an experimental group are compared, and subgroups can be characterized by differential expression for only a subgroup-specific set of genes or proteins. Finding such genes and corresponding patient subgroups can help in understanding pathological pathways, diagnosis and defining drug targets. The size of the subgroup and the type of differential expression determine the optimal strategy for subgroup identification. To date, commonly used software packages hardly provide statistical tests and methods for the detection of such subgroups. Different univariate methods for subgroup detection are characterized and compared, both on simulated and on real data. We present an advanced design for simulation studies: Data is simulated under different distributional assumptions for the expression of the subgroup, and performance results are compared against theoretical upper bounds. For each distribution, different degrees of deviation from the majority of observations are considered for the subgroup. We evaluate classical approaches as well as various new suggestions in the context of omics data, including outlier sum, PADGE, and kurtosis. We also propose the new FisherSum score. ROC curve analysis and AUC values are used to quantify the ability of the methods to distinguish between genes or proteins with and without certain subgroup patterns. In general, FisherSum for small subgroups and -test for large subgroups achieve best results. We apply each method to a case-control study on Parkinson''s disease and underline the biological benefit of the new method.     

THE GENOMIC TRAJECTORY OF HYBRID SWARMS: OUTCOMES OF REPEATED CROSSES BETWEEN POPULATIONS OF TIGRIOPUS CALIFORNICUS

Introgressive hybridization between genetically divergent populations is an important evolutionary process. The degree to which repeated hybridization events between the same parental taxa lead to similar genomic outcomes is unknown. This study addressed this question by following genomic trajectories of replicate hybrid swarms of the copepod Tigriopus californicus over many generations of free mating. Swarm composition was determined both by differential reproductive success of founder individuals and subsequent selection on hybrid genotypes. For one cross, between two populations showing differential fitness in the laboratory and no hybrid breakdown, the genetic trajectory was highly repeatable: replicates rapidly became dominated by alleles from the fitter parent. In a second cross, between two populations showing similar fitness and significant F2 hybrid breakdown, alleles from alternative populations dominated different replicates. Swarms exhibited a general temporal trend of decreasing cytonuclear mismatch. Some patterns of differential introgression across the genome were strikingly congruent amongst swarm replicates, both within and between cross types, and reflected patterns of segregation distortion previously observed within controlled crosses between the same parental populations. Differences in heterozygosity between the sexes, and evidence for a previously suspected sex‐distortion locus, suggest that complex interactions between sex and genotype influence hybrid swarm outcome.     

Explaining the coexistence of asexuals with their sexual progenitors: no evidence for general-purpose genotypes in obligate parthenogens of the peach-potato aphid, Myzus persicae

In parthenogens, selection acts on entire genotypes rather than individual alleles. The general‐purpose genotype hypothesis (GPG) predicts that temporally variable environments select for clones with broad ecological tolerances. These general‐purpose genotypes should exhibit low fitness variance and high geometric mean fitness across environments. We tested this hypothesis by comparing the fitness of obligately and cyclically parthenogenetic genotypes of the peach‐potato aphid, Myzus persicae, on three unrelated host plants. We found genetic variation for the relative performance on different hosts, but no difference in geometric mean fitness between obligate and cyclical parthenogens. Thus, for an environmental variable of major importance to aphids, the GPG hypothesis was not supported. In addition, the lack of an overall fitness difference between reproductive modes suggests that cyclical parthenogens incur no cost of polyphenism, but neither can they compensate for the cost of sex during the parthenogenetic phase of their life cycle.     

Wealth, status, and fitness: a historical study of Norwegians in variable environments

Wealth and status covary with lifetime reproductive success in preindustrial human populations. Local ecology is likely to modify this association, but details of this presumed relationship are not yet known. We sought to determine whether local ecology modifies the relationship between status and fitness (number of grandchildren). Our approach to the problem was to measure variation in fitness relative to status (landless or with land) and to local ecology (inland versus coastal communities). We also analyzed life history traits that might explain observed variations in fitness. Our results confirm previous findings that both status (landless=9.9 vs. with land=16.5) and ecology (inland=12.3 vs. coast=14.1) affect the number of grandchildren produced by a female in pre-industrial society. We also found that the differences in number of children between the status groups were less pronounced on the coast (landless=12.0 vs. with land=16.1) than inland (landless=7.8 vs. with land=16.8). Our findings are novel because they suggest that the fitness consequences of human status may depend on details of local ecology. We discuss four different mechanisms that could account for these fitness differences: (1) differential reproductive rate of mothers, (2) differential marriage rate of children (3) differential survival rate of children, and (4) different social practices (breastfeeding, inheritance of property and diet).     

Optimization of inclusive fitness

The first fully explicit argument is given that broadly supports a widespread belief among whole-organism biologists that natural selection tends to lead to organisms acting as if maximizing their inclusive fitness. The use of optimization programs permits a clear statement of what this belief should be understood to mean, in contradistinction to the common mathematical presumption that it should be formalized as some kind of Lyapunov or even potential function. The argument reveals new details and uncovers latent assumptions. A very general genetic architecture is allowed, and there is arbitrary uncertainty. However, frequency dependence of fitnesses is not permitted. The logic of inclusive fitness immediately draws together various kinds of intra-genomic conflict, and the concept of 'p-family' is introduced. Inclusive fitness is thus incorporated into the formal Darwinism project, which aims to link the mathematics of motion (difference and differential equations) used to describe gene frequency trajectories with the mathematics of optimization used to describe purpose and design. Important questions remain to be answered in the fundamental theory of inclusive fitness.     

Maintenance of clonal diversity in Dipsa bifurcata (Fallén, 1810) (Diptera: Lonchopteridae). II. Diapause stabilizes clonal coexistence

We analyze a selection model analogous to a one-locus, two-allele haploid system that can explain recurrent seasonal changes in diversity for communities with diapausing species or populations with diapausing clones. The model demonstrates the potential influence of differential diapause on the stability of species and clonal coexistence and, by extension, on the maintenance of genetic polymorphism in general. Using estimates of clonal fitness values from populations of the parthenogenetic spear-winged fly Dipsa bifurcata (Fallén, 1810) (Diptera: Lonchopteridae), the model explains the long-term stable oscillation of clonal frequencies exhibited by these populations. In general, clones or species that share the same spatial habitat can persist in stable coexistence if there are differences not only in their temporarily fluctuating fitness values but also in their dormancy patterns.     

Canalisation in the wild: effects of developmental conditions on physiological traits are inversely linked to their association with fitness

Ecological conditions affect fitness, but mechanisms causing such effects are not well known, while evolved responses to environmental variation may depend on the underlying mechanisms. Consequences of environmental conditions vary strongly between traits, but a framework to interpret such variation is lacking. We propose that variation in trait response may be explained by differential canalisation, with traits with larger fitness effects showing weaker responses to environmental perturbations due to preferential resource allocation to such traits. We tested the canalisation hypothesis using brood size manipulation in wild jackdaw nestlings in which we measured eight physiological traits (mainly oxidative stress markers), and two feather traits. For each trait, we estimated manipulation response and association with fitness (over‐winter survival). As predicted, a strong negative correlation emerged between manipulation response and association with fitness (r =?0.76). We discuss the consequences of differential trait canalisation for the study of mechanisms mediating environmental effects on fitness.     

Effects of the soil microbiome on the demography of two annual prairie plants

1. Both mutualistic and pathogenic soil microbes are known to play important roles in shaping the fitness of plants, likely affecting plants at different life cycle stages.
2. In order to investigate the differential effects of native soil mutualists and pathogens on plant fitness, we compared survival and reproduction of two annual tallgrass prairie plant species (Chamaecrista fasciculata and Coreopsis tinctoria) in a field study using 3 soil inocula treatments containing different compositions of microbes. The soil inocula types included fresh native whole soil taken from a remnant prairie containing both native mutualists and pathogens, soil enhanced with arbuscular mycorrhizal (AM) fungi derived from remnant prairies, and uninoculated controls.
3. For both species, plants inoculated with native prairie AM fungi performed much better than those in uninoculated soil for all parts of the life cycle. Plants in the native whole prairie soil were either generally similar to plants in the uninoculated soil or had slightly higher survival or reproduction.
4. Overall, these results suggest that native prairie AM fungi can have important positive effects on the fitness of early successional plants. As inclusion of prairie AM fungi and pathogens decreased plant fitness relative to prairie AM fungi alone, we expect that native pathogens also can have large effects on fitness of these annuals. Our findings support the use of AM fungi to enhance plant establishment in prairie restorations.

     

Effects of selective neutrality on the evolution of molecular species

We introduce a model of evolution on a fitness landscape possessing a tunable degree of neutrality. The model allows us to study the general properties of molecular species undergoing neutral evolution. We find that a number of phenomena seen in RNA sequence-structure maps are present also in our general model. Examples are the occurrence of ''common'' structures that occupy a fraction of the genotype space which tends to unity as the length of the genotype increases, and the formation of percolating neutral networks that cover the genotype space in such a way that a member of such a network can be found within a small radius of any point in the space. We also describe a number of new phenomena that appear to be general properties of systems possessing selective neutrality. In particular, we show that the maximum fitness attained during the adaptive walk of a population evolving on such a fitness landscape increases with increasing degree of neutrality, and is directly related to the fitness of the most fit percolating network.     

Bet-hedging--a triple trade-off between means, variances and correlations

In unpredictably varying environments, strategies that have a reduced variance in fitness can invade a population consisting of individuals that on average do better. Such strategies 'hedge their evolutionary bets' against the variability of the environment. The idea of bet-hedging arises from the fact that appropriate measure of long-term fitness is sensitive to variance, leading to the potential for strategies with a reduced mean fitness to invade and increase in frequency. Our aim is to review the conceptual foundation of bet-hedging as a mechanism that influences short- and long-term evolutionary processes. We do so by presenting a general model showing how evolutionary changes are affected by variance in fitness and how genotypic variance in fitness can be separated into variance in fitness at the level of the individuals and correlations in fitness among them. By breaking down genotypic fitness variance in this way the traditional divisions between conservative and diversified strategies are more easily intuited, and it is also shown that this division can be considered a false dichotomy, and is better viewed as two extreme points on a continuum. The model also sheds light on the ideas of within- and between-generation bet-hedging, which can also be generalized to be seen as two ends of a different continuum. We use a simple example to illustrate the virtues of our general model, as well as discuss the implications for systems where bet-hedging has been invoked as an explanation.     

EVOLUTION IN FLUCTUATING ENVIRONMENTS: DECOMPOSING SELECTION INTO ADDITIVE COMPONENTS OF THE ROBERTSON–PRICE EQUATION

We analyze the stochastic components of the Robertson–Price equation for the evolution of quantitative characters that enables decomposition of the selection differential into components due to demographic and environmental stochasticity. We show how these two types of stochasticity affect the evolution of multivariate quantitative characters by defining demographic and environmental variances as components of individual fitness. The exact covariance formula for selection is decomposed into three components, the deterministic mean value, as well as stochastic demographic and environmental components. We show that demographic and environmental stochasticity generate random genetic drift and fluctuating selection, respectively. This provides a common theoretical framework for linking ecological and evolutionary processes. Demographic stochasticity can cause random variation in selection differentials independent of fluctuating selection caused by environmental variation. We use this model of selection to illustrate that the effect on the expected selection differential of random variation in individual fitness is dependent on population size, and that the strength of fluctuating selection is affected by how environmental variation affects the covariance in Malthusian fitness between individuals with different phenotypes. Thus, our approach enables us to partition out the effects of fluctuating selection from the effects of selection due to random variation in individual fitness caused by demographic stochasticity.     

Models of general frequency-dependent selection and mating-interaction effects and the analysis of selection patterns in Drosophila inversion polymorphisms

We investigate mechanisms of balancing selection by extending two deterministic models of selection in a one-locus two-allele genetic system to allow for frequency-dependent fitnesses. Specifically we extend models of constant selection to allow for general frequency-dependent fitness functions for sex-dependent viabilities and multiplicative fertilities, while non-multiplicative mating-dependent components remain constant. We compute protected polymorphism conditions that take the form of harmonic means involving both the frequency- and the mating-dependent parameters. This allows for a direct comparison of the equilibrium properties of the frequency-dependent models with those of the constant models and for an analysis of equilibrium of the general model of constant fertility. We then apply the theory to analyze the maintenance of inversion polymorphisms in Drosophila subobscura and D. pseudoobscura, for which data on empirical fitness component estimates are available in the literature. Regression on fitness estimates obtained at different starting frequencies enables us to implement explicit fitness functions in the models and therefore to perform complete studies of equilibrium and stability for particular sets of data. The results point to frequency dependence of fitness components as the main mechanism responsible for the maintenance of the inversion polymorphisms considered, particularly in relation to heterosis, although we also discuss the contribution of other selection mechanisms.     

Structural cost of shoot modules and its implications on plant potential fitness in a Mediterranean perennial shrub, Retama sphaerocarpa (L.) Boiss

This paper introduces a methodology to analyse the structural costs on plant potential fitness, empirically exemplified in the hierarchical shoot system of a Mediterranean perennial plant, Retama sphaerocarpa (L.) Boiss. During growing season every year (March-August), the terminal shoot (which is the basic unit of growth) develops inflorescences, flowers and fruits, as well as new shoots (first-, second- and third-order branching shoots) which have the potential to "behave" as terminal shoots in the following year. Different morphological and demographical aspects of the modules within the terminal shoot were measured in 100 terminal shoots selected from different plants of a natural population of R. sphaerocarpa. Complementary samples of 100 shoots of different branching orders were collected to obtain biomass estimations of the terminal shoots. We propose a simple procedure to estimate structural cost (biomass investment) on plant potential fitness (flowering buds) as a methodology for interpreting and comparing the consequences on fitness of different plant growth patterns. The results of this study exemplify how differential allocation patterns among plant structural modules, depending on their position within the shoot system, can be quantified to estimate their influence upon plant potential fitness.     

Imperfect Vertical Transmission of the Endophyte <Emphasis Type="Italic">Neotyphodium</Emphasis> in Exotic Grasses in Grasslands of the Flooding Pampa

Cool-season grasses establish symbioses with vertically transmitted Neotyphodium endophytes widespread in nature. The frequency of endophyte-infected plants in closed populations (i.e., without migrations) depends on both the differential fitness between infected and non-infected plants, and the endophyte-transmission efficiency. Most studies have been focused on the first mechanism ignoring the second. Infection frequency and endophyte transmission from vegetative tissues to seeds were surveyed in two grasses growing in vegetation units that differ in flood and grazing regimes, and soil salinity. Transmission efficiency and infection frequency for tall fescue did not vary significantly and were 0.98 and 1.00, respectively. For Italian ryegrass, transmission efficiency and infection frequency were 0.88 and 0.57 in humid prairies, and 0.96 and 0.96 in the other vegetation units. Only in humid mesophytic meadows, the observed pattern was irrespective of the presence or absence of grazers. Our results suggest that selection forces for endophyte infection are different for both species. Imperfect transmission was only compensated in tall fescue through an increased fitness of infected plants. Interpreting variations of infection frequency only in terms of differential fitness can be misleading, considering that endophyte transmission can be imperfect and variable in nature. Therefore, this study highlights the importance of measuring transmission efficiency.     

Exploiting the Adaptation Dynamics to Predict the Distribution of Beneficial Fitness Effects

Adaptation of asexual populations is driven by beneficial mutations and therefore the dynamics of this process, besides other factors, depends on the distribution of beneficial fitness effects. It is known that on uncorrelated fitness landscapes, this distribution can only be of three types: truncated, exponential and power law. We performed extensive stochastic simulations to study the adaptation dynamics on rugged fitness landscapes, and identified two quantities that can be used to distinguish the underlying distribution of beneficial fitness effects. The first quantity studied here is the fitness difference between successive mutations that spread in the population, which is found to decrease in the case of truncated distributions, remains nearly a constant for exponentially decaying distributions and increases when the fitness distribution decays as a power law. The second quantity of interest, namely, the rate of change of fitness with time also shows quantitatively different behaviour for different beneficial fitness distributions. The patterns displayed by the two aforementioned quantities are found to hold good for both low and high mutation rates. We discuss how these patterns can be exploited to determine the distribution of beneficial fitness effects in microbial experiments.     

Multilocus Behavior in Random Environments I. Random Levene Models

In this paper the consequences of natural selection acting on several loci simultaneously in a spatially fluctuating environment are described. The fitnesses of the genotypes are assumed to be additive both within and between loci. The environment is assumed to be made up of a very large (effectively infinite) number of patches in which fitnesses are assigned at random. The resulting deterministic model is called a Random Levene Model and its properties are approximate by a system of differential equations. The main equilibrium properites are that (1) the linkage disequilibrium is zero and (2) the correlations in fitness between alleles at different loci are the principle determinants of the dynamic inter-locus interactions. Although there is no epistasis as conventionally defined, the equilibrium state at the two loci are highly interdependent, the governing principle being that two alleles at different loci whose fitness are negatively correlated across environments have a higher overall fitness due to the reduction in their variance in fitness through the negative correlation. When a large number of loci are considered, they naturally fall into correlation groupings which lead to an enhanced likelihood for polymorphism over that predicted by single-locus theory.     

Increasing floral diversity for selective enhancement of biological control agents: A double-edged sward?

Floral resource subsidies can have differential effects on insect herbivores compared with the herbivores’ natural enemies. While the nectar of many plant species enhances parasitoid fitness, it may also increase damage by herbivores. This may occur as a result of enhanced herbivore fitness or by enhancing fourth-trophic-level processes, possibly disrupting a trophic cascade as a result. The responses of different arthropod guilds to different floral resource subsidies were compared using Plutella xylostella (Hyponomeutidae), its parasitoid Diadegma semiclausum (Ichneumonidae) and data from two other published herbivore–parasitoid systems. These were Dolichogenidea tasmanica (Braconidae) and its host Epiphyas postvittana, and Copidosoma koehleri (Encyrtidae) and its host Phthorimaea operculella. The parasitoids and hosts in the three systems exhibited differential responses to the nectar sources. The differential response was not explained by morphology, demonstrating that physical access to nectaries alone does not determine the potential of flowers as a food source. For some flowering plants, enhancement of herbivore and parasitoid fitness occurred. Other flowering plants, such as buckwheat and phacelia, conferred a selective enhancement on parasitoids by increasing only their fitness. More effective conservation biocontrol may be achieved by the provision of selective floral resources. Attempts to ‘engineer’ agroecosystems to enhance biological control require an extensive knowledge of the ecology of the herbivore, its enemies and their interactions with potential resource subsidies.     

Predation Determines Different Selective Pressure on Pea Aphid Host Races in a Complex Agricultural Mosaic

Field assessments were conducted to examine the interplay between host plant and predation in complex agricultural mosaic on pea aphid clover and alfalfa races. In one experiment, we examined the relative fitness on clover race (CR) and alfalfa race (AR) pea aphids on broad bean, red clover and alfalfa alone. But because clover is typically grown in a more complex agricultural mosaic with alfalfa and broad bean, a second experiment was conducted to assess the fitness consequences under predation in a more complex agricultural field setting that also included potential apparent competition with AR pea aphids. In a third experiment we tested for the effect of differential host race density on the fitness of the other host race mediated by a predator effect. CR pea aphids always had fitness losses when on broad bean (had lower fitness on broad bean relative to red clover) and fitness benefits when on red clover (higher fitness on red clover relative to broad bean), whether or not in apparent competition with alfalfa race aphids on bean and alfalfa. AR suffered fitness loss on both alfalfa and bean in apparent competition with CR on clover. Therefore we can conclude that the predation rate between host races was highly asymmetrical. The complexity of the agricultural mosaic thus can influence prey selection by predators on different host plants. These may have evolutionary consequences through context dependent fitness benefits on particular host plants.