Reproductive Value and Fluctuating Selection in an Age-Structured Population

Fluctuations in age structure caused by environmental stochasticity create autocorrelation and transient fluctuations in both population size and allele frequency, which complicate demographic and evolutionary analyses. Following a suggestion of Fisher, we show that weighting individuals of different age by their reproductive value serves as a filter, removing temporal autocorrelation in population demography and evolution due to stochastic age structure. Assuming weak selection, random mating, and a stationary distribution of environments with no autocorrelation, we derive a diffusion approximation for evolution of the reproductive value weighted allele frequency. The expected evolution obeys an adaptive topography defined by the long-run growth rate of the population. The expected fitness of a genotype is its Malthusian fitness in the average environment minus the covariance of its growth rate with that of the population. Simulations of the age-structured model verify the accuracy of the diffusion approximation. We develop statistical methods for measuring the expected selection on the reproductive value weighted allele frequency in a fluctuating age-structured population.THE evolutionary dynamics of age-structured populations were formalized by Charlesworth (1980, 1994) and Lande (1982) on the basis of earlier ideas of Fisher (1930, 1958), Medawar (1946, 1952), and Hamilton (1966), showing that the strength of selection on genes affecting the vital rates of survival or fecundity depends on their age of action (reviewed by de Jong 1994; Charlesworth 2000). Fisher defined the reproductive value of individuals of a given age as their expected contribution to future population growth, determined by the age-specific vital rates. This has the property that in a constant environment the total reproductive value in a population always increases at a constant rate. The total population size, however, undergoes transient fluctuations as the stable age distribution is approached, and the total population size only asymptotically approaches a constant growth rate (Caswell 2001).Environmental stochasticity creates continual fluctuations in age structure, producing temporal autocorrelation in population size and in allele frequencies, which seriously complicate demographic and evolutionary analyses. Fisher (1930, 1958, p. 35) suggested for analysis of genetic evolution that individuals should be weighted by their reproductive value to compensate for deviations from the stable age distribution. Here we apply this suggestion to study weak fluctuating selection in an age-structured population in a stochastic environment.One of the central conceptual paradigms of evolutionary biology was described by Wright (1932). His adaptive topography represents a population as a point on a surface of population mean fitness as a function of allele frequencies. Assuming weak selection, random mating, and loose linkage (implying approximate Hardy–Weinberg equilibrium within loci and linkage eqilibrium among loci), natural selection in a constant environment causes the population to evolve uphill of the mean fitness surface (Wright 1937, 1945, 1969; Arnold et al. 2001; Gavrilets 2004). Evolution by natural selection thus tends to increase the mean fitness of a population in a constant environment.Lande (2007, 2008) generalized Wright''s adaptive topography to a stochastic environment, allowing density-dependent population growth but assuming density-independent selection, showing that the expected evolution maximizes the long-run growth rate of the population at low density, . Here r is population growth rate at low density in the average environment and is the environmental variance in population growth rate among years, which are standard parameters in stochastic demography (Cohen 1977, 1979; Tuljapurkar 1982; Caswell 2001; Lande et al. 2003). In this model of stochastic evolution the adaptive topography describing the expected evolution is derived by expressing r and as functions of allele frequencies with parameters being the mean Malthusian fitnesses of the genotypes and their temporal variances and covariances. These results are based on diffusion approximations for the coupled stochastic processes of population size and allele frequencies in a fluctuating environment.Diffusion approximations are remarkably accurate for many problems in evolution and ecology (Crow and Kimura 1970; Lande et al. 2003). Because a diffusion process is subject to white noise with no temporal autocorrelation, the approximation is most accurate if the noise in the underlying biological process is approximately uncorrelated among years. Despite temporal autocorrelation in total population size produced by age-structure fluctuations, the stochastic demography of age-structured populations over timescales of a generation or more can nevertheless be accurately approximated by a diffusion process (Tuljapurkar 1982; Lande and Orzack 1988; Engen et al. 2005a, 2007). The success of the diffusion approximation for total population size occurs because the noise in the total reproductive value is nearly white, with no temporal autocorrelation to first order, and the log of total population size fluctuates around the log of reproductive value with a return time to equilibrium on the order of a few generations (Engen et al. 2007). Hence the diffusion approximation is well suited to describe the stochastic dynamics of total reproductive value as well as total population size.This article extends Lande''s (2008) model of fluctuating selection without age structure by deriving a diffusion approximation for the evolution of an age-structured population in a stochastic environment. Assuming weak selection at all ages, random mating, and a stationary distribution of environments with no temporal autocorrelation, we show that the main results of the model remain valid, provided that the model parameters are expressed in terms of means, variances, and covariances of age-specific vital rates and that allele frequencies are defined by weighting individuals of different age by their reproductive value, as suggested by Fisher (1930, 1958). We perform simulations to verify the accuracy of the diffusion approximation and outline statistical methods for estimating the expected selection acting on the reproductive value weighted allele frequency.     

Global responses of Aliivibrio salmonicida to hydrogen peroxide as revealed by microarray analysis

Aliivibrio salmonicida causes "cold-water vibriosis" (or "Hitra disease") in fish, including marine-reared Atlantic salmon. During development of the disease the bacterium will encounter macrophages with antibacterial activities such as production of damaging reactive oxygen species (ROS). To defend itself the bacterium will presumably start producing detoxifying enzymes, reducing agents, and proteins involved in DNA and protein repair systems. Even though responses to oxidative stress are well studied for a few model bacteria, little work has been done in general to explain how important groups of pathogens, like members of the Vibrionaceae family, can survive at high levels of ROS. We have used bioinformatic tools and microarray to study how A. salmonicida responds to hydrogen peroxide (H(2)O(2)). First, we used the recently published genome sequence to predict potential binding sites for OxyR (H(2)O(2) response regulator). The computer-based search identified OxyR sites associated with 20 single genes and 8 operons, and these predictions were compared to experimental data from Northern blot analysis and microarray analysis. In general, OxyR binding site predictions and experimental results are in agreement. Up- and down regulated genes are distributed among all functional gene categories, but a striking number of ≥2 fold up regulated genes encode proteins involved in detoxification and DNA repair, are part of reduction systems, or are involved in carbon metabolism and regeneration of NADPH. Our predictions and -omics data corroborates well with findings from other model bacteria, but also suggest species-specific gene regulation.     

High sensitivity assays for docetaxel and paclitaxel in plasma using solid-phase extraction and high-performance liquid chromatography with UV detection

Background  

The taxanes paclitaxel and docetaxel have traditionally been used in high doses every third week in the treatment of cancer. Lately there has been a trend towards giving weekly low doses to improve the therapeutic index. This article describes the development of high performance liquid chromatographic (HPLC) methods suitable for monitoring taxane levels in patients, focusing on patients receiving low-dose therapy.     

Comparison of SH3 and SH2 domain dynamics when expressed alone or in an SH(3+2) construct: the role of protein dynamics in functional regulation

Protein dynamics play an important role in protein function and regulation of enzymatic activity. To determine how additional interactions with surrounding structure affects local protein dynamics, we have used hydrogen exchange and mass spectrometry to investigate the SH2 and SH3 domains of the protein tyrosine kinase Hck. Exchange rates of isolated Hck SH3 and SH2 domains were compared with rates for the same domains when part of a larger SH(3+2) construct. Increased deuterium incorporation was observed for the SH3 domain in the joint construct, particularly near the SH2 interface and the short sequence that connects SH3 to SH2, implying greater flexibility of SH3 when it is part of SH(3+2). Slow cooperative unfolding of the SH3 domain occurred at the same rate in isolated SH3 as in the SH(3+2) construct, suggesting a functional significance for this unfolding. The SH2 domain displayed relatively smaller changes in flexibility when part of the SH(3+2) construct. These results suggest that the domains influence each other. Further, our results imply a link between functional regulation and structural dynamics of SH3 and SH2 domains.     

Regulation of c-Fes tyrosine kinase activity by coiled-coil and SH2 domains: analysis with Saccharomyces cerevisiae

The c-Fes protein-tyrosine kinase regulates the growth and differentiation of diverse cell types, including myeloid hematopoietic cells, vascular endothelial cells, and neurons. Structurally, Fes is composed of a unique N-terminal region with coiled-coil oligomerization motifs, followed by SH2 and kinase domains. Although Fes kinase activity is tightly regulated in cells, the structural basis for its negative regulation is not clear. In this report, c-Fes was expressed in Saccharomyces cerevisiae to determine whether regulation is kinase-intrinsic or dependent upon protein factors found in mammalian cells. Wild-type Fes kinase activity was completely repressed in yeast and did not affect cell growth. Mutation or deletion of the more N-terminal c-Fes coiled-coil domain reversed negative regulation, leading to strong kinase activation and suppression of yeast cell growth. Similarly, replacement of the wild-type SH2 domain with that of v-Src induced strong kinase activation and the growth-inhibitory phenotype. Immunoblotting with phosphospecific antibodies shows that activation of Fes by either mechanism induced autophosphorylation of the activation loop tyrosine residue (Tyr 713). These data support the idea that Fes naturally adopts an inactive conformation in vivo, and that maintenance of the inactive structure requires the coiled-coil and SH2 domains.     

Estimating density dependence from population time series using demographic theory and life-history data

For populations with a density-dependent life history reproducing at discrete annual intervals, we analyze small or moderate fluctuations in population size around a stable equilibrium, which is applicable to many vertebrate populations. Using a life history having age at maturity alpha, with stochasticity and density dependence in adult recruitment and mortality, we derive a linearized autoregressive equation with time lags from 1 to alpha yr. Contrary to current interpretations, the coefficients corresponding to different time lags in the autoregressive dynamics are not simply measures of delayed density dependence but also depend on life-history parameters. The theory indicates that the total density dependence in a life history, D, should be defined as the negative elasticity of population growth rate per generation with respect to change in population size, [Formula: see text], where lambda is the asymptotic multiplicative growth rate per year, T is the generation time, and N is adult population size. The total density dependence in the life history, D, can be estimated from the sum of the autoregression coefficients. We estimate D in populations of seven vertebrate species for which life-history studies and unusually long time series of complete population censuses are available. Estimates of D were statistically significant and large, on the order of 1 or higher, indicating strong density dependence in five of the seven species. We also show that life history can explain the qualitative features of population autocorrelation functions and power spectra and observations of increasing empirical variance in population size with increasing length of time series.     

Analyzing spatial structure of communities using the two-dimensional poisson lognormal species abundance model

The joint spatial and temporal fluctuations in the community structure of tropical butterflies are analyzed by fitting the bivariate Poisson lognormal distribution to a large number of observations in space and time. By applying multivariate dependent diffusions for describing the fluctuations in the abundances, the environmental variance is estimated to be very large and so is the strength of local density regulation. The variance in the lognormal species abundance distribution is partitioned into components expressing the heterogeneity between the species, independent noise components for the different species, a demographic stochastic component, and a component due to overdispersion in the sampling. In disagreement with the neutral theory, the estimates show that the heterogeneity component is the dominating one, representing 81% of the total variance in the lognormal model. Different spatial components of diversity, the alpha, beta, and gamma diversity, are also estimated. The spatial scale of the autocorrelation function for the community is of order 1 km, while sampling of a quadrat would need to be 10 km on a side to yield the total diversity for the community.     

The Approach to Sample Acquisition and Its Impact on the Derived Human Fecal Microbiome and VOC Metabolome

Recent studies have illustrated the importance of the microbiota in maintaining a healthy state, as well as promoting disease states. The intestinal microbiota exerts its effects primarily through its metabolites, and metabolomics investigations have begun to evaluate the diagnostic and health implications of volatile organic compounds (VOCs) isolated from human feces, enabled by specialized sampling methods such as headspace solid-phase microextraction (hSPME). The approach to stool sample collection is an important consideration that could potentially introduce bias and affect the outcome of a fecal metagenomic and metabolomic investigation. To address this concern, a comparison of endoscopically collected (in vivo) and home collected (ex vivo) fecal samples was performed, revealing slight variability in the derived microbiomes. In contrast, the VOC metabolomes differ widely between the home collected and endoscopy collected samples. Additionally, as the VOC extraction profile is hyperbolic, with short extraction durations more vulnerable to variation than extractions continued to equilibrium, a second goal of our investigation was to ascertain if hSPME-based fecal metabolomics studies might be biased by the extraction duration employed. As anticipated, prolonged extraction (18 hours) results in the identification of considerably more metabolites than short (20 minute) extractions. A comparison of the metabolomes reveals several analytes deemed unique to a cohort with the 20 minute extraction, but found common to both cohorts when the VOC extraction was performed for 18 hours. Moreover, numerous analytes perceived to have significant fold change with a 20 minute extraction were found insignificant in fold change with the prolonged extraction, underscoring the potential for bias associated with a 20 minute hSPME.     

Serological cloning of cancer/testis antigens expressed in prostate cancer using cDNA phage surface display

Serological cloning of tumor-associated antigens (TAAs) using patient autoantibodies and tumor cDNA expression libraries (SEREX) has identified a wide array of tumor proteins eliciting B-cell responses in patients. However, alternative cloning strategies with the possibility of high throughput analysis of patient sera and tumor libraries may be of interest. We explored the pJuFo phage surface display system, allowing display of recombinant tumor proteins on the surface of M13 filamentous phage, for cloning of TAAs in prostate cancer (PC). Control experiments established that after a few rounds of selection on immobilized specific IgG, a high degree of enrichment of seroreactive clones was achieved. With an increasing number of selection rounds, a higher yield of positive clones was offset by an apparent loss of diversity in the repertoire of selected clones. Using autologous patient serum IgG in a combined biopanning and immunoscreening approach, we identified 13 different TAAs. Three of these (NY-ESO-1, Lage-1, and Xage-1) were known members of the cancer/testis family of TAAs, and one other protein had previously been isolated by SEREX in cancer types other than PC. Specific IgG responses against NY-ESO-1 were found in sera from 4/20 patients with hormone refractory PC, against Lage-1 in 3/20, and Xage-1 in 1/20. No reactivity against the remaining proteins was detected in other PC patients, and none of the TAAs reacted with serum from healthy subjects. The results demonstrate that phage surface display combined with postselection immunoscreening is suitable for cloning a diverse repertoire of TAAs from tumor tissue cDNA libraries. Furthermore, candidate TAAs for vaccine development of PC were identified.