Genetic Drift in Clines Which Are Maintained by Migration and Natural Selection

Genetic drift will cause a migration-selection cline to wobble about its expected position. A rough linear approximation is developed, valid when local populations are large. This is used to calculate effects of genetic drift on clines in a stepping-stone model with abrupt and with gradual changes of selection coefficients at a single haploid locus. Among the quantities calculated are measures of slope, standardized variation of gene frequencies around their expected values, and correlation among neighboring populations with respect to deviations from the expected gene frequencies. These quantities appear to be primarily functions of Ns and Nm for a given pattern of selection. Computer simulation gives rough confirmation of these results. Standardized variances of gene frequencies and correlation of neighbors differ along the cline in the case of smooth changes in selection. In no case is pathological behavior of gene frequency deviations found near the boundaries of selective regions. Local behavior of gene frequences of nearby colonies is approximately predicted by a simple adaptation of the stepping-stone theory of Kimura and Weiss. Approximate measures of the lateral variation of the midpoint of a cline and the probability of non-monotonicity are also calculated and discussed.     

Correlations in Multi-Locus Genetic Systems: A Mathematical Model

A spin model with parallels to a multi-locus genetic model is presented which makes it possible to calculate the correlation between allelic states at any two loci in a population at equilibrium. The main features are: (1) The decay of correlation with distance may be expressed essentially as a linear combination of two exponentials, one of which dominates when the two loci are sufficiently far apart. (2) The correlation between two loci a specified distance apart is increased as the number of loci in the entire system increases. The results are compared with those of other theoretical models and discussed in the light of available experimental data. Possible ways of generalizing the model are outlined. However, additional experimental data is clearly needed to indicate the genetic relevance of work of this nature.     

Equilibrium between Genetic Drift and Migration at Various Mutation Rates: Simulation Analysis

Rates of approach to equilibrium values of F _ST /R _ST at various mutation rates and using different mutation models (K-allele model KAM and stepwise model SMM) were analyzed numerically for the finite island model and the one-dimensional stepping stone models of migration, using simulation. In the island model of migration and the KAM mutation model, the rate of approach to the equilibrium F _ST value was appreciably higher and the equilibrium value was almost twofold lower at μ (mutation rate) = m (migration rate) than at μ ≪ m. In the one-dimensional stepping stone model of migration and the KAM model of mutation, the mutation rate significantly affected both the rate of approaching F _ST equilibrium and the equilibrium value. In both island and one-dimensional stepping stone models and SMM, R _ST was not influenced by various mutation rates. The rate of approach to the equilibrium values of both F _ST and R _ST was lower for the stepping stone model than to the island model. R _ST was rather resistant to deviations from the SMM mutation model. __________ Translated from Genetika, Vol. 41, No. 9, 2005, pp. 1283–1288. Original Russian Text Copyright ? 2005 by Efremov.     

Dynamics and Equilibrium Behavior of Cytonuclear Disequilibria under Genetic Drift, Mutation, and Migration

A simple two-locus drift model for cytonuclear systems is developed, in which the stochastic dynamics of cytonuclear genotypic frequencies are specified. Random union of zygotes is assumed. Trajectories for the first two moments of both genotypic and allelic disequilibria are given under three scenarios: (i) random drift alone; (ii) random drift with mutation; and (iii) random drift with migration. Steady state solutions for the cytonuclear disequilibria are reported. The utility of this simple two-locus drift model in testing the neutrality of mitochondrial DNA markers in artificial hybrid zones is briefly illustrated     

Genetic Drift in a Cline

A model is developed of genetic drift in a cline maintained by spatially varying natural selection and local dispersal of individuals. The model is analyzed by an approximation scheme which is valid for weak selection and small migration rates. The results, which are based on numerical iterations of the approximate equations, are that the cline is less steep than predicted on the basis of the deterministic theory but that for weak selection the correlation between random fluctuations in neighboring colonies is approximately the same as in models of migration and drift in the absence of selection.     

Stereological Determination of Orientations,Second-Order Quantities and Correlations for Random Spatial Fibre Systems

This paper presents methods for the stereological analysis of spatial fibre systems on the base of planar or thin sections. Under the assumption that the cross-section figures of the tubular fibres can be measured, the orientation distribution of the fibre system and its line density L_v can be determined from one section only and without distributional assumptions. A simple way to study the degree of randomness of fibre systems consists in the statistical analysis of the point pattern of centres of intersection figures. More sophisticated methods are of stereological nature and yield the spatial reduced second moment measure. Similarly also correlations between two fibre systems can be quantified. The methods are demonstrated by two examples concerning samples of human brain.     

Polarization-Controlled TIRFM with Focal Drift and Spatial Field Intensity Correction

Total internal reflection fluorescence microscopy (TIRFM) is becoming an increasingly common methodology to narrow the illumination excitation thickness to study cellular process such as exocytosis, endocytosis, and membrane dynamics. It is also frequently used as a method to improve signal/noise in other techniques such as in vitro single-molecule imaging, stochastic optical reconstruction microscopy/photoactivated localization microscopy imaging, and fluorescence resonance energy transfer imaging. The unique illumination geometry of TIRFM also enables a distinct method to create an excitation field for selectively exciting fluorophores that are aligned either parallel or perpendicular to the optical axis. This selectivity has been used to study orientation of cell membranes and cellular proteins. Unfortunately, the coherent nature of laser light, the typical excitation source in TIRFM, often creates spatial interference fringes across the illuminated area. These fringes are particularly problematic when imaging large cellular areas or when accurate quantification is necessary. Methods have been developed to minimize these fringes by modulating the TIRFM field during a frame capture period; however, these approaches eliminate the possibility to simultaneously excite with a specific polarization. A new, to our knowledge, technique is presented, which compensates for spatial fringes while simultaneously permitting rapid image acquisition of both parallel and perpendicular excitation directions in ∼25 ms. In addition, a back reflection detection scheme was developed that enables quick and accurate alignment of the excitation laser. The detector also facilitates focus drift compensation, a common problem in TIRFM due to the narrow excitation depth, particularly when imaging over long time courses or when using a perfusion flow chamber. The capabilities of this instrument were demonstrated by imaging membrane orientation using DiO on live cells and on lipid bilayers that were supported on a glass slide (supported lipid bilayer). The use of the approach to biological problems was illustrated by examining the temporal and spatial dynamics of exocytic vesicles.     

Polarization-Controlled TIRFM with Focal Drift and Spatial Field Intensity Correction

Total internal reflection fluorescence microscopy (TIRFM) is becoming an increasingly common methodology to narrow the illumination excitation thickness to study cellular process such as exocytosis, endocytosis, and membrane dynamics. It is also frequently used as a method to improve signal/noise in other techniques such as in vitro single-molecule imaging, stochastic optical reconstruction microscopy/photoactivated localization microscopy imaging, and fluorescence resonance energy transfer imaging. The unique illumination geometry of TIRFM also enables a distinct method to create an excitation field for selectively exciting fluorophores that are aligned either parallel or perpendicular to the optical axis. This selectivity has been used to study orientation of cell membranes and cellular proteins. Unfortunately, the coherent nature of laser light, the typical excitation source in TIRFM, often creates spatial interference fringes across the illuminated area. These fringes are particularly problematic when imaging large cellular areas or when accurate quantification is necessary. Methods have been developed to minimize these fringes by modulating the TIRFM field during a frame capture period; however, these approaches eliminate the possibility to simultaneously excite with a specific polarization. A new, to our knowledge, technique is presented, which compensates for spatial fringes while simultaneously permitting rapid image acquisition of both parallel and perpendicular excitation directions in ∼25 ms. In addition, a back reflection detection scheme was developed that enables quick and accurate alignment of the excitation laser. The detector also facilitates focus drift compensation, a common problem in TIRFM due to the narrow excitation depth, particularly when imaging over long time courses or when using a perfusion flow chamber. The capabilities of this instrument were demonstrated by imaging membrane orientation using DiO on live cells and on lipid bilayers that were supported on a glass slide (supported lipid bilayer). The use of the approach to biological problems was illustrated by examining the temporal and spatial dynamics of exocytic vesicles.     

Genetic Drift of HIV Populations in Culture

Populations of Human Immunodeficiency Virus type 1 (HIV-1) undergo a surprisingly large amount of genetic drift in infected patients despite very large population sizes, which are predicted to be mostly deterministic. Several models have been proposed to explain this phenomenon, but all of them implicitly assume that the process of virus replication itself does not contribute to genetic drift. We developed an assay to measure the amount of genetic drift for HIV populations replicating in cell culture. The assay relies on creation of HIV populations of known size and measurements of variation in frequency of a neutral allele. Using this assay, we show that HIV undergoes approximately ten times more genetic drift than would be expected from its population size, which we defined as the number of infected cells in the culture. We showed that a large portion of the increase in genetic drift is due to non-synchronous infection of target cells. When infections are synchronized, genetic drift for the virus is only 3-fold higher than expected from its population size. Thus, the stochastic nature of biological processes involved in viral replication contributes to increased genetic drift in HIV populations. We propose that appreciation of these effects will allow better understanding of the evolutionary forces acting on HIV in infected patients.     

Genetic Variation and Random Drift in Autotetraploid Populations

The rate of decay of genetic variation is determined for randomly mating autotetraploid populations of finite size, and the equilibrium homozygosity under mutation and random drift is calculated. It is shown that heterozygosity is lost at a slower rate than in diploid populations, and that the equilibrium heterozygosity with mutation and random drift is higher than for diploids. Outcrossing populations as well as populations that randomly self are analyzed. A method of comparing genetic variation between autotetraploid and diploid populations is proposed. Our treatment suggests that the ``gametic homozygosity' provides a unified approach for comparing genotypes within a population as well as comparing genetic variation between populations with different levels of ploidy.     

Beads and Dice in a Genetic Drift Exercise

Natural selection driving adaptive changes is a powerful and intuitive explanation for the evolution of the living world around us. Evolution at the molecular level, however, is chiefly ruled by random genetic drift. The idea that an advantageous allele may be lost by chance in a natural population is rather difficult to explore in the classroom. Low-cost and hands-on educational resources are needed to make genetic drift more intuitive among students. In this exercise, we use colored beads and the roll of a die to simulate drift and selection jointly affecting the fate of the genetic variants in an evolving population. Our aim is to teach students that natural selection does not determine but simply influences the fate of advantageous alleles because random genetic drift is always present. We have been using this exercise successfully for over a decade for the Biological Sciences students at the Federal University of Rio de Janeiro.     

Genetic Diversity and Spatial Genetic Structure of the Grassland Perennial Saxifraga granulata along Two River Systems

Due to changes in land use, the natural habitats of an increasing number of plant species have become more and more fragmented. In landscapes that consist of patches of suitable habitat, the frequency and extent of long-distance seed dispersal can be expected to be an important factor determining local genetic diversity and regional population structure of the remaining populations. In plant species that are restricted to riparian habitats, rivers can be expected to have a strong impact on the dynamics and spatial genetic structure of populations as they may enable long-distance seed dispersal and thus maintain gene flow between fragmented populations. In this study, we used polymorphic microsatellite markers to investigate the genetic diversity and the spatial genetic structure of 28 populations of Saxifraga granulata along two rivers in central Belgium. We hypothesized that rivers might be essential for gene flow among increasingly isolated populations of this species. Genetic diversity was high (H_S = 0.68), which to a certain extent can be explained by the octoploid nature of S. granulata in the study area. Populations along the Dijle and Demer rivers were also highly differentiated (G”_ST = 0.269 and 0.164 and D_EST = 0.190 and 0.124, respectively) and showed significant isolation-by-distance, indicating moderate levels of gene flow primarily between populations that are geographically close to each other. Along the river Demer population genetic diversity was higher upstream than downstream, suggesting that seed dispersal via the water was not the primary mode of dispersal. Overall, these results indicate that despite increasing fragmentation populations along both rivers were highly genetically diverse. The high ploidy level and longevity of S. granulata have most likely buffered negative effects of fragmentation on genetic diversity and the spatial genetic structure of populations in riparian grasslands.     

Laboratory Estimates of Heritabilities and Genetic Correlations in Nature

A lower bound on heritability in a natural environment can be determined from the regression of offspring raised in the laboratory on parents raised in nature. An estimate of additive genetic variance in the laboratory is also required. The estimated lower bounds on heritabilities can sometimes be used to demonstrate a significant genetic correlation between two traits in nature, if their genetic and phenotypic correlations in nature have the same sign, and if sample sizes are large, and heritabilities and phenotypic and genetic correlations are high.     

Genetic Similarity of Flag Shoot and Ascospore Subpopulations of Erysiphe necator in Italy

The overwintering mode of the grape powdery mildew fungus, Erysiphe necator (syn. Uncinula necator), as mycelium in dormant buds (resulting in symptoms known as flag shoots) or as ascospores in cleistothecia, affects the temporal dynamics of epidemics early in the growing season. We tested whether distinct genetic groups (I and III) identified previously in E. necator correlate to overwintering modes in two vineyards in Tuscany, Italy, to determine whether diagnostic genetic markers could be used to predict overwintering. Samples from one vineyard were collected from flag shoots; the other vineyard, 60 km away, had no flag shoots, and mildew colonies were assumed to be derived from ascospores. Genetic markers putatively diagnostic for groups I and III showed that both types were common in the flag shoot subpopulation. Both genetic types were found in the ascospore population, although group III was dominant. We did not find strong genetic differentiation between the two subpopulations based on inter-simple sequence repeat markers. Although there was significant (P < 0.001) genetic differentiation between these subpopulations in 1997 and when 1997 and 1998 subpopulations were pooled (θ = 0.214 and 0.150, respectively), no differentiation was evident between vineyards in 1998 (θ = 0.138, P = 0.872). Moreover, we did not observe distinct lineages corresponding to overwintering modes, as observed in previous studies. We could not determine if differentiation resulted from biological differences or restricted gene flow between the two vineyards. Our samples were taken from both subpopulations early in the epidemic, while previous studies confounded overwintering mode and sampling time. These results do not support a strong correlation between overwintering and genetic groups, highlighting the need to base population biology studies on sound biological and epidemiological knowledge.     

Influence of Spatial Resolution on Space-Time Disease Cluster Detection

Background

Utilizing highly precise spatial resolutions within disease outbreak detection, such as the patients’ address, is most desirable as this provides the actual residential location of the infected individual(s). However, this level of precision is not always readily available or only available for purchase, and when utilized, increases the risk of exposing protected health information. Aggregating data to less precise scales (e.g., ZIP code or county centroids) may mitigate this risk but at the expense of potentially masking smaller isolated high risk areas.

Methods

To experimentally examine the effect of spatial data resolution on space-time cluster detection, we extracted administrative medical claims data for 122500 viral lung episodes occurring during 2007–2010 in Tennessee. We generated 10000 spatial datasets with varying cluster location, size and intensity at the address-level. To represent spatial data aggregation (i.e., reduced resolution), we then created 10000 corresponding datasets both at the ZIP code and county level for a total of 30000 datasets. Using the space-time permutation scan statistic and the SaTScan™ cluster software, we evaluated statistical power, sensitivity and positive predictive values of outbreak detection when using exact address locations compared to ZIP code and county level aggregations.

Results

The power to detect disease outbreaks did not largely diminish when using spatially aggregated data compared to more precise address information. However, aggregations negatively impacted the ability to more accurately determine the exact spatial location of the outbreak, particularly in smaller clusters (<800 km²).

Conclusions

Spatial aggregations do not necessitate a loss of power or sensitivity; rather, the relationship is more complex and involves simultaneously considering relative risk within the cluster and cluster size. The likelihood of spatially over-estimating outbreaks by including geographical areas outside the actual disease cluster increases with aggregated data.     

Spatial Autocorrelation Analysis of Migration and Selection

We test various assumptions necessary for the interpretation of spatial autocorrelation analysis of gene frequency surfaces, using simulations of Wright's isolation-by-distance model with migration or selection superimposed. Increasing neighborhood size enhances spatial autocorrelation, which is reduced again for the largest neighborhood sizes. Spatial correlograms are independent of the mean gene frequency of the surface. Migration affects surfaces and correlograms when immigrant gene frequency differentials are substantial. Multiple directions of migration are reflected in the correlograms. Selection gradients yield clinal correlograms; other selection patterns are less clearly reflected in their correlograms. Sequential migration from different directions and at different gene frequencies can be disaggregated into component migration vectors by means of principal components analysis. This encourages analysis by such methods of gene frequency surfaces in nature. The empirical results of these findings lend support to the inference structure developed earlier for spatial autocorrelation analysis.     

Genetic Drift Suppresses Bacterial Conjugation in Spatially Structured Populations

Conjugation is the primary mechanism of horizontal gene transfer that spreads antibiotic resistance among bacteria. Although conjugation normally occurs in surface-associated growth (e.g., biofilms), it has been traditionally studied in well-mixed liquid cultures lacking spatial structure, which is known to affect many evolutionary and ecological processes. Here we visualize spatial patterns of gene transfer mediated by F plasmid conjugation in a colony of Escherichia coli growing on solid agar, and we develop a quantitative understanding by spatial extension of traditional mass-action models. We found that spatial structure suppresses conjugation in surface-associated growth because strong genetic drift leads to spatial isolation of donor and recipient cells, restricting conjugation to rare boundaries between donor and recipient strains. These results suggest that ecological strategies, such as enforcement of spatial structure and enhancement of genetic drift, could complement molecular strategies in slowing the spread of antibiotic resistance genes.     

Genetic Drift Suppresses Bacterial Conjugation in Spatially Structured Populations

Conjugation is the primary mechanism of horizontal gene transfer that spreads antibiotic resistance among bacteria. Although conjugation normally occurs in surface-associated growth (e.g., biofilms), it has been traditionally studied in well-mixed liquid cultures lacking spatial structure, which is known to affect many evolutionary and ecological processes. Here we visualize spatial patterns of gene transfer mediated by F plasmid conjugation in a colony of Escherichia coli growing on solid agar, and we develop a quantitative understanding by spatial extension of traditional mass-action models. We found that spatial structure suppresses conjugation in surface-associated growth because strong genetic drift leads to spatial isolation of donor and recipient cells, restricting conjugation to rare boundaries between donor and recipient strains. These results suggest that ecological strategies, such as enforcement of spatial structure and enhancement of genetic drift, could complement molecular strategies in slowing the spread of antibiotic resistance genes.