Part III. Abstracts of Gene Flow Workshop Presentations
 (Return to Proceedings on Gene flow workshop)

Adams, W. Thomas, Department of Forest Science, Oregon State University, Corvallis, OR 97331-7501. Mating patterns and effective pollen dispersal in two western conifers: Douglas-fir and knobcone pine.

Because pollen density drops off rapidly with increasing distance from its source, most mating in conifer stands might be expected to occur among near neighbors. The "neighborhood" model was applied to multilocus allelic (allozyme) arrays observed in pollen gametes of seeds from individual mother trees to estimate mating pattern parameters in a high density stand of knobcone pine (kp, Pinus attenuata Lemmon.), and in one high density (Dfhd) and one low density (Dfld) stand of Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco). In the neighborhood model, an arbitrarily specified area around a mother tree (with radius r) is designated its neighborhood, and the paternity of the mother tree's offspring is partitioned into three sources: selfing (with probability s), outcrossing to males outside the neighborhood (m), and outcrossing to males within the neighborhood (1-s-m). In kp (mean tree height = 6 m), neighborhoods (r = 11 m) included an average of 44 potential outcross males, while in Douglas-fir, neighborhoods (r = 70 m) included 18 potential outcross males in Dfld (mean height = 46 m) and 44 in Dfhd (mean height = 38 m).

Estimated s was zero or nearly so in all three stands, but m was quite high (0.84 in Dfld, 0.74 in Dfhd, and 0.56 in kp). In addition, mating success of outcross males within neighborhoods was only weakly associated, at best, with distance from the mother tree. Thus, near neighbors accounted for only a small percentage of the effective mating in these stands, such that the effective number of mates for each mother tree was quite large. As expected, males within neighborhoods contributed to a higher proportion of the mating in Dfhd than in Dfld, but only marginally so. The lower estimate of m in kp neighborhoods is probably because kp was more isolated from other populations of the same species (i.e., less gene flow), than the Douglas-fir stands.

Campbell, Diane R. Dept. of Ecology & Evolutionary Biology, University of California Irvine, CA 92697. Estimating gene flow within and between populations in a plant hybrid zone

Natural hybridization is common in plants. If plant distribution is patchy across the region of hybridization, we can distinguish four kinds of gene movement in a hybrid zone. Intraspecific gene flow can occur within or between local populations. Interspecific gene flow can occur between distinct patches each occupied by a single species, or within a patch (hybrid swarm). Using two hybridizing species of Ipomopsis (Polemoniaceae) as a model system, I discuss ongoing efforts to estimate these four kinds of gene movement and the methods appropriate in each case.

 The primary means of gene movement in this system is transfer of pollen by hummingbirds. Behavioral observations of hummingbirds, combined with measures of pollen carryover from flower to flower, explain the highly localized pollen movement (usually a few m) within local populations. Similar mechanistic studies predict asymmetrical gene movement between I. aggregata and I. tenuituba and generally high rates of interspecific gene flow. These predictions were tested using a single genetic marker in mixed-species experimental populations. Work in progress uses multiple RAPD markers to estimate patterns of gene movement within a naturally hybridizing population.

At the between population level, paternity analysis with multiple allozyme markers suggests moderately high rates of gene flow from outside. Minimum rates of gene flow ranged from 9-25% into experimental populations isolated by as much as 150 m. The discrepancy between these results and the short distances of pollen flow within populations suggests that gene movement between versus within populations may result from different pollinator behaviors, making it difficult to extrapolate across scales. Determining the distance of gene flow between populations presents a special challenge. These studies illustrate the value of combining genetic markers with mechanistic methods in determining patterns of gene flow.
 

Davis, Frank W. NCEAS, University of California at Santa Barbara. Spatially explicit modeling of landscape-scale transport processes.

Gene flow across landscapes is accomplished by gravity, wind, water, and animals. These transport processes are increasingly studied using dynamic, spatially explicit models. The purpose of this talk is to provide an overview of these models and discuss there potential applicability to studying gene flow in fragmented and managed forests.

 In the most general sense, it is useful to distinguish two classes of spatial models: "object" models, which track discrete spatially referenced features floating in space (e.g. habitat islands), and "field" models, which divide continuous space into smaller elements and assign a value to each element. Most spatially explicit models in ecology are field models that utilize a 2- or 3-dimensional lattice to represent landscape properties such as elevation, vegetation, location of organisms, etc. Movement across such grids is usually modeled by local rules. Examples of field models include cellular automata, discrete reaction diffusion models, and cellular networks. Object models are sometimes used to represent individual animals or populations for individual-based models and metapopulation models, respectively.

 There are several different data structures for representing spatio-temporal dynamics (e.g., image sequences, polygons with a vector of temporal attributes for each polygon). Modern GIS systems now provide some useful spatial analytical capabilities relevant to modeling gene flow (e.g., distance and neighborhood analyses, diffusion models, path cost analysis), but are still very limited for dynamic modeling, which is instead usually performed using specially designed research software. Generic issues in the use of spatial dynamic models include: defining the spatial extent, resolution, and time step for the model, treatment of boundary effects, and movement/connection rules (e.g., rules governing the relationship between diagonal cells on a square grid).

 Among physical transport processes, modeling movement of water is well developed and a variety of programs are available to model both surface and subsurface flow at spatial scales from local to continental. Wind transport models have mainly been developed to represent larger scale atmospheric processes, although landscape models have also been developed to study urban microclimate, valley and land-sea wind systems, and local snow and sand transport. These wind models are generally computationally very intensive and require extensive parameterization. Simpler models have been developed based on surface aerodynamic resistance and fetch that could be useful in studying local gene flow in rugged or heterogeneous terrain.

 Spatially explicit diffusion models have been used to study a variety of biological processes, for example, biological invasions, seed dispersal, and disease spread. Animal movements have been simulated using simple diffusion and cellular automate models, as well as more complex, spatially explicit individual-based models and metapopulation models, some of which require large-scale computing resources. Simpler approaches to studying gene flow among animal populations include analysis of topography, vegetation, or other surface features to calculate path costs for varying dispersal routes as a way of modeling likely patterns of animal dispersal on complex landscapes.

 My sense is that spatially-explicit models represent an as yet relatively untapped set of tools which could be used to study gene flow in continuous versus fragmented landscapes. Even relatively simple applications of widely available GIS software could be useful for managing and visualizing gene flow data as well as for some simple modeling procedures. There are obvious opportunities here for collaboration between geneticists measuring gene flow in the field and landscape ecologists with expertise in dynamic spatial models.
 
 

Dyer, Rodney J., Department of Biology, University of Missouri-St. Louis, Paternity analysis and gene flow in Northern Red Oak (Quercus rubra L.)

For wind pollinated oaks, the rate of pollen migration into the stand is the most important factor governing gene flow. However, determining the significance of the resultant pollen distance distribution is problematic because of the nature of fractional paternity assignment. This study utilized starch gel electrophoresis and fractional paternity analysis to estimate rates of apparent and cryptic gene flow into a stand of red oak in central Missouri. Progeny arrays from three maternal trees and 234 putative fathers from a 4 ha stand revealed 15 of the 137 offspring resulting from gene flow into the stand. Furthermore, Monte Carlo simulations predicted one offspring to be the result of cryptic gene flow. Total gene flow, converted to Nm, was 2.0. Resultant pollen distance distributions suggest a leptokertic distribution, however truncation of individuals with ambiguous paternity prevents statistical testing. Male fertilities had no significant relationship with dbh, distance to maternal tree, and/or direction. Suggestions for statistical analysis of the pollen distribution are offered.
 
Fig. 1.  
 

Juan F. Fernandez-M., Department of Biology, University of Missouri, St. Louis. Estimating optimal sample size for genetic differentiation using analytical and bootstrap techniques.

Precision in the analysis of the distribution of genetic diversity and estimation of gene flow rates among populations, is constrained by the sampling design i.e., number of populations and number of individuals per population. Few attempts have been made to analytically determine a sample size large enough that will yield statistically significant estimates of genetic differentiation or gene flow e.g., . Here, I use the methods proposed by to estimate the optimal sample size per population when the total sample size is held constant based on the premise of minimizing the variance of Gst from known genetic data. Allozyme genetic data from five loci (AAT-2, AAT-3, DIA-1, DIA-2, and MNR-2) from Sassafras albidum (Lauraceae) from 36 subpopulations from the Missouri Ozarks, was analyzed using the program HaploDiv (Petit 1995). Although the program is intended for haploid data , it yields close results to a diploid procedure if the species is outcrossed (Petit, pers. comm.). The original sample sizes were between 24 and 48 individuals per population.

Only the loci that showed a significant genetic differentiation (MNR-2 Gst = 0.3389, and DIA-2 Gst = 0.0991) were useful in estimating the optimal sample size. The results indicate that 4 diploid individuals for the MNR-2 locus, and 9 for the DIA-2 locus per population are enough to detect population differentiation at those loci.

For the low differentiated loci (AAT-2, AAT-3 and DIA-1) a resample analysis was performed simulating the 36 populations with a constant sample size (n = 10, 20, ...100) per population to estimate empirically when the bootstrap 95% confidence interval on Gst values approached the observed value for the total data. The simulated samplings suggested: 1) that at least 20 individuals per population are required for a 95% confidence interval to overalap with the true mean Gst ; 2) that the estimated variance stabilizes when sample size is greater than 30 individuals per population; and 3) that the estimator that approaches the true value the better is the Gst estimator proposed by Pons and Chaouche (1995). For a locus by locus analysis, the least differntiated locus will determine the minimum sample requirements.

            Literature Cited

Gilpin, Michael. Department of Biology, University of California-San Diego. Gene Flow and selection under extinction/recolonization dynamics for self incompatible plants.

The S-Allele for self-incompatability in plants has long been a subject for theoretical analysis, since, through frequency dependence, it maintains dozens of alleles in even small populations. Previous work has been based on single patch models or on stepping-stone configurations with constant population sizes. In collaboration with Josh Kohn (UCSD) and Adam Richman (Montana State University), I'm developing java-based model that incorporates local extinction of a patch followed by a colonization and founder event. The model tracks alleles and genetic distance data, such as FST. Metapopulation dynamics increase isolation with distance and reduce the regional number of alleles.
 
 
 

Hamrick, James L. Departments of Botany and Genetics, University of Georgia, Athens, GA. Predicting the genetic consequences of gene flow: problems and solutions.

The availability of molecular genetic markers coupled with advanced statistical estimation procedures have significantly increased our ability to estimate gene flow rates and other population parameters for many plant species. The improved ability to accurately estimate gene flow into plant populations allows us to predict the genetic consequences of small population size, habitat fragmentation, and isolation distance. However, when gene flow is estimated in conjunction with male reproductive success or effective population sizes, some problems can arise. For example, when estimating male reproductive success in populations that experience high rates of gene flow, the assignment of progeny to certain pollen donors may be biased towards individuals with multi locus genotypes that most closely approximate gene frequencies in the immigrant donor population. Perhaps a more serious problem is the observation that individual trees do not sample the pollen pool at random as is assumed by most estimation procedures. There is considerable evidence from the plant mating system literature that individual maternal trees often receive genetically different pollen. This is probably also true of pollen that immigrates into a population. Thus, a second generation of gene flow estimation procedures are needed that can take into account such heterogeneity in the immigrant pollen pool and use iterative procedures to better estimate the immigrant pollen pool for individual trees as well as populations.

  

Nason, John. Dept. of Biological Sciences, University of Iowa, Iowa City, IA 52242-1324. Measurement of gene flow through pollen and seed in continuous and discontinuous populations.

Due to differences in their physical properties and in the vectors that disperse them, pollen and seed movement may generate spatial patterns of gene dispersion that differ in both continuous and discontinuous populations. Studies of pollen flow have employed statistical genetic approaches that fall into one of two categories; those that estimate rates of pollen flow into discrete populations but do not provide estimates of male fertility and pollen movement within populations and, conversely, those that infer male fertilities but do not adjust these estimates for cryptic pollen flow originating outside of the study population. Combining statistical approaches, I will present a model that simultaneously estimates rates of total gene flow and male fertilities adjusted for cryptic pollen gene flow from genotypic data. In contrast to the problems of quantifying pollen dispersal, the development and application of statistical models to estimate gene flow via seed has been hampered by the limited availability of suitable maternally inherited chloroplast and mitochondrial markers. As a solution to this problem, I will present a general framework for estimating pollen and seed components of gene flow from the observed distribution of genotypes at biparentally inherited loci. The model much more rapidly generates direct estimates of the levels of pollen flow received by individual maternal plants and populations than does currently available methods. Moreover, once a population level estimate of pollen flow has been obtained, nuclear markers, such as allozymes, can be used to obtain direct estimates of seed immigration from the multilocus genotypes of dispersed seeds and seedlings. The application of these models to investigating pollen, seed, and gene movement in continuous and spatially isolated populations will be discussed.
 
 

Neigel, Joseph E. Department of Biology, The University of Southwestern Louisiana. Gene flow analysis based on spatial dispersion of individual lineages.

The spatial dispersion of an organismal lineage from a single descendant is a direct consequence of gene flow. Thus, an analysis of this process can be similar to that used for direct estimates of gene flow from mark-and-recapture data. Development of this approach as a method for estimating gene flow requires genetic markers that delineate lineages of sufficiently recent origin, and models that provide a framework for estimating dispersion parameters. This approach has been applied to large scale patterns of animal mtDNA variation, with encouraging results.
 
 

Petit, Rémy J. INRA Forest genetics and tree improvement laboratory, Bordeaux, France. Contribution of cytoplasmic markers to studies of gene flow in plants.

It may seem inappropriate to investigate chloroplast DNA (cpDNA) or mitochondrial DNA (mtDNA) to get insights of gene flow in plants. Indeed, the bulk of gene exchanges is mediated by pollen, and cytoplasmic genomes are usually maternally inherited. But seed flow may be significant in some species, whereas cpDNA is paternally inherited in an important group of forest trees (Gymnosperms). In general, inferring the relative importance of pollen and seed flow seems important. Indeed, even if often less mobile than pollen grains, seeds are the only vehicle to move to new environments ('The haploid phase of environmental exploration cannot act further than what has already been colonized by the diploid phase' to quote Harper). Also, for some species, humans have moved seeds and plants around. Cytoplasmic markers may in such cases be extremely useful to differentiate introduced from native material. Indeed, genetic structure is often much stronger for maternally inherited markers compared to biparentally (or paternally) inherited ones. In parentage analyses, a set of highly polymorphic nuclear microsatellites may be used to identify the parents of a given seedlings but the differentiation of the mother from the father may be difficult. On the other hand, if combined with cytoplasmic markers, a complete picture may be obtained. Clonally evolving genomes are very appropriate for reconstructing phylogenies, an information sometimes useful to consider in gene flow studies. Finally, 'interspecific gene flow' also called 'cytoplasmic captures' are reported to be very frequent in plants. Actually, these expressions may be misleading, since it is probably often the nuclear genome which moves over a static maternal bedrock. Nevertheless, it remains true that one may often get better insights of interspecific gene flow with cytoplasmic than with nuclear markers.
 
 

Petit, Rémy J. INRA Forest genetics and tree improvement laboratory, Bordeaux, France. Measuring genetic differentiation with molecular markers to identify populations for conservation.

 The purpose of this talk was to introduce some work done in collaboration with Odile Pons (INRA, Jouy-en Josas) on the estimation of genetic differentiation in various contexts. Among the questions studied are the following: How to obtain confidence intervals for estimates of genetic differentiation (GST)? How to optimize sampling in order to obtain a better (more precise) estimate of differentiation? How to measure differentiation while taking into account information on the nature of the alleles (NST (sequence) or RST (microsatellite) data)? How to compare differentiation for ordered versus unordered alleles? What does this difference mean? How to get pairwise measures of differentiation? How to measure the differentiation of one population from the rest ? Is a given population important to conserve because it is variable or because it is distinct, or because of both? How to measure that? How to compare measures of allelic richness? What do statements such as: 10% of the diversity is distributed among populations' really mean?

 

Savolainen,Outi. Department of Biology, University of Oulu, Finland. Gene flow and local adaptation in Scots pine.

Scots pine can serve as a case study for considering many aspects of gene flow. The reproductive biology of Scots pine is better known than that of most other conifers (Sarvas 1962, Koski 1970). The distribution of quantitative genetic variation of adaptive traits has been extensively studied, and for many important traits the populations are highly differentiated (Mikola 1982, Karhu et al. 1996, Hurme et al. 1997, Hurme and Savolainen in prep). The distribution of variation in molecular markers has been well characterized. Until now, all markers, isozymes, RFLP, RAPD, microsatellites, have shown very limited degrees of differentiation. Thus, so far we have not found markers for those parts of the genome that are differentiated. At least many northern conifers may share similar patterns of biology (Savolainen and Kuittinen, in press). The basic findings of gene flow in Scots pine, through direct measures by marking pollen, paternity analysis and indirect genetic inference all suggest that gene flow through pollen is likely to be extensive. The influence of timing of flowering in different populations is in the direction of facilitating south to north gene flow. There is strong selection for adaptation to local environmental conditions. The results of the contrasting influences of migration and selection result in these divergent patterns of differentiation discussed above. These results can also be used for considering the consequences of fragmentation and management.

             For literature cited see:

Savolainen, O. and Hurme, P. 1997. Conifers from the cold. Pp. 43-62 in Environmental stress, adaptation and evolution (R. Bijlsma and V. Loeschcke, eds.). Birkhäuser Verlag.

Smouse1, Peter E. Sylvan R. Kaufman1, and Elena R. Alvarez-Bullya2. 1Department of Ecology, Evolution & Natural Resources and Center for Theoretical & Applied Genetics, Cook College, Rutgers University; 2Centro de Ecologia, Universidad Nacional Autonoma de Mexico. Use of parentage analysis in the assessment of gene flow.

Much attention has been directed to the use of F-statistics (and similar measures) for the indirect estimation of gene flow between populations. While such approaches allow estimation from a crosscutting survey of a single generation, they have their limitations. An alternative is to use a two-generation approach, based on paternity analysis. There are many different situations one can treat, given proper mendelian inheritance of a set of genetic markers, but we will concentrate on the situation with known mothers and offspring, coupled with candidate male (pollen donor) populations of "well-estimated" genetic composition. This approach is a simple extension of single-male analysis, not unlike a mixed stock (migrational) fisheries analysis. We can also model the respective contributions of the pollen donor populations, in terms of interesting features or in terms of their distance from the recipient (female) population. We will illustrate with a tropical pioneer tree species, Cecropia obtusifolia, for which the appropriate data provide a telling demonstration of patterned gene flow. Parentage analysis, while it requires additional information, would appear to be more powerful than F-statistics analysis, in elucidating gene flow.
 
 

Smouse1, Peter E. and Rod Peakall2. 1Department of Ecology, Evolution & Natural Resources and Center for Theoretical & Applied Genetics, Cook College, Rutgers University; 2 Dept. Botany and Zoology, Australian National University.  Micro-spatial autocorrelation analysis for multiple-locus, multi-allelic genetic data

Until recently, most spatial autocorrelation analysis of genetic data has been conducted with univariate techniques. Each allele at each locus has been analyzed separately, yielding many different analyses, usually treated (incorrectly) as independent replicates of the process, thought to be (broadly) demographic and spatial. With the recent interest in micro satellite loci, with myriad alleles, this univariate strategy is hopelessly cumbersome. Various workers, notably such people as Sokal, Barbujani, and Epperson, have begun to switch over to a multiple-character treatment. We show that by switching to genetic distance techniques, we can produce a completely general multivariate treatment, can use multiple-alleles, multiple-loci, weighted or unweighted information, and so on. We then illustrate new non-parametric testing procedures on the entire autocorrelation profile. We illustrate with published allozyme data on the Australian orchid, Caledenia tentaculata. The new analysis is easily tractable and very powerful, reliably detecting pattern when it is there, and demonstrating its absence when it is not.
 
 

Sork, Victoria L. Sabbatical Research Fellow, NCEAS, University of California-Santa Barbara and Department of Biology, University of Missouri-St. Louis.  Introduction to workshop:  studying gene flow on an ecological time scale.

Gene flow among populations can be studied using an evolutionary time frame or an on going time frame. Evolutionary questions concerning the role of gene flow in genetic diversity, population differentiation, species identity, and speciation emphasize the  evolutionary time scale. However, conservation biological questions concerning the role of gene flow in future patterns must rely on estimates of on-going gene flow under current landscape conditions. My question, and to some extent the main question of the workshop, is to evaluate the extent to which gene flow models developed to answer evolutionary questions in an evolutionary framework can be used to estimate on-going gene flow.  In this introductory talk, I will briefly review categories of gene flow models--some of which will be developed in more detail by workshop participants. Then, I will present evidence of ecological and landscape influences on patterns of gene flow. My talk will end with a list of questions about which models are most appropriate for the estimation of on-going gene flow and whether new models should be developed which utilize metapopulation approaches or the spatially explicit models.
 
 

Steinberg, Eleanor L University of Washington. Using and individual-based, spatially-explicit simulation model to evaluate the power of FST as an indicator of recent habitat fragmentation.

The ecological impacts of habitat fragmentation due to human-induced landscape modifications are of serious concern to conservation biologists. Such fragmentation may reduce the exchange of individuals between populations, resulting in isolated patches made vulnerable to extinction due to environmental stochasticity and/or inbreeding depression. Unfortunately, studies of species at risk are typically plagued by logistical problems, making it difficult to collect the detailed but large-scale demographic data necessary to address this issue. Conservation biologists have thus increasingly been turning to molecular genetics to study threatened populations. One goal of these studies is to use current patterns of genetic structure to elucidate underlying population processes, in particular, those dealing with migration dynamics. However, this approach has some serious limitations. Importantly, because many different population processes lead to similar patterns of genetic structure, particular processes are difficult to infer from pattern. In addition, the population genetics models most commonly applied to these systems are based on equilibrium conditions not typically found in nature, and are framed in abstract terms that are difficult to link to biological data. Finally, influences of current and historical conditions are not easily separated. I will present an individual-based simulation model (based on pocket gopher biology) that incorporates genetics and demography to explore scenarios of change in genetic structure as a result of habitat fragmentation. In particular, I will use the simulation to illustrate limitations in using models based on F-statistics as a generic tool (particularly for management applications), and will suggest possible future directions for applying this modeling approach to interpret both spatial and temporal patterns of genetic variation.

 
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