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Hybrid potato breeding has become a novel alternative to con-ventional potato breeding allowing breeders to overcome intractable barriers (e.g. tetrasomic inheritance, masked deleterious alleles, obligate clonal propagation) with the benefit of seed-based propagule, flexible population design, and the potential of hybrid vigour. Until now, however, no formal inquiry has adequately examined the relevant genetic components for complex traits in hybrid potato populations. In this present study, we use a two-step modelling approach to estimate the relevant variance components to assess the magnitude of the general and specific combining abilities (GCA and SCA, respectively) in diploid hybrid potato (DHP). SCA effects were identified for all yield components studied here warranting evidence of non-additive genetic effects in hybrid potato yield. However, the estimated GCA effects were on average two times larger than their respective SCA quantile across all yield phenotypes. Tuber number GCA’s and SCA’s were found to be highly correlated with total yield’s genetic components. Tuber volume appearing under-selected in this population. The prominence of additive effects found for all traits presents evidence that breeders can perform hybrid potato evaluation using the mid-parent value alone. Heterotic vigour stands be useful in bolstering simpler traits but this will be very dependent on the target market of a population. This study represents the first diallel analysis of its kind in diploid potato using material derived from a commercial hybrid breeding programme.

Hybrid potato breeding has become a novel alternative to conventional potato breeding allowing breeders to overcome intractable barriers (e.g. tetrasomic inheritance, masked deleterious alleles, obligate clonal propagation) with the benefit of seed-based propagule, flexible population design, and the potential of hybrid vigor. Until now, however, no formal inquiry has adequately examined the relevant genetic components for complex traits in hybrid potato populations. In this present study, we use a 2-step multivariate modeling approach to estimate the variance components to assess the magnitude of the general and specific combining abilities in diploid hybrid potato. Specific combining ability effects were identified for all yield components studied here warranting evidence of nonadditive genetic effects in hybrid potato yield. However, the estimated general combining ability effects were on average 2 times larger than their respective specific combining ability quantile across all yield phenotypes. Tuber number general combining abilities and specific combining abilities were found to be highly correlated with total yield’s genetic components. Tuber volume was shown to have the largest proportion of additive and nonadditive genetic variation suggesting under-selection of this phenotype in this population. The prominence of additive effects found for all traits presents evidence that the mid-parent value alone is useful for hybrid potato evaluation. Heterotic vigor stands to be useful in bolstering simpler traits but this will be dependent on target phenotypes and market requirements. This study represents the first diallel analysis of its kind in diploid potato using material derived from a commercial hybrid breeding program.

Construction of genetic linkage maps has become a routine step for mapping quantitative trait loci (QTL), particularly in animal and plant breeding populations. Many multiparental populations have recently been produced to increase genetic diversity and QTL mapping resolution. However, few software packages are available for map construction in these populations. In this paper, we build a general framework for the construction of genetic linkage maps from genotypic data in diploid populations, including bi- and multiparental populations, cross-pollinated (CP) populations, and breeding pedigrees. The framework is implemented as an automatic pipeline called magicMap, where the maximum multilocus likelihood approach utilizes genotypic information efficiently. We evaluate magicMap by extensive simulations and eight real datasets: one biparental, one CP, four multiparent advanced generation intercross (MAGIC), and two nested association mapping (NAM) populations, the number of markers ranging from a few hundred to tens of thousands. Not only is magicMap the only software capable of accommodating all of these designs, it is more accurate and robust to missing genotypes and genotyping errors than commonly used packages.

In diploid species, many multi-parental populations have been developed to increase genetic diversity and quantitative trait loci (QTL) mapping resolution. In these populations, haplotype reconstruction has been used as a standard practice to increase QTL detection power in comparison with the marker-based association analysis. To realize similar benefits in tetraploid species (and eventually higher ploidy levels), a statistical framework for haplotype reconstruction has been developed and implemented in the software PolyOrigin for connected tetraploid F1 populations with shared parents. Haplotype reconstruction proceeds in two steps: first, parental genotypes are phased based on multi-locus linkage analysis; second, genotype probabilities for the parental alleles are inferred in the progeny. PolyOrigin can utilize genetic marker data from single nucleotide polymorphism (SNP) arrays or from sequence-based genotyping; in the latter case, bi-allelic read counts can be used (and are preferred) as input data to minimize the influence of genotype call errors at low depth. To account for errors in the input map, PolyOrigin includes functionality for filtering markers, inferring inter-marker distances, and refining local marker ordering. Simulation studies were used to investigate the effect of several variables on the accuracy of haplotype reconstruction, including the mating design, the number of parents, population size, and sequencing depth. PolyOrigin was further evaluated using an autotetraploid potato dataset with a 3×3 half-diallel mating design. In conclusion, PolyOrigin opens up exciting new possibilities for haplotype analysis in tetraploid breeding populations.

Key message The identity-by-descent (IBD)-based mixed model approach introduced in this study can detect quantitative trait loci (QTLs) referring to the parental origin and simultaneously account for multilevel relatedness of individuals within and across families. This unified approach is proved to be a powerful approach for all kinds of multiparental population (MPP) designs. Abstract Multiparental populations (MPPs) have become popular for quantitative trait loci (QTL) detection. Tools for QTL mapping in MPPs are mostly developed for specific MPPs and do not generalize well to other MPPs. We present an IBD-based mixed model approach for QTL mapping in all kinds of MPP designs, e.g., diallel, Nested Association Mapping (NAM), and Multiparental Advanced Generation Intercross (MAGIC) designs. The first step is to compute identity-by-descent (IBD) probabilities using a general Hidden Markov model framework, called reconstructing ancestry blocks bit by bit (RABBIT). Next, functions of IBD information are used as design matrices, or genetic predictors, in a mixed model approach to estimate variance components for multiallelic genetic effects associated with parents. Family-specific residual genetic effects are added, and a polygenic effect is structured by kinship relations between individuals. Case studies of simulated diallel, NAM, and MAGIC designs proved that the advanced IBD-based multi-QTL mixed model approach incorporating both kinship relations and family-specific residual variances (IBD.MQMkin_F) is robust across a variety of MPP designs and allele segregation patterns in comparison to a widely used benchmark association mapping method, and in most cases, outperformed or behaved at least as well as other tools developed for specific MPP designs in terms of mapping power and resolution. Successful analyses of real data cases confirmed the wide applicability of our IBD-based mixed model methodology.

Use of genomic prediction (GP) in tetraploid is becoming more common. Therefore, we think it is the right time for a comparison of GP models for tetraploid potato. GP models were compared that contrasted shrinkage with variable selection, parametric vs. non-parametric models and different ways of accounting for non-additive genetic effects. As a complement to GP, association studies were carried out in an attempt to understand the differences in prediction accuracy. We compared our GP models on a data set consisting of 147 cultivars, representing worldwide diversity, with over 39 k GBS markers and measurements on four tuber traits collected in six trials at three locations during 2 years. GP accuracies ranged from 0.32 for tuber count to 0.77 for dry matter content. For all traits, differences between GP models that utilised shrinkage penalties and those that performed variable selection were negligible. This was surprising for dry matter, as only a few additive markers explained over 50% of phenotypic variation. Accuracy for tuber count increased from 0.35 to 0.41, when dominance was included in the model. This result is supported by Genome Wide Association Study (GWAS) that found additive and dominance effects accounted for 37% of phenotypic variation, while significant additive effects alone accounted for 14%. For tuber weight, the Reproducing Kernel Hilbert Space (RKHS) model gave a larger improvement in prediction accuracy than explicitly modelling epistatic effects. This is an indication that capturing the between locus epistatic effects of tuber weight can be done more effectively using the semi-parametric RKHS model. Our results show good opportunities for GP in 4x potato.

Over the last decade, multiparental populations have become a mainstay of genetics research in diploid species. Our goal was to extend this paradigm to autotetraploids by developing software for quantitative trait locus (QTL) mapping in connected F1 populations derived from a set of shared parents. For QTL discovery, phenotypes are regressed on the dosage of parental haplotypes to estimate additive effects. Statistical properties of the model were explored by simulating half-diallel diploid and tetraploid populations with different population sizes and numbers of parents. Across scenarios, the number of progeny per parental haplotype (pph) largely determined the statistical power for QTL detection and accuracy of the estimated haplotype effects. Multiallelic QTL with heritability 0.2 were detected with 90% probability at 25 pph and genome-wide significance level 0.05, and the additive haplotype effects were estimated with over 90% accuracy. Following QTL discovery, the software enables a comparison of models with multiple QTL and nonadditive effects. To illustrate, we analyzed potato tuber shape in a half-diallel population with three tetraploid parents. A well-known QTL on chromosome 10 was detected, for which the inclusion of digenic dominance lowered the Deviance Information Criterion (DIC) by 17 points compared to the additive model. The final model also contained a minor QTL on chromosome 1, but higher-order dominance and epistatic effects were excluded based on the DIC. In terms of practical impacts, the software is already being used to select offspring based on the effect and dosage of particular haplotypes in breeding programs.

Many different types of multiparental populations have recently been produced to increase genetic diversity and resolution in QTL mapping. Low-coverage, genotyping-by-sequencing (GBS) technology has become a cost-effective tool in these populations, despite large amounts of missing data in offspring and founders. In this work, we present a general statistical framework for genotype imputation in such experimental crosses from low-coverage GBS data. Generalizing a previously developed hidden Markov model for calculating ancestral origins of offspring DNA, we present an imputation algorithm that does not require parental data and that is applicable to bi- and multiparental populations. Our imputation algorithm allows heterozygosity of parents and offspring as well as error correction in observed genotypes. Further, our approach can combine imputation and genotype calling from sequencing reads, and it also applies to called genotypes from SNP array data. We evaluate our imputation algorithm by simulated and real data sets in four different types of populations: the F2, the advanced intercross recombinant inbred lines, the multiparent advanced generation intercross, and the cross-pollinated population. Because our approach uses marker data and population design information efficiently, the comparisons with previous approaches show that our imputation is accurate at even very low (

Diploid hybrid potato breeding is emerging as an alternative to breeding tetraploid potato clones. The development of diploid breeding varieties involves recent, shallow pedigrees with a limited number of founders. Within this context, alternative QTL detection methodologies should be considered to enable identification of relevant QTLs and characterize the founders of the pedigree. To that end, we are using a dataset of multiple diploid potato $$\hbox {F}_3$$ F 3 families under selection derived by a cross between an inbred Solanum chacoense and an outbred diploid Solanum tuberosum, and identify QTLs for tuber fresh weight. We used three methods for QTL detection: (1) a Genome Wide Association Study model, (2) a linkage approach tailored to the population under study and (3) a more general approach for modelling multiallelic QTLs in complex pedigrees using identity-by-descent (IBD) probabilities. We show that all three approaches enable detection of QTLs in the population under study, but the method that makes better use of IBD information has a more direct and detailed interpretation by linking QTL alleles to the founders.

Due to the advantages of XLPE cable, it is frequently used in power transmission and distribution systems. For long-term use, there are inevitable insulation defects. To detect the status of cable insulation, an improved capacitive sensor that fully covers the cable is proposed, which can be used for nondestructive monitoring of cable insulation, especially for cable joints. In this paper, the geometric structure of the fully-covered interdigital capacitance sensor is designed, and a 3D model of the sensor is built with COMSOL Multiphysics. Three parameters i.e. signal strength, sensitivity and penetration depth are defined for sensor optimization. The influences of electrode length, width, and thickness on interdigital capacitance sensors are discussed. When the length exceeds 5 cm, the length of the electrode does not affect the sensitivity. Electrodes with larger width lead to better signal strength and sensitivity, but the penetration depth decreases. With the increase in the electrode number, the signal strength increases while the sensitivity and penetration depth decrease. Taking YJV1*185 cable as an example, the electrodes of equal width and with a thickness of 0.02-0.12 mm could achieve better measurement results.

It has long been recognised that polyploid species do not always neatly fall into the categories of auto- or allopolyploid, leading to the term ‘segmental allopolyploid’ to describe everything in between. The meiotic behaviour of such intermediate species is not fully understood, nor is there consensus as to how to model their inheritance patterns. In this study we used a tetraploid cut rose (Rosa hybrida) population, genotyped using the 68K WagRhSNP array, to construct an ultra-high-density linkage map of all homologous chromosomes using methods previously developed for autotetraploids. Using the predicted bivalent configurations in this population we quantified differences in pairing behaviour among and along homologous chromosomes, leading us to correct our estimates of recombination frequency to account for this behaviour. This resulted in the re-mapping of 25 695 SNP markers across all homologues of the seven rose chromosomes, tailored to the pairing behaviour of each chromosome in each parent. We confirmed the inferred differences in pairing behaviour among chromosomes by examining repulsion-phase linkage estimates, which also carry information about preferential pairing and recombination. Currently, the closest sequenced relative to rose is Fragaria vesca. Aligning the integrated ultra-dense rose map with the strawberry genome sequence provided a detailed picture of the synteny, confirming overall co-linearity but also revealing new genomic rearrangements. Our results suggest that pairing affinities may vary along chromosome arms, which broadens our current understanding of segmental allopolyploidy.

Many empirical studies of metacommunities have focused on the classification of observational patterns into four contrasting paradigms characterized by different levels of movement and habitat heterogeneity. However, deeper insight into the underlying local and regional processes may be derived from a combination of long-term observational data and experimental studies. With the aim of exploring forces structuring the insect metacommunity on oak, we fit a hierarchical Bayesian state-space model to data from observations and experiments. The fitted model reveals large variation in species-specific dispersal abilities and basic reproduction numbers, R0. The residuals from the model show only weak correlations among species, suggesting a lack of strong interspecific interactions. Simulations with model-derived parameter estimates indicate that habitat configuration and species attributes both contribute substantially to structuring insect communities. Overall, our findings demonstrate that community-level variation in movement and life history are key drivers of metacommunity dynamics.

The models for the mosaic structure of an individual’s genome from multiparental populations have been developed primarily for autosomes, whereas X chromosomes receive very little attention. In this paper, we extend our previous approach to model ancestral origin processes along two X chromosomes in a mapping population, which is necessary for developing hidden Markov models in the reconstruction of ancestry blocks for X-linked quantitative trait locus mapping. The model accounts for the joint recombination pattern, the asymmetry between maternally and paternally derived X chromosomes, and the finiteness of population size. The model can be applied to various mapping populations such as the advanced intercross lines (AIL), the Collaborative Cross (CC), the heterogeneous stock (HS), the Diversity Outcross (DO), and the Drosophila synthetic population resource (DSPR). We further derive the map expansion, density (per Morgan) of recombination breakpoints, in advanced intercross populations with L inbred founders under the limit of an infinitely large population size. The analytic results show that for X chromosomes the genetic map expands linearly at a rate (per generation) of two-thirds times 1 – 10/(9L) for the AIL, and at a rate of two-thirds times 1 – 1/L for the DO and the HS, whereas for autosomes the map expands at a rate of 1 – 1/L for the AIL, the DO, and the HS.

Bloom date is an important production trait in sour cherry (Prunus cerasus L.) as the risk of crop loss to floral freeze injury increases with early bloom time. Knowledge of the major loci controlling bloom date would enable breeders to design crosses and select seedlings with late bloom date. As sour cherry is a segmental allotetraploid, quantitative trait locus (QTL) analysis for bloom date was performed based on haplotype reconstruction by identifying the parental origins of marker alleles in sour cherry. A total of 338 sour cherry individuals from five F1 populations were genotyped using the cherry 6K Illumina Infinium® SNP array and phenotyped for bloom date in 3 years. A total of four QTLs were identified on linkage group (G)1, G2, G4, and G5, respectively. For these QTLs, 14 haplotypes constructed for the QTL regions were significantly associated with bloom date, accounting for 10.1–27.9% of the bloom date variation within individual populations. The three most significant haplotypes, which were identified for the G4 (G4-k), G2 (G2-j), and G1 (G1-c) QTLs, were associated with 2.8, 1.8, and 1.0 days bloom delay, respectively. These three haplotypes were also demonstrated to have additive effects on delaying bloom date for both individual and multiple QTLs. These results demonstrate that bloom date is under polygenic control in sour cherry; yet, pyramiding late blooming haplotypes for single and multiple QTLs would be an effective strategy to obtain later blooming offspring.

In both pedigree linkage studies and in population-based association studies there has been much interest in the use of modern dense genetic marker data to infer segments of gene identity by descent (ibd) among individuals not known to be related, to increase power and resolution in localizing genes affecting complex traits. In this article, we present a hidden Markov model (HMM) for ibd among a set of chromosomes and describe methods and software for inference of ibd among the four chromosomes of pairs of individuals, using either phased (haplotypic) or unphased (genotypic) data. The model allows for missing data and typing error, but does not model linkage disequilibrium (LD), because fitting an accurate LD model requires large samples from well-studied populations. However, LD remains a major confounding factor, since LD is itself a reflection of coancestry at the population level. To study the impact of LD, we have developed a novel simulation approach to generate realistic dense marker data for the same set of markers but at varying levels of LD. Using this approach, we present results of a study of the impact of LD on the sensitivity and specificity of our HMM model in estimating segments of ibd among sets of four chromosomes and between genotype pairs. We show that, despite not incorporating LD, our model has been quite successful in detecting segments as small as 106 bp (1 Mpb); we present also comparisons with fastIBD which uses an LD model in estimating ibd.

Dispersal comprises a complex life-history syndrome that influences the demographic dynamics of especially those species that live in fragmented landscapes, the structure of which may in turn be expected to impose selection on dispersal. We have constructed an individual-based evolutionary sexual model of dispersal for species occurring as metapopulations in habitat patch networks. The model assumes correlated random walk dispersal with edge-mediated behaviour (habitat selection) and spatially correlated stochastic local dynamics. The model is parametrized with extensive data for the Glanville fritillary butterfly. Based on empirical results for a single nucleotide polymorphism (SNP) in the phosphoglucose isomerase ( Pgi ) gene, we assume that dispersal rate in the landscape matrix, fecundity and survival are affected by a locus with two alleles, A and C, individuals with the C allele being more mobile. The model was successfully tested with two independent empirical datasets on spatial variation in Pgi allele frequency. First, at the level of local populations, the frequency of the C allele is the highest in newly established isolated populations and the lowest in old isolated populations. Second, at the level of sub-networks with dissimilar numbers and connectivities of patches, the frequency of C increases with decreasing network size and hence with decreasing average metapopulation size. The frequency of C is the highest in landscapes where local extinction risk is high and where there are abundant opportunities to establish new populations. Our results indicate that the strength of the coupling of the ecological and evolutionary dynamics depends on the spatial scale and is asymmetric, demographic dynamics having a greater immediate impact on genetic dynamics than vice versa.

We describe a Bayesian random effects model of mark-recapture data that accounts for age-dependence in survival and individual heterogeneity in capture probabilities and survival. The model is applied to data on the Glanville fritillary butterfly (Melitaea cinxia) collected from a population enclosed in a large cage in the field. The cage population consisted of a mixture of butterflies originating from newly established and old populations in a large metapopulation in the Aland Islands in Finland. The explanatory variables in the model included the effects of temperature, sex, and population type (new vs. old) on capture probabilities, and the effects of age, sex, population type, and day vs. night on survival. We found that mortality rate increased with age, that mortality rate was much higher during the day than during the night, and that the life span of females originating from newly established populations was shorter than the life span of females from old populations. Capture probability decreased with increasing temperature and decreased with increasing mobility of individuals.

We present a general hidden Markov model framework called reconstructing ancestry blocks bit by bit (RABBIT) for reconstructing genome ancestry blocks from single-nucleotide polymorphism (SNP) array data, a required step for quantitative trait locus (QTL) mapping. The framework can be applied to a wide range of mapping populations such as the Arabidopsis multiparent advanced generation intercross (MAGIC), the mouse Collaborative Cross (CC), and the diversity outcross (DO) for both autosomes and X chromosomes if they exist. The model underlying RABBIT accounts for the joint pattern of recombination breakpoints between two homologous chromosomes and missing data and allelic typing errors in the genotype data of both sampled individuals and founders. Studies on simulated data of the MAGIC and the CC and real data of the MAGIC, the DO, and the CC demonstrate that RABBIT is more robust and accurate in reconstructing recombination bin maps than some commonly used methods.

The next generation of QTL (quantitative trait loci) mapping populations have been designed with multiple founders, where one to a number of generations of intercrossing are introduced prior to the inbreeding phase to increase accumulated recombinations and thus mapping resolution. Examples of such populations are Collaborative Cross (CC) in mice and Multiparent Advanced Generation Inter-Cross (MAGIC) lines in Arabidopsis. The genomes of the produced inbred lines are fine-grained random mosaics of the founder genomes. In this article, we present a novel framework for modeling ancestral origin processes along two homologous autosomal chromosomes from mapping populations, which is a major component in the reconstruction of the ancestral origins of each line for QTL mapping. We construct a general continuous time Markov model for ancestral origin processes, where the rate matrix is deduced from the expected densities of various types of junctions (recombination breakpoints). The model can be applied to monoecious populations with or without self-fertilizations and to dioecious populations with two separate sexes. The analytic expressions for map expansions and expected junction densities are obtained for mapping populations that have stage-wise constant mating schemes, such as CC and MAGIC. Our studies on the breeding design of MAGIC populations show that the intercross mating schemes do not matter much for large population size and that the overall expected junction density, and thus map resolution, are approximately proportional to the inverse of the number of founders.

There has been much interest in detecting genomic identity by descent (IBD) segments from modern dense genetic marker data and in using them to identify human disease susceptibility loci. Here we present a novel Bayesian framework using Markov chain Monte Carlo (MCMC) realizations to jointly infer IBD states among multiple individuals not known to be related, together with the allelic typing error rate and the IBD process parameters. The data are phased single nucleotide polymorphism (SNP) haplotypes. We model changes in latent IBD state along homologous chromosomes by a continuous time Markov model having the Ewens sampling formula as its stationary distribution. We show by simulation that this model for the IBD process fits quite well with the coalescent predictions. Using simulation data sets of 40 haplotypes over regions of 1 and 10 million base pairs (Mbp), we show that the jointly estimated IBD states are very close to the true values, although the presence of linkage disequilibrium decreases the accuracy. We also present comparisons with the ibd_haplo program, which estimates IBD among sets of four haplotypes. Our new IBD detection method focuses on the scale between genome-wide methods using simple IBD models and complex coalescent-based methods that are limited to short genome segments. At the scale of a few Mbp, our approach offers potentially more power for fine-scale IBD association mapping.

We propose a genealogy-sampling algorithm, Sequential Markov Ancestral Recombination Tree (SMARTree), that provides an approach to estimation from SNP haplotype data of the patterns of coancestry across a genome segment among a set of homologous chromosomes. To enable analysis across longer segments of genome, the sequence of coalescent trees is modeled via the modified sequential Markov coalescent (Marjoram and Wall, Genetics 7:16, 2006). To assess performance in estimating these local trees, our SMARTree implementation is tested on simulated data. Our base data set is of the SNPs in 10 DNA sequences over 50 kb. We examine the effects of longer sequences and of more sequences, and of a recombination and/or mutational hotspot. The model underlying SMARTree is an approximation to the full recombinant-coalescent distribution. However, in a small trial on simulated data, recovery of local trees was similar to that of LAMARC (Kuhner et al. Genetics 156:1393-1401, 2000a), a sampler which uses the full model.

While it is well understood that the pace of evolution depends on the interplay between natural selection, random genetic drift, mutation, and gene flow, it is not always easy to disentangle the relative roles of these factors with data from natural populations. One popular approach to infer whether the observed degree of population differentiation has been influenced by local adaptation is the comparison of neutral marker gene differentiation (as reflected in FST) and quantitative trait divergence (as reflected in QST). However, this method may lead to compromised statistical power, because FST and QST are summary statistics which neglect information on specific pairs of populations, and because current multivariate tests of neutrality involve an averaging procedure over the traits. Further, most FST–QST comparisons actually replace QST by its expectation over the evolutionary process and are thus theoretically flawed. To overcome these caveats, we derived the statistical distribution of population means generated by random genetic drift and used the probability density of this distribution to test whether the observed pattern could be generated by drift alone. We show that our method can differentiate between genetic drift and selection as a cause of population differentiation even in cases with FST = QST and demonstrate with simulated data that it disentangles drift from selection more accurately than conventional FST–QST tests especially when data sets are small.

We modeled hierarchical multiscale colonization-extinction dynamics of two aphid species living in a shared host plant. We parameterized the model with data collected at the level of individual ramets of the host plant, with the plants being organized as groups within islands. As expected, the extinction rates and per capita colonization rates decreased with increasing spatial scale. The per capita colonization rates were greater for winged than for unwinged individuals, but as the unwinged individuals were much more abundant, they actually performed most of the colonizations. Colonizations and extinctions were negatively correlated, so that when the colonization rate in a given island was high, the extinction rate in the same island was low. There was a clear indication of interspecific interaction, with the presence of one species increasing the extinction rate and decreasing the colonization rate of the other species. Further simulation results based on the parameterized model show a contrasting pattern between the two species, with Metopeurum fuscoviride (with relatively stable dynamics) being favored by a highly aggregated distribution of the ramets, whereas for Macrosiphoniella tanacetaria (with a high turnover rate), an equally high persistence time follows if the plants are distributed in a segregated manner over several islands.

Quantifying dispersal is crucial both for understanding ecological population dynamics, and for gaining insight into factors that affect the genetic structure of populations. The role of dispersal becomes pronounced in highly fragmented landscapes inhabited by spatially structured populations. We consider a landscape consisting of a set of habitat patches surrounded by unsuitable matrix, and model dispersal by assuming that the individuals follow a random walk with parameters that may be specific to the habitat type. We allow for spatial variation in patch quality, and account for edge-mediated behavior, the latter meaning that the individuals bias their movement towards the patches when close to an edge between a patch and the matrix. We employ a diffusion approximation of the random walk model to derive analytical expressions for various characteristics of the dispersal process. For example, we derive formulae for the time that an individual is expected to spend in its current patch i, and for the time that it will spend in the matrix, both conditional on the individual hitting next a given patch j before hitting any of the other patches or dying. The analytical formulae are based on the assumptions that the landscape is infinitely large, that the patches are circularly shaped, and that the patches are small compared to interpatch distances. We evaluate the effect of these assumptions by comparing the analytical results to numerical results in a real patch network that violates all of the three assumptions. We then consider a landscape that fulfills the assumptions, and show that in this case the analytical results are in a very good agreement with the numerical results. The results obtained here allow the construction of computationally efficient dispersal models that can be used as components of metapopulation models.

Using a linear optical diffraction technique, we have systematically investigated the defect effects on quantum surface diffusion of hydrogen on Pt(111) surfaces. The quantum tunneling effect was clearly observed for hydrogen diffusion at low temperatures as manifested by a leveling off of the diffusion coefficient on flat surfaces. The strong influence of surface defects on the quantum diffusion is in good agreement with the creation of an inhomogeneous surface with adsorption sites of different binding energies.

Step effects on surface diffusion of hydrogen on stepped $\mathrm{Pt}(111)$ have been studied by linear optical diffraction technique over a temperature range from 90 to $150\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Diffusion anisotropy on stepped $\mathrm{Pt}(111)$ surfaces has been observed: the unexpected enhanced diffusion perpendicular to steps cannot be explained within the lattice gas model on stepped substrates, indicating a nonlocal and directional step effect. The coverage-dependent diffusion coefficient on flat $\mathrm{Pt}(111)$ surface was also measured over a wide coverage range from 0.1 to $0.8\phantom{\rule{0.3em}{0ex}}\mathrm{ML}$. They were analyzed within the framework of the lattice gas model using quasichemical approximation, indicating that $\mathrm{H}\text{\ensuremath{-}}\mathrm{H}$ repulsive interaction can significantly affect the energy of saddle point as well as that at the adsorption sites.

We have used the linear optical diffraction method to study the diffusion of hydrogen atoms on flat and stepped W(100) surfaces. At 0.17-monolayer (ML) H coverage, the diffusion coefficient (D) shows a strong anomalous dip at the substrate reconstructive phase transition temperature in an Arrhenius plot for diffusion on both surfaces. No anomalous diffusion behavior is observed at 1.2-ML H coverage on both surfaces in the entire range studied, 240--380 K, consistent with the absence of the phase transition at this H coverage. The strong reduction of D can be attributed to the diverging friction damping near the transition. Steps do not suppress the substrate phase transition and affect the diffusion anomaly very little. For both H coverages, the only effect of steps is to introduce a small Schwoebel-Ehrlich barrier (\ensuremath{\sim}2.2 kcal/mol for 1.2 ML and \ensuremath{\sim}2.8 kcal/mol for 0.17 ML) near the step edges, which slows down H diffusion perpendicular to steps. Measurements of H diffusion parallel to steps reveals no obvious enhancement due to step edge diffusion.