spag e d i version 1.0 is a software primarily designed to characterize the spatial genetic structure of mapped individuals or populations using genotype data of codominant markers. It computes various statistics describing genetic relatedness or differentiation between individuals or populations by pairwise comparisons and tests their significance by appropriate numerical resampling. spag e d i is useful for: (i) detecting isolation by distance within or among populations and estimating gene dispersal parameters; (ii) assessing genetic relatedness between individuals and its actual variance, a parameter of interest for marker based inferences of quantitative inheritance; (iii) assessing genetic differentiation among populations, including the case of haploids or autopolyploids.

Many empirical studies have assessed fine-scale spatial genetic structure (SGS), i.e. the nonrandom spatial distribution of genotypes, within plant populations using genetic markers and spatial autocorrelation techniques. These studies mostly provided qualitative descriptions of SGS, rendering quantitative comparisons among studies difficult. The theory of isolation by distance can predict the pattern of SGS under limited gene dispersal, suggesting new approaches, based on the relationship between pairwise relatedness coefficients and the spatial distance between individuals, to quantify SGS and infer gene dispersal parameters. Here we review the theory underlying such methods and discuss issues about their application to plant populations, such as the choice of the relatedness statistics, the sampling scheme to adopt, the procedure to test SGS, and the interpretation of spatial autocorrelograms. We propose to quantify SGS by an 'Sp' statistic primarily dependent upon the rate of decrease of pairwise kinship coefficients between individuals with the logarithm of the distance in two dimensions. Under certain conditions, this statistic estimates the reciprocal of the neighbourhood size. Reanalysing data from, mostly, published studies, the Sp statistic was assessed for 47 plant species. It was found to be significantly related to the mating system (higher in selfing species) and to the life form (higher in herbs than trees), as well as to the population density (higher under low density). We discuss the necessity for comparing SGS with direct estimates of gene dispersal distances, and show how the approach presented can be extended to assess (i) the level of biparental inbreeding, and (ii) the kurtosis of the gene dispersal distribution.

We investigate the distribution of sizes of fragments obtained from the amplified fragment length polymorphism (AFLP) marker technique. We find that empirical distributions obtained in two plant species, Phaseolus lunatus and Lolium perenne, are consistent with the expected distributions obtained from analytical theory and from numerical simulations. Our results indicate that the size distribution is strongly asymmetrical, with a much higher proportion of small than large fragments, that it is not influenced by the number of selective nucleotides nor by genome size but that it may vary with genome-wide GC-content, with a higher proportion of small fragments in cases of lower GC-content when considering the standard AFLP protocol with the enzyme MseI. Results from population samples of the two plant species show that there is a negative relationship between AFLP fragment size and fragment population frequency. Monte Carlo simulations reveal that size homoplasy, arising from pulling together nonhomologous fragments of the same size, generates patterns similar to those observed in P. lunatus and L. perenne because of the asymmetry of the size distribution. We discuss the implications of these results in the context of estimating genetic diversity with AFLP markers.

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