How to estimate variability in affinity relationships in partially observed groups of domestic herbivores?

Animal sociability measurements based on inter-individual distances or nearest-neighbour distributions can be obtained automatically with telemetry collars. So far, all the indices that have been used require the whole group to be observed. Here, we propose an index of the variability in affinity relationships in groups of domestic herbivores, whose definition does not depend on group size and that can be used even if some data are missing. This index and its estimators are based on a function that measures how frequently an animal is closer than another one from a third animal. When no data are missing, we show that our estimator and the variance of the sociability matrix sensu Sibbald (considered as the reference method) are strongly correlated. We then consider two cases of missing data. In the first case, some animals are randomly missing, that is, to account for random breakdown of telemetry collars. Our estimator is unbiased by such missing data and its variance decreases as the number of observation dates increases. In the second case, the same animals are missing at all observation dates, that is, in large herds where there are more individuals to be observed than available telemetry collars. Our estimator of affinity variance within a group is biased by such missing data. Thus, it requires changing animals equipped with telemetry collars regularly during the experiment. Conversely, the estimator remains unbiased at the population level, that is, if several independent groups are being analysed. We finally illustrate how this estimator can be used by investigating changes in the variability of affinities according to group size in grazing heifers.

Quantitative resistance affects the speed of frequency increase but not the diversity of the virulence alleles overcoming a major resistance gene to Leptosphaeria maculans in oilseed rape.

Quantitative resistance mediated by multiple genetic factors has been shown to increase the potential for durability of major resistance genes. This was demonstrated in the Leptosphaeria maculans/Brassica napus pathosystem in a 5year recurrent selection field experiment on lines harboring the qualitative resistance gene Rlm6 combined or not with quantitative resistance. The quantitative resistance limited the size of the virulent isolate population. In this study we continued this recurrent selection experiment in the same way to examine whether the pathogen population could adapt and render the major gene ineffective in the longer term. The cultivars Eurol, with a susceptible background, and Darmor, with quantitative resistance, were used. We confirmed that the combination of qualitative and quantitative resistance is an effective approach for controlling the pathogen epidemics over time. This combination did not prevent isolates virulent against the major gene from amplifying in the long term but the quantitative resistance significantly delayed for 5years the loss of effectiveness of the qualitative resistance and disease severity was maintained at a low level on the genotype with both types of resistance after the fungus population had adapted to the major gene. We also showed that diversity of AvrLm6 virulence alleles was comparable in isolates recovered after the recurrent selection on lines carrying either the major gene alone or in combination with quantitative resistance: a single repeat-induced point mutation and deletion events were observed in both situations. Breeding varieties which combine qualitative and quantitative resistance can effectively contribute to disease control by increasing the potential for durability of major resistance genes.

Spatial distribution of bacterial colonies in a model cheese.

In most ripened cheeses, bacteria are responsible for the ripening process. Immobilized in the cheese matrix, they grow as colonies. Therefore, their distribution as well as the distance between them are of major importance for ripening steps since metabolites diffuse within the cheese matrix. No data are available to date about the spatial distribution of bacterial colonies in cheese. This is the first study to model the distribution of bacterial colonies in a food-type matrix using nondestructive techniques. We compared (i) the mean theoretical three-dimensional (3D) distances between colonies calculated on the basis of inoculation levels and considering colony distribution to be random and (ii) experimental measurements using confocal microscopy photographs of fluorescent colonies of a Lactococcus lactis strain producing green fluorescent protein (GFP) inoculated, at different levels, into a model cheese made by ultrafiltration (UF). Enumerations showed that the final numbers of cells were identical whatever the inoculation level (10(4) to 10(7) CFU/g). Bacterial colonies were shown to be randomly distributed, fitting Poisson's model. The initial inoculation level strongly influenced the mean distances between colonies (from 25 µm to 250 µm) and also their mean diameters. The lower the inoculation level, the larger the colonies were and the further away from each other. Multiplying the inoculation level by 50 multiplied the interfacial area of exchange with the cheese matrix by 7 for the same cell biomass. We finally suggested that final cell numbers should be discussed together with inoculation levels to take into account the distribution and, consequently, the interfacial area of colonies, which can have a significant influence on the cheese-ripening process on a microscopic scale.