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Abstract Armillaria ostoyae is an important disease of Pinus pinaster in north-west Spain, which kills trees following a heterogeneous spatial structure. In a progeny trial of P.

Pinaster seedlings, spatial heterogeneity and autocorrelation of neighbour mortality caused by A. Ostoyae impeded proper analysis of the disease incidence. We used variography and kriging methods to describe the spatial distribution of the infection probability and the genetic variation of the resistance to A. Ostoyae among families. The spatial structure of disease incidence was modelled, and the probability of survival was corrected by kriging at each tree location.

Cumulative mortality 3 years after planting was 65.1 per cent. Significant differences among P. Pinaster families in terms of mortality to A. Microsoft Office 2003 Proofing Tools Arabic. Ostoyae were found, with low individual ( h i 2 = 0.08) and moderate family ( h f 2 = 0.35) heritability estimates. According to a theoretical semivariogram, the patch size of the disease incidence was ∼63 m wide. This is the first time variography and kriging are used to select P.

Pinaster resistant to Armillaria root rot. It is concluded that geostatistics provides forest pathologists with a powerful tool for screening resistant trees in field conditions.

Only trees killed by Armillaria were used for further analysis. Residuals of tree survival were used to explore the spatial heterogeneity of Armillaria root rot mortality within the experimental area. Mean family survival was calculated and subtracted from each individual observation of the family member.

The spatial structure of the resulting residuals was analysed using a semivariogram, which plots the semivariance between individual trees as a function of the distance separating them. The semivariance g( h) was calculated as. Where n is the number of observation pairs separated by distance h (called the lag distance), z( s i) is the value for a tree located at s i and z( s i+h) is the value for a tree located at a distance h from s i. For randomly distributed data, little change in the semivariance will be obtained when h increases, and the semivariogram will be essentially flat. If spatial dependence is present, semivariance will be lower at short distances, it will increase for intermediate distances and it will typically reach an asymptote for long distances. The distance at which the asymptote begins, if present, indicates the range or patch size of heterogeneity below which data are stochastically dependent (). By common convention, the analysis is restricted to distances of half the dimension of the study area.

The experimental semivariogram was constructed using the VARIOGRAM procedure of the SAS System ().Spherical and exponential models were fitted to the experimental semivariogram using the NLIN procedure in SAS (). Since the exponential model fitted better than spherical model, this model was used to partition the variation of survival residuals into spatially autocorrelated variation and random error with the kriging method. Kriging computes surfaces of best linear unbiased predictions of values based on the spatial structure defined by the theoretical semivariogram. In our case, this surface was interpreted as the spatial distribution of the probability of survival of trees to Armillaria root rot.

Thus, the kriging values at each tree location were used to correct the original survival values in relation to the spatial variation. Because being alive in a free Armillaria zone is not the same as being alive in a high-risk infection zone, original survival values were corrected by removing the kriging estimate.

This new variable varies, theoretically, between −1 (dead plant in a totally Armillaria free area) and +1 (non-symptomatic plant in a completely infected area) and was considered as an indication of the resistance to the disease. The kriging analysis was performed using the KRIGE2D SAS procedure ().

Genetic parameter estimates. Where S ij is the value of the corrected survival of family i in block j, μ is the overall mean, F i and B j are the random effects of family i ( i = 1–111) and block j ( j = 1–25), respectively, and ∈ ij is the random error. Variance components of random effects were estimated using the restricted maximum likelihood (REML) method of the MIXED procedure in SAS ().

Individual and family heritabilities were calculated upon the variance components as described in. Standard errors were estimated using the formulae described in.

Results Overall mortality 3 years after planting was 65.1 per cent. Most trees died during summer and autumn 2003.

Within the F 1 population, family mortality rate varied between 40 and 88 per cent. Control seed lots mortality rate varied between 56 and 76 per cent. More than 95 per cent of the dead trees presented typical mycelial fans under the bark and ∼90 per cent of recently killed trees presented white mycelium at the root collar. Both the compatibility method and the RFLP-PCR detected A.

Ostoyae in root samples. The spatial heterogeneity of the incidence of Armillaria root rot disease was evident from the plot of survival residuals (), some areas being much more affected than others. This heterogeneity was confirmed by the experimental semivariogram () which clearly indicated that neighbouring trees tend to have more similar values than trees far away. Semivariogram for survival of Pinus pinaster adjusted for family effects, i.e.

Survival family mean subtracted to each individual observation. The exponential function fitted well to the experimental semivariogram (), with a regression coefficient between observed and expected values of 0.94 ( P.

Abstract Armillaria ostoyae is an important disease of Pinus pinaster in north-west Spain, which kills trees following a heterogeneous spatial structure. In a progeny trial of P. Pinaster seedlings, spatial heterogeneity and autocorrelation of neighbour mortality caused by A.

Ostoyae impeded proper analysis of the disease incidence. We used variography and kriging methods to describe the spatial distribution of the infection probability and the genetic variation of the resistance to A. Ostoyae among families.

The spatial structure of disease incidence was modelled, and the probability of survival was corrected by kriging at each tree location. Cumulative mortality 3 years after planting was 65.1 per cent. Significant differences among P. Pinaster families in terms of mortality to A. Ostoyae were found, with low individual ( h i 2 = 0.08) and moderate family ( h f 2 = 0.35) heritability estimates. According to a theoretical semivariogram, the patch size of the disease incidence was ∼63 m wide. This is the first time variography and kriging are used to select P.

Pinaster resistant to Armillaria root rot. It is concluded that geostatistics provides forest pathologists with a powerful tool for screening resistant trees in field conditions. Only trees killed by Armillaria were used for further analysis. Residuals of tree survival were used to explore the spatial heterogeneity of Armillaria root rot mortality within the experimental area. Mean family survival was calculated and subtracted from each individual observation of the family member. The spatial structure of the resulting residuals was analysed using a semivariogram, which plots the semivariance between individual trees as a function of the distance separating them.

The semivariance g( h) was calculated as. Where n is the number of observation pairs separated by distance h (called the lag distance), z( s i) is the value for a tree located at s i and z( s i+h) is the value for a tree located at a distance h from s i. For randomly distributed data, little change in the semivariance will be obtained when h increases, and the semivariogram will be essentially flat. If spatial dependence is present, semivariance will be lower at short distances, it will increase for intermediate distances and it will typically reach an asymptote for long distances. The distance at which the asymptote begins, if present, indicates the range or patch size of heterogeneity below which data are stochastically dependent ().

By common convention, the analysis is restricted to distances of half the dimension of the study area. The experimental semivariogram was constructed using the VARIOGRAM procedure of the SAS System ().Spherical and exponential models were fitted to the experimental semivariogram using the NLIN procedure in SAS ().

Since the exponential model fitted better than spherical model, this model was used to partition the variation of survival residuals into spatially autocorrelated variation and random error with the kriging method. Kriging computes surfaces of best linear unbiased predictions of values based on the spatial structure defined by the theoretical semivariogram.

In our case, this surface was interpreted as the spatial distribution of the probability of survival of trees to Armillaria root rot. Thus, the kriging values at each tree location were used to correct the original survival values in relation to the spatial variation. Because being alive in a free Armillaria zone is not the same as being alive in a high-risk infection zone, original survival values were corrected by removing the kriging estimate. This new variable varies, theoretically, between −1 (dead plant in a totally Armillaria free area) and +1 (non-symptomatic plant in a completely infected area) and was considered as an indication of the resistance to the disease.

The kriging analysis was performed using the KRIGE2D SAS procedure (). Genetic parameter estimates.

Where S ij is the value of the corrected survival of family i in block j, μ is the overall mean, F i and B j are the random effects of family i ( i = 1–111) and block j ( j = 1–25), respectively, and ∈ ij is the random error. Variance components of random effects were estimated using the restricted maximum likelihood (REML) method of the MIXED procedure in SAS (). Individual and family heritabilities were calculated upon the variance components as described in. Standard errors were estimated using the formulae described in. Results Overall mortality 3 years after planting was 65.1 per cent.

Most trees died during summer and autumn 2003. Within the F 1 population, family mortality rate varied between 40 and 88 per cent. Control seed lots mortality rate varied between 56 and 76 per cent. More than 95 per cent of the dead trees presented typical mycelial fans under the bark and ∼90 per cent of recently killed trees presented white mycelium at the root collar. Both the compatibility method and the RFLP-PCR detected A. Ostoyae in root samples.

The spatial heterogeneity of the incidence of Armillaria root rot disease was evident from the plot of survival residuals (), some areas being much more affected than others. This heterogeneity was confirmed by the experimental semivariogram () which clearly indicated that neighbouring trees tend to have more similar values than trees far away. Semivariogram for survival of Pinus pinaster adjusted for family effects, i.e. Survival family mean subtracted to each individual observation. The exponential function fitted well to the experimental semivariogram (), with a regression coefficient between observed and expected values of 0.94 ( P.