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Marine research survey data on fish stocks often show a small proportion of very high-density values, as for many environmental data. This makes the estimation of second-order statistics, such as the variance and the variogram, non-robust. The high fish density values are generated by fish aggregative behaviour, which may vary greatly at small scale in time and space. The high values are thus imprecisely known, both in their spatial occurrence and order of magnitude. To map such data, three indicator-based geostatistical methods were considered, the top-cut model, min–max autocorrelation factors (MAF) of indicators, and multiple indicator kriging. In the top-cut and MAF approaches, the variable is decomposed into components and the most continuous ones (those corresponding to the low and medium values) are used to guide the mapping. The methods are proposed as alternatives to ordinary kriging when the variogram is difficult to estimate. The methods are detailed and applied on a spatial data set of anchovy densities derived from a typical fish stock acoustic survey performed in the Bay of Biscay, which show a few high-density values distributed in small spatial patches and also as solitary events. The model performances are analyzed by cross-validating the data and comparing the kriged maps. Results are compared to ordinary kriging as a base case. The top-cut model had the best cross-validation performance. The indicator-based models allowed mapping high-value areas with small spatial extent, in contrast to ordinary kriging. Practical guidelines for implementing the indicator-based methods are provided.

Marine research survey data on fish stocks often show a small proportion of very high-density values, as for many environmental data. This makes the estimation of second-order statistics, such as the variance and the variogram, non-robust. The high fish density values are generated by fish aggregative behaviour, which may vary greatly at small scale in time and space. The high values are thus imprecisely known, both in their spatial occurrence and order of magnitude. To map such data, three indicator-based geostatistical methods were considered, the top-cut model, min–max autocorrelation factors (MAF) of indicators, and multiple indicator kriging. In the top-cut and MAF approaches, the variable is decomposed into components and the most continuous ones (those corresponding to the low and medium values) are used to guide the mapping. The methods are proposed as alternatives to ordinary kriging when the variogram is difficult to estimate. The methods are detailed and applied on a spatial data set of anchovy densities derived from a typical fish stock acoustic survey performed in the Bay of Biscay, which show a few high-density values distributed in small spatial patches and also as solitary events. The model performances are analyzed by cross-validating the data and comparing the kriged maps. Results are compared to ordinary kriging as a base case. The top-cut model had the best cross-validation performance. The indicator-based models allowed mapping high-value areas with small spatial extent, in contrast to ordinary kriging. Practical guidelines for implementing the indicator-based methods are provided.

Marine research survey data on fish stocks often show a small proportion of very high-density values, as for many environmental data. This makes the estimation of second-order statistics, such as the variance and the variogram, non-robust. The high fish density values are generated by fish aggregative behaviour, which may vary greatly at small scale in time and space. The high values are thus imprecisely known, both in their spatial occurrence and order of magnitude. To map such data, three indicator-based geostatistical methods were considered, the top-cut model, min–max autocorrelation factors (MAF) of indicators, and multiple indicator kriging. In the top-cut and MAF approaches, the variable is decomposed into components and the most continuous ones (those corresponding to the low and medium values) are used to guide the mapping. The methods are proposed as alternatives to ordinary kriging when the variogram is difficult to estimate. The methods are detailed and applied on a spatial data set of anchovy densities derived from a typical fish stock acoustic survey performed in the Bay of Biscay, which show a few high-density values distributed in small spatial patches and also as solitary events. The model performances are analyzed by cross-validating the data and comparing the kriged maps. Results are compared to ordinary kriging as a base case. The top-cut model had the best cross-validation performance. The indicator-based models allowed mapping high-value areas with small spatial extent, in contrast to ordinary kriging. Practical guidelines for implementing the indicator-based methods are provided.

Marine research survey data on fish stocks often show a small proportion of very high-density values, as for many environmental data. This makes the estimation of second-order statistics, such as the variance and the variogram, non-robust. The high fish density values are generated by fish aggregative behaviour, which may vary greatly at small scale in time and space. The high values are thus imprecisely known, both in their spatial occurrence and order of magnitude. To map such data, three indicator-based geostatistical methods were considered, the top-cut model, min–max autocorrelation factors (MAF) of indicators, and multiple indicator kriging. In the top-cut and MAF approaches, the variable is decomposed into components and the most continuous ones (those corresponding to the low and medium values) are used to guide the mapping. The methods are proposed as alternatives to ordinary kriging when the variogram is difficult to estimate. The methods are detailed and applied on a spatial data set of anchovy densities derived from a typical fish stock acoustic survey performed in the Bay of Biscay, which show a few high-density values distributed in small spatial patches and also as solitary events. The model performances are analyzed by cross-validating the data and comparing the kriged maps. Results are compared to ordinary kriging as a base case. The top-cut model had the best cross-validation performance. The indicator-based models allowed mapping high-value areas with small spatial extent, in contrast to ordinary kriging. Practical guidelines for implementing the indicator-based methods are provided.

Within the genus Rosa numerous species have been described. Circumscription of the dogrose section Caninae is straightforward, but the delineation of species and subsections within this section is less clear, partly due to hybridisation between species. We have investigated the extent to which DNA marker-based information of wild populations corroborates present-day dogrose taxonomy and hypotheses about the origination of taxa. Sampling was conducted in a transect across Europe, collecting over 900 specimens of all encountered dogrose taxa. For comparison, we also included more than 200 samples of species belonging to other sections. Two lines of statistical analyses were used to investigate the genetic structure based on AFLP data: 1) an unstructured model with principal coordinate analysis and hierarchical clustering, and 2) a model with a superimposed taxonomic structure based on analysis of genetic diversity using a novel approach combining assignment tests with canonical discriminant analysis. Support was found for five of the seven subsections, whereas R. balsamica apparently belongs to subsection Caninae thus omitting the need for recognizing subsection Tomentellae. For R. stylosa, a hybridogenic origin with a non-dogrose section member has been suggested, and it can be treated either as a separate subsection or within subsection Caninae. Within the subsection Rubigineae, a species cluster with low support for the taxa R. micrantha, R. rubiginosa and the putatively hybridogenous R. gremlii was identified. Similarly, several species in the subsection Caninae overlapped considerably, and are best regarded as one common species complex. This population genetic approach provides a general method to validate the taxonomic system in complex and polyploid taxa.

Question Is native species occurrence related to soil nutrients in highly invaded Californian annual grasslands? What is the best method to analyze this relationship, given that native species occur in very low numbers and are absent from many locations? Location California, USA. Methods We investigated the effects of soil characteristics and livestock grazing on native plant occurrence at 40 plots from six sites during the period 2003-2005. Low absolute cover (< 5.8%) of native species resulted in strongly skewed, zero-inflated data sets. To overcome problems in the analysis created by non-normality and correlations within plots, we used GLMs and GLMMs, either with a Poisson or a negative binomial distribution, to analyse native species richness and Nassella pulchra cover. Results N. pulchra cover was strongly associated with low phosphorus in sandy soils, whereas native species richness was highest in soils with low available nitrogen (high CN). Conclusion Under current conditions, phosphorus seems to be a critical factor influencing abundance of N. pulchra. Low fertility soils may provide refugia for native species in highly invaded California grasslands as they may be below a threshold required for non-native annuals to completely dominate. By using non-normal distributions in linear models with random components, we report well fitted models with more accurately tested significant covariates. © IAVS; Opulus Press.