Pierre Dutilleul

Modifying the t test for assessing the correlation between two spatial processes

Clifford, Richardson, and Hm they require the estimation of an effective sample size that takes into account the spatial structure of both processes. Clifford et al. developed their method on the basis of an approximation of the variance of the sample correlation coefficient and assessed it by Monte Carlo simulations for lattice and non-lattice networks of moderate to large size. In the present paper, the variance of the sample covariance is computed for a finite number of locations, under the multinormality assumption, and the mathematical derivation of the definition of effective sample size is given. The theoretically expected number of degrees of freedom for the modified t test with renewed modifications is compared with that computed on the basis of equation (2.9) of Clifford et al. (1989). The largest differences are observed for small numbers of locations and high autocorrelation, in particular when the latter is present with opposite sign in the two processes. Basic references that were missing in Clifford et al. (1989) are given and inherent ambiguities are discussed.

Spatial Heterogeneity and the Design of Ecological Field Experiments

Experimental design should be accommodated to spatial heterogeneity in nature as well as indoors, whether it is a nuisance or a characteristic of interest, combined or not with assessment of treatment effects. The following analysis—of—variance approach to quantification of spatial heterogeneity is based on the adequate design of ecological field experiments, according to the type and the scale of heterogeneity of concern (at small scale, patches, one— or two—dimensional gradients). There are no recipes for doing so and judgment must be exercised every time: the experimenters knowledge about the experimental material, combined with premanipulation or control, then, provides a useful prerequisite. For patches and environmental gradients, in the presence of treatment assignment, recommended designs require the blocking principle of grouping similar experimental units, which allows avoidance of spurious treatment effects and inflated error mean square. Completely randomized designs should only be used in the very particular case of spatial homogeneity at large scale. Illustrations in ecological field experimentation are given and discussed.

Advances in the implementation of the box-counting method of fractal dimension estimation

The box-counting analysis is an appropriate method of fractal dimension estimation for images with or without self-similarity. However, this technique, including processing of the image and definition of the range of box sizes, requires a proper implementation to be effective in practice. The objectives of this study were thus (1) to determine how to prepare an image for box-counting analysis; (2) to define reasonable preferences for using the Fractal Dimension Calculator software; and (3) to develop a routine procedure for defining the most appropriate range of box sizes for any one-piece image. Four fractal images were chosen for this study: the Koch curve, Koch coastline, Koch boxes, and Cross-tree. Our results show that the skeletons provide better material for the box-counting method since only lines and/or curves are responsible for the fractal dimension value. In the procedure of box counting for fractal dimension estimation, the image must be surrounded by a four-square frame with the least possible area and the condition of linear relationship must be satisfied in a log-log plot. Fractal dimension is to be estimated over the minimum number of boxes covering the image for each box size, after superimposing a reasonable number of grid offsets. In many cases, 25% of the shorter image side may provide an appropriate value for largest box size. However, for noisy or dispersed patterns, a smaller box size than this is needed. In the log-log plot with 12 box sizes, some points corresponding to smaller box sizes deviate from the straight line from a certain point on. The box size corresponding to this breakpoint will provide an appropriate smallest box size. The exercise of determining the most appropriate range of box sizes must be performed repeatedly for every individual image.

Farm-scale evaluation of the impacts of transgenic cotton on biodiversity, pesticide use, and yield

Higher yields and reduced pesticide impacts are needed to mitigate the effects of agricultural intensification. A 2-year farm-scale evaluation of 81 commercial fields in Arizona show that use of transgenic Bacillus thuringiensis (Bt) cotton reduced insecticide use, whereas transgenic cotton with Bt protein and herbicide resistance (BtHr) did not affect herbicide use. Transgenic cotton had higher yield than nontransgenic cotton for any given number of insecticide applications. However, nontransgenic, Bt and BtHr cotton had similar yields overall, largely because higher insecticide use with nontransgenic cotton improved control of key pests. Unlike Bt and BtHr cotton, insecticides reduced the diversity of nontarget insects. Several other agronomic and ecological factors also affected biodiversity. Nevertheless, pairwise comparisons of diversity of nontarget insects in cotton fields with diversity in adjacent noncultivated sites revealed similar effects of cultivation of transgenic and nontransgenic cotton on biodiversity. The results indicate that impacts of agricultural intensification can be reduced when replacement of broad-spectrum insecticides by narrow-spectrum Bt crops does not reduce control of pests not affected by Bt crops.

The mle algorithm for the matrix normal distribution

The maximum likelihood estimation (MLE) of the parameters of the matrix normal distribution is considered. In the absence of analytical solutions of the system of likelihood equations for the among-row and among-column covariance matrices, a two-stage algorithm must be solved to obtain their maximum likelihood estimators. A necessary and sufficient condition for the existence of maximum likelihood estimators is given and the question of their stability as solutions of the system of likelihood equations is addressed. In particular, the covariance matrix parameters and their maximum likelihood estimators are defined up to a positive multiplicative constant; only their direct product is uniquely defined. Using simulated data undertwovariance-covariancestructures that, otherwise, are indistinguishable by semivariance analysis, further specific aspects of the procedure are studied: (1) the convergence of the MLE algorithm is assessed; (2) the empirical bias of the direct product ofcovariance matrix estimators ...

Head Blight Gradients Caused by Gibberella zeae from Area Sources of Inoculum in Wheat Field Plots

ABSTRACT The spread of Fusarium head blight of wheat from a small area inoculum source was examined in wheat plots (100, 625, or 2,500 m(2)) inoculated in the center with Gibberella zeae-colonized corn kernels or macro-conidia sprayed on heads at anthesis. With the first inoculation method, disease foci were produced from ascospores released from perithecia formed on inoculated kernels. With the second inoculation method, disease foci were produced by macroconidia directly applied to the heads. Some plots were misted during anthesis. Plots were divided into grids, and disease incidence on spikelets and seeds was assessed at the grid intersections. Isopath contour maps were constructed using an interpolation procedure based on a weighted least squares method. Disease gradients were constructed from the isopath contours in the direction parallel to average nightly wind vectors using an exponential model. This study was conducted over a 3-year period at two sites: one in Quebec and one in Ontario. Both inoculation methods resulted in a discrete, primary focus of head blight in each plot, with one or two smaller secondary foci in some plots. The highest incidence of disease on spikelets or seed was commonly displaced somewhat from the inoculum source, usually downwind. The gradient slopes of seed and spikelet infection ranged from -0.10 to -0.43 m(1) in plots with ascospore inoculum and from -0.48 to -0.79 m(1) in plots inoculated with macroconidia. Seed infection declined to 10% of the maximum within 5 to 22 m from the focal center in asco-spore-inoculated plots, and within 5 m in a macroconidia-inoculated plot. Gradients were usually steeper upwind compared with downwind of the inoculum source. In misted plots, incidence of disease was higher and more diffuse than in nonirrigated plots. Based on gradients and dispersal patterns, disease foci in plots inoculated with G. zeae-colonized corn kernels probably arose from airborne ascospores rather than from splash-borne macroconidia and were the result of infection events that occurred over a short period of time. Comparison of conidial- and ascospore-derived disease gradients indicated a lack of secondary infection, confirming that Fusarium head blight is primarily a monocyclic disease.

The Mantel Test Versus Pearson's Correlation Analysis: Assessment of the Differences for Biological and Environmental Studies

The space-time clustering procedure of Mantel was originally designed to relate a matrix of spatial distance measures and a matrix of temporal distance measures in a generalized regression approach. The procedure, known as the Mantel test in the biological and environmental sciences, includes any analysis relating two distance matrices or, more generally, two proximity matrices. In this paper, we discuss the extent to which a Mantel type of analysis between two proximity matrices agrees with Pearsons correlation analysis when both methods are applicable (i.e., the raw data used to calculate proximities are available). First, we demonstrate that the Mantel test and Pearsons correlation analysis should lead to a similar decision regarding their respective null hypothesis when squared Euclidean distances are used in the Mantel test and the raw bivariate data are normally distributed. Then we use fish and zooplankton biomass data from Lake Erie (North American Great Lakes) to show that Pearsons correlation statistic may be nonsignificant while the Mantel statistic calculated on nonsquared Euclidean distances is significant. After small-size artificial examples, seven bivariate distributional models are tried to simulate data reproducing the difference between analyses, among which three do reproduce it. These results and some extensions are discussed. In conclusion, particular attention must be paid whenever relations established between proximities are backtransposed to raw data, especially when these may display patterns described in the body of this paper.

A GIS-based approach for areawide pest management: the scales of Lygus hesperus movements to cotton from alfalfa, weeds, and cotton

Understanding the effect of cropping patterns on population dynamics, dispersal, and habitat selection of insect pests has been an unresolved challenge. Here, we studied the western tarnished plant bug, Lygus hesperus (Knight) (Heteroptera: Miridae), in cotton during early summer in central Arizona. We used a general approach based on global positioning system (GPS) and geographic information system (GIS) technologies combined with spatial statistics to assess the maximum distance at which forage and seed alfalfa, fallow fields with weeds, and cotton affect L. hesperus population density. Using a set of 50 cotton fields as focal fields, we found that forage and seed alfalfa as well as weeds acted as L. hesperus sources for these cotton fields. The source effect did not extend beyond 375, 500, and 1500 m for forage alfalfa, weeds, and seed alfalfa, respectively. Conversely, cotton fields acted as L. hesperus sinks, but this effect did not extend further than 750 m from the focal cotton fields. These findings suggest that specific spatial arrangements of these field types could reduce L. hesperus damage to cotton. The spatially explicit approach used here provides a direct evaluation of the effects of agroecosystem heterogeneity on pest population dynamics, dispersal, and habitat selection, which is a significant asset for the development and improvement of areawide pest management.

Inter-relationships of applied nitrogen, SPAD, and yield of leafy and non-leafy maize genotypes

The SPAD chlorophyll meter was found to be a reliable, quick, and non-destructive tool used for directly measuring leaf chlorophyll and indirectly assessing the proportional parameter of leaf, and by extension, plant nitrogen (N) status. The meter has been used successfully to assess leaf N in conventional maize crops, but it has not been used with new maize (Zea mays L.) genotypes containing leafy (L) and reduced stature (RS) traits. SPAD meter readings were collected on the uppermost fully developed leaves (before silking) and on the ear leaf (after silking) of field grown maize genotypes with and without the L and RS traits. The experiment was conducted during 1996 and 1997 at two sites in Eastern Canada (Ottawa and Montreal). At each site in each year, a split plot arrangement of two treatment factors was used in a randomized complete block design with four blocks. The main plot treatments were levels of N (0, 85, 170, and 255 kg ha−1), with six maize genotypes as subplot treatments. The hybrids included: (i) leafy reduced-stature, LRS, (ii) non-leafy normal stature, NLNS, (iii) leafy normal stature, (LNS), (iv) non-leafy reduced-stature, NLRS, (v) conventional commercial hybrids, Pioneer 3905 as the hybrid check for late maturity, and (vi) Pioneer 3979, a check for early maturity. The hybrids were chosen on the basis of their contrasting canopies and root architecture. The SPAD meter readings were collected on the same five plant genotypes over time (six times per site per year, except four times for the Ottawa site in 1997). All genotypes showed increasing meter reading values as plants aged until silking. In general, SPAD meter readings increased as N fertilization level increased at each measurement date for both sites and years. In general, LNS and P3905 hybrids showed greater SPAD meter readings than other hybrids at all sampling dates for both sites and growing seasons. Applied N rates were significantly correlated with the SPAD meter readings. More highly significant relationships were found for N fertilizer levels and SPAD meter readings for the hybrids in 1997 than for the hybrids in 1996. For the Montreal site in 1997, LRS, LNS and P3905 hybrids were among those showing the highest r values between N level and SPAD readings. The correlation coefficients between SPAD readings and grain yield were generally lower. However, the NLNS hybrid had a high SPAD-yield correlation at the Macdonald site in 1997.

Neighborhood effects and size-asymmetric competition in a tree plantation varying in diversity.

A plantation of native trees was established in Panama in 2001 to study the relationship between biodiversity and ecosystem functioning. Five years later, mixed-species plots had experienced enhanced tree growth compared with monocultures. Searching for underlying mechanisms, we developed a neighborhood model isolating size and identity effects. We found that the size of neighbors is, by far, the largest source of variation in individual-tree diameter and height. Size-asymmetric competition appears as a structuring factor in the plantation. The relative growth rate of small trees was significantly lower than that of large trees, and their height and basal diameter were most variable. The 50 smallest trees of the plantation suffered a disproportionate amount of death, and the proportion of small trees was highest in monoculture. Increased biomass allocation to branches for trees growing in three-species plots suggests that competition for light might be taking place. Clearly, local neighborhood plays a central role in determining productivity, suggesting that scale needs to be incorporated in the theoretical development and analysis of biodiversity and ecosystem functioning.