Joe N. Perry

MEASURES OF SPATIAL PATTERN FOR COUNTS

SADIE (Spatial Analysis by Distance IndicEs) is a new methodology to detect and measure the degree of nonrandomness in the two-dimensional spatial patterns of populations. It applies the same principles to data in the form of maps as to data in the form of counts at specified locations, but with different techniques. This paper considers data in the form of counts such as occur commonly in ecology. For such data the method has an advantage over traditional approaches that measure only statistical variance heterogeneity, because all the spatial information in the sample is used. Two indices and associated tests are reviewed, one based on the total distance of the sample from a completely regular arrangement, the other from a completely crowded arrangement. A new diagnostic plot is presented to aid interpretation. Results from some artificial data are studied to survey the properties of both indices for defined patterns of clustering. Indices based on the distance to regularity are powerful at detecting aggregation when several clusters are present; those based on the distance to crowding have the power to detect aggregation only when a single cluster is present. Methods are presented to estimate the typical cluster size and intercluster distance, suitable for data from sample units in the form of a contiguous grid. Examples are given for cyst-nematode field data and plant virus disease.

Spatial analysis by distance indices

1. A new method of quantifying spatial pattern was introduced for two-dimensional mapped data, with an associated index of aggregation and a test for departures from randomness, based on an attractive algorithm in which individuals in the sample move to a regular arrangement which resembles a hexagonal lattice, using Voronoi tessellations. The algorithm incorporates a biological model for the dispersal of individuals from a source, in which each individual is assigned a dynamic territory. The method is one of a class known as Spatial Analysis by Distance IndicEs (SADIE). 2. Two diagnostic plots were introduced, each based on the distance of the sample from the final, regular arrangement, to aid the description of the observed spatial pattern. 3. By backtracking from the observed sample points away from the final arrangement, the presence of clusters in the sample may be detected more easily, and heuristic estimates derived of the cluster foci. 4. Examples are given for seven sets of data, with analyses of over 20 subsets at several spatial scales, concerning: aphids, beetle larvae, ant mounds, sparrowhawk nesting territories, pine seedlings, redwood seedlings, and biological cells.

A new method to measure spatial association for ecological count data

Abstract A new method is introduced to assess the spatial association between two sets of count data. This features a measure of local association for counts, defined for each sample unit. The new measure is based on a comparison of the spatial SADIE clustering index of the two sets at each sample unit; the mean of the measure is represented by the simple correlation coefficient between the clustering indices of the two sets. The randomization method allows the construction of a test and critical values. For the first time, spatial association may be mapped for count data; clusters of units with positive association or negative dissociation may be identified. The method is exemplified by analysis of spatial pattern and spatial association of counts of male and female tupelo trees from three plots in a South Carolina swamp forest. In addition, methods are presented to distinguish larger-scale apparent association between the sexes, caused by indirect effects, from direct smaller-scale association. No tendency was found for the sexes to occur together at the small-scale, only an apparent affinity caused through their co-location in particular subareas of each plot. The conversion from mapped to count data requires a choice of unit size; the conclusions of these analyses were not affected greatly by changes in unit size.

The within-field spatial and temporal distribution of arthropods in winter wheat

The within-field spatial distribution of some common farmland arthropods from the Carabidae, Araneae and Collembola was assessed using two-dimensional grids of pitfall traps distributed across whole winter wheat fields. In the first year, the extent to which arthropod capture was influenced by location within the field and sampling intensity was examined using a nested grid design (1.5 m, 7.5 m and 30 m spacings). In the second year, distributions within two different-sized winter wheat fields were compared. Spatial pattern and association between arthropods and weed cover were analysed using SADIE and trend surfaces were used to visualize distributions. Many of these arthropod groups exhibited aggregated distributions within the fields in clusters larger than 30 m across, demonstrating that the numbers captured will vary depending on the location of sampling within a field. Amara species, Bembidion lampros Herbst, Carabidae and Lycosidae were predominantly found within 60 m of the field edge. Nebria brevicollis Fabricius and Pterostichus madidus Illiger were found within the field in patches of one and two hectares, respectively. Linyphiidae were relatively homogeneously distributed across the fields. There was some evidence of clustering by Collembola. The spermophagous Carabidae and Lycosidae were positively associated with the degree of weed cover. SADIE analytical techniques were useful for identifying the importance and location of patches with greater and less than average numbers, although a minimum of 36 sample points is recommended.

Diversity and abundance of the coleopteran fauna from organic and conventional management systems in southern England

1 Studies of the epigeal coleopteran fauna on five pairs of organic and conventional farms were carried out between May and July 1994 in southern England using pitfall trapping. A total of 27 749 individuals and 140 species were identified. Overall, abundance of Coleoptera was greatest on organically managed farms.

Range of action of moth sex-attractant sources

Observations and experiments which indicate the range of attraction of a sex‐attractant source are distinguished from those which show its range of stimulation or sampling range. Published evidence of these ranges for lepidopteran sex‐attractant sources is reviewed. In particular, evidence for the values of these three parameters for traps containing 100 μg of synthetic sex‐pheromone of the pea moth, Cydia nigricana (F.), is presented, including the results of a timed mark and recapture experiment. It is concluded that for C. nigricana the ranges of attraction, stimulation and the daily sampling range for such a source placed in a cereal crop are at least 200, 500 and 500 m respectively.

Effects on weed and invertebrate abundance and diversity of herbicide management in genetically modified herbicide-tolerant winter-sown oilseed rape

We evaluated the effects of the herbicide management associated with genetically modified herbicide-tolerant (GMHT) winter oilseed rape (WOSR) on weed and invertebrate abundance and diversity by testing the null hypothesis that there is no difference between the effects of herbicide management of GMHT WOSR and that of comparable conventional varieties. For total weeds there were few treatment differences between GMHT and conventional cropping, but large and opposite treatment effects were observed for dicots and monocots. In the GMHT treatment, there were fewer dicots and more monocots than in conventional crops. At harvest, dicot biomass and seed rain in the GMHT treatment were one-third of that in the conventional, while monocot biomass was threefold greater and monocot seed rain almost fivefold greater in the GMHT treatment than in the conventional. These differential effects persisted into the following two years of the rotation. Bees and butterflies that forage and select for dicot weeds were less abundant in GMHT WOSR management in July. Year totals for Collembola were greater under GMHT management. There were few other treatment effects on invertebrates, despite the marked effects of herbicide management on the weeds.

Spatial distribution of pest insects in oilseed rape: implications for integrated pest management

Abstract Insect pests, plant growth and plant yield in a crop of winter oilseed rape ( Brassica napus L.) were studied to assess the potential value of spatial information in integrated pest management for this crop. Ceutorhynchus assimilis Payk., Ceutorhynchus pallidactylus (Marsh.), Meligethes aeneus (Fab.) and Dasineura brassicae Winn. were sampled from the nodes of a rectangular grid across the crop. Their spatial distributions were mapped, analysed and compared using Spatial Analysis by Distance IndicEs (SADIE). The relationships between the distributions of insects, plant growth and yield were assessed using regression techniques. The distributions of C. assimilis , C. pallidactylus and M. aeneus were complex with differing irregular patterns of aggregation, whereas D. brassicae was edge-distributed. Stem injury, chiefly caused by larval Psylliodes chrysocephala L., was associated with significant yield loss and the spatial distribution of stem injury was reflected in the distribution of oil yield. The distribution of larval M. aeneus was dissociated from that of pods which shed their seed before harvest. Spatial heterogeneity in plant maturation as a result of infestation could delay the choice of harvest date beyond the optimum to prevent seed loss from less injured plants. Some of the variability (21–31%) in insect numbers within the crop was explained by variation in plant density and in growth stage at mid-flowering. The spatial ecology of these pests is discussed in terms of the roles of environmental factors, behavioural responses and the implications of spatial patterns for yield loss and for developing sustainable integrated crop protection. The data indicate that decision support systems should use sampling strategies which incorporate spatial information to model crop loss more accurately and that there may be potential for spatially targeted applications of insecticide to optimise the influence of biocontrol agents in oilseed rape.

The spatial and temporal distribution of the grain aphid Sitobion avenae in winter wheat

The spatial and temporal distribution of the grain aphid Sitobion avenae F. (Homoptera: Aphididae) was studied within a field of winter wheat during the summer of 1996. Sampling was done using four nested grids comprising 133 locations. Analysis by Taylors power law gave results typical for insect populations. Analysis by SADIE (Spatial Analysis by Distance Indices) showed spatial pattern due to edge effects and sampling scale, and positive but mild spatial association, although spatial patterns were ephemeral. Reasons for these findings and the implications for integrated crop management are discussed.

Estimation of the negative binomial parameter κ by maximum quasi-likelihood

We investigate estimation of the parameter, K, of the negative binomial distribution for small samples, using a method-of-moments estimate (MME) and a maximum quasi-likelihood estimate (MQLE). Previous work is reviewed; the importance of indirect estimation of K through its reciprocal, a, and of allowance for negative estimates of K (or a) are discussed. Samples of size 50 are simulated 10,000 times for each of several parameter combinations to examine the properties of the estimates. Samples of sizes 10, 20, 30, and 50 are simulated 1,000 times to investigate the effect of sample size. Both estimators perform reasonably well except when the mean is small and the sample size does not exceed 20. Three examples are given, one of a designed experiment, for which the MQLE is especially suited; confidence limits are derived for the MQLE. Further work along these lines is required for adequate assessment of the usual maximum likelihood estimate.