Weed maps are typically produced from data sampled at discrete intervals on a regular grid. Errors are expected to occur as data are sampled at increasingly coarse scales. To demonstrate the potential effect of sampling strategy on the quality of weed maps, we analyzed a data set comprising the counts of capeweed in 225,000 quadrats completely covering a 0.9-ha area. The data were subsampled at different grid spacings, quadrat sizes, and starting points and were then used to produce maps by kriging. Spacings of 10 m were found to overestimate the geostatistical range by 100% and missed details apparently resulting from the spraying equipment. Some evidence was found supporting the rule of thumb that surveys should be conducted at a spacing of about half the scale of interest. Quadrat size had less effect than spacing on the map quality. At wider spacings the starting position of the sample grid had a considerable effect on the qualities of the maps but not on the estimated geostatistical range. Continued use of arbitrary survey designs is likely to miss the information of interest to biologists and may possibly produce maps inappropriate to spray application technology.

Descriptions of the fine scale distribution of organisms have frequently been used to investigate various ecological phenomena. Unfortunately, the most widely used spatial analysis techniques are based on single index statistics, which convey only minimal information about the biological processes underlying the studied distributions. Such statistics cannot detect changes in pattern over different scales, and cannot identify some types of distribution. Additionally, both the use of such statistics on the distribution of individuals which have a non-negligible size, and the frequent failure to use an edge correction for points close to the boundaries of a sampled area, have led to the over-reporting of ‘spaced out’ (‘regular’) distributions. Using two spatial distributions recently analysed with a single index statistic (termite mounds, and earthmounds created by termites), I illustrate the benefits gained from using the spatial functions K(t), G(y) and F(x) to analyse both ‘point events’ and events which have a non-negligible size. These functions are considerably more informative about the nature of a spatial pattern and offer wide scope for the fitting of spatial models to biological distributions.

In a sequence of independent Bernoulli trials the probability for success in the kth trial is pk, k = 1, 2, …. The number of strings with a given number of failures between two subsequent successes is studied. Explicit expressions for distributions and moments are obtained for the case in which pk = a/(a + b + k − 1), a > 0, b ≥ 0. Also, the limit behaviour of the longest failure string in the first n trials is considered. For b = 0, the strings correspond to cycles in random permutations.

Introduction. A project was undertaken to study the nutrient cycling from Musa mother plants to daughter suckers based on the physiological stages of the mother plant. It also reports on the dependency or competition at critical stages of flowering and fruiting and the combinations of different densities and sucker retention at different physiological stages of the mother plant. Materials and methods. A combination of three spacings and five sucker retention phases formed 15 treatments. 32P was given through injection into the mother plant pseudostem. The experiment was carried out over two years, the first being a rain-fed crop and the second being under irrigated conditions. Results. Differential aspects of nutrient cycling were observed between rain-fed and irrigated crops with regard to spacing. In the case of sucker retention phases, in the first year, it was retention at fruit maturity, shooting and flower bud differentiation stages which showed higher radioactivity recovery whereas, in the second year, it was the early phases of retention which showed significantly higher recovery. In the case of interaction effects, in the first year, the highest recovery was found in various combinations of spacing with the stages of bud initiation and shooting and, in the second year, the maximum recovery observed was in the combination of the closest spacing with the stage of flower bud initiation. In both years, recovery was observed in the border row plants. Conclusion. The study confirmed that activity extruded out from the treated plant and was absorbed by the border plants, revealing that nutrient sharing takes place in banana. This result opens up another concept that banana recommendation should not only be at an individual plant level but at block or plot level also. Hastening and improving the efficiency of nutrient cycling to the sucker is suggested as a future line of investigation.

Fifty radio-tagged long-tailed bats Chalinolobus tuberculatus, belonging to three social groups numbering on average 72–132 bats each, ranged over an area of 11 700 ha in Nothofagus rainforest in the Eglinton Valley, Fiordland, New Zealand, during the austral summers of 1993–96. Bats were followed for 12.7 ± 6.3 (sd) days. Home-range sizes were among the largest published for Microchiroptera. Median minimum convex polygons (100% MCPs) for adult males were 1589 ha (max = 5629 ha), 1361 ha for post-lactating females, and 657 ha for non-reproductive females. Ranges of lactating females (median = 330 ha), were significantly smaller. Juveniles that were volant for < 2 weeks had the smallest ranges (median = 237 ha) but movements increased significantly after c. 2 weeks to a median of 2006 ha. Movements were frequent and rapid within the range (790 ± 471 sd m/15 min) and average range lengths were 3.3–10.9 km (max = 19 km). Despite their large home ranges, bats concentrated their activity (85% of fixes) in small core areas that represented a mean of 5.7 ± 1.5% (sd) of the 100% MCPs. Ranges of roosting sites were also small, averaging 9.4 ± 1.8% (sd) of total range size. Bats followed similar movement patterns each night but core areas only overlapped by 43 ± 14% (sd) from one night to the next. Moderately low levels of overlap of home ranges (31–68%) and of core areas (23–56%) among individuals of the same reproductive class suggest a degree of spatial segregation among bats from the same roosting group. A prediction that C. tuberculatus has large ranges to minimize overlap between foraging bats, reflecting scarcity of food, requires testing. Range sizes were probably underestimates of seasonal, annual, and life-time range requirements. Nevertheless, large range size and the degree of individual spacing implies that conservation areas designed for bats should be large and that protection of roosting areas alone would not be sufficient to protect bat populations.

The response of two cotton varieties (TCH 1002 and 77/10) and two hybrids (TCHB 213 and DCH 32) to damage caused by the American bollworm, Helicoverpa armigera was evaluated under two spacings and three fertiliser levels each. Variety TCH 1002 was less damaged than 77/10, whereas between hybrids, DCH 32 was less preferred than TCHB 213. Damage was higher when the varieties were grown at a spacing of 50 × 20 cm and the hybrids at a spacing of 120 × 45 cm compared to 75 × 30 and 120 × 60 cm, respectively. Increasing the amount of fertiliser applied did not have any significant effect on damage caused by the pest. Tannin and gossypol contents were found to influence levels of damage caused by H. armigera. A combination of high tannin and gossypol resulted in reduced damage. The highest tannin content in varieties was recorded in leaves of TCH 1002 grown at a spacing of 75 × 30 cm, with a fertiliser level of 120:60:60 NPK kg/ha. The highest gossypol content was recorded in flowers of TCH 1002 under similar spacing and management levels. In the hybrids, the highest tannin and gossypol contents were recorded when DCH 32 was grown at 120 × 60 cm spacing with a fertiliser regime of 120:60:60 NPK kg/ha. Cotton was damaged to a greater extent when grown at a closer spacing. Increasing levels of nitrogen resulted in higher damage levels.

A linear mosaic is a process of random line segments distributed according to a Poisson process. This paper presents a wide-ranging treatment of limit theory for the two major macroscopic properties of a linear mosaic: total vacancy, and total number of spacings (or clumps). These quantities do not admit an explicit, exact treatment, and are perhaps most informatively studied by means of limit theory. We permit segment length to have a general distribution, and study the implications of tail properties of this distribution. Necessary and sufficient conditions are given for vacancy on an interval [0, t] to admit a normal approximation as t →∞. An approximate formula is provided for the probability of complete coverage, in the case of general segment length distribution. In all cases, properties of vacancy and number of spacings are studied together, by means of joint limit theorems, rather than individually, as in some earlier work.