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Taylor's Power Law (taylor + power_law)
Selected AbstractsIs optimal foraging a realistic expectation in orb-web spiders?ECOLOGICAL ENTOMOLOGY, Issue 4 2009WILL EDWARDS Abstract 1.,Explanations for web relocation invoking optimal foraging require reliable differentiation between individual sites and overall habitat quality. We characterised natural conditions of resource variability over 20 days in artificial webs of the orb-web spider Gasteracantha fornicata to examine this requirement. 2.,Variability in catch success was high. Day-to-day catch success in 90% (18/20) catch sites fitted negative binomial distributions, whereas 10% fitted Poisson distributions. Considered across trap sites (overall habitat), variance in catch success increased proportionally faster than the mean (i.e. Taylor's Power Law, variance = 0.54mean1.764). 3.,We compared the confidence intervals for the expected cumulative catch in randomly drawn sequential samples from a frequency distribution representing the overall habitat (based on the parameters for Taylor's power law) and the frequency distribution of expected cumulative catch within each individual catch site [via randomisation based on the mean and negative binomial exponent (k)]. 4.,In all cases and across all sample sizes, median values for the power to differentiate habitat and catch sites never exceeded 0.2, suggesting that principles involved in optimal foraging, if operating, must be accompanied by a very high degree of uncertainty. 5.,Under conditions of high resource variability, many days must be spent in a single catch site if movement decisions are based on an ability to differentiate current catch site from overall habitat. Empirical evidence suggests this is never met. This may explain why proximal mechanisms that illicit quickly resolved behavioural responses have been more successful in describing web relocation patterns than those associated with optimal foraging. [source] Sampling plan for the coffee leaf miner Leucoptera coffeella with sex pheromone trapsJOURNAL OF APPLIED ENTOMOLOGY, Issue 6 2008T. Bacca Abstract The population density of the coffee leaf miner Leucoptera coffeella (Guérin-Méneville & Perrottet) (Lep., Lyonetiidae) can be estimated using pheromone traps in coffee fields as male capture reflects this pest damage based on previous correlational study. However, the spatial distribution of pheromone traps and their density are necessary to optimize the sampling procedure with pheromone traps. Therefore, the objectives of the present study were to determine the pheromone trap density required per hectare to sample coffee leaf miner populations and to determine the spatial distribution of the males of this pest species. The males were sampled every 8 days in 12 consecutive evaluations. Taylor's power law and frequency distributions were used to recognize the distribution of the male capture data, which followed a negative binomial distribution. A common K was obtained, allowing the establishment of a single conventional sampling plan for the 12 fields investigated. The adjusted sampling plan requires eight traps in an area of 30 ha for a 25% precision error. Kriging-generated maps allowed the simulation of male captures for 8, 12 and 20 traps per 30 ha and the results were compared with those obtained with absolute sampling resulting in R2 -values of 0.30, 0.57 and 0.60 respectively. The traps were able to identify the more highly infested areas within the field and are a precise and efficient tool for sampling populations of L. coffeella. [source] Seasonal dynamics, dispersion, sequential sampling plans and treatment thresholds for the citrus leafminer, Phyllocnistis citrella Stainton (Lepidoptera: Gracillariidae), in a mature lemon block in coastal New South Wales, AustraliaAUSTRALIAN JOURNAL OF ENTOMOLOGY, Issue 3 2008Zhong Min Liu Abstract, Studies of citrus leafminer in a coastal orchard in NSW, Australia indicated that an increase in abundance to about one mine per flush was followed during the midseason flush by a rapid increase in population that was related to an increase in the percentage of leaves infested within flushes and the number of mines per leaf. The fits of frequency distributions and Iwao's patchiness regression indicated that populations were highly contagious initially, and as the exponent k of the negative binomial distribution increased with increasing population density, the distribution approached random. Concurrently, the coefficient of variation of mines per flush (which was strongly related to the proportion of un-infested flushes) decreased to about unity as the proportion of un-infested flushes reached zero and fell further as the number of mines per flush increased. Both numerative and binomial sequential sampling plans were developed using a decision threshold based on 1.2 mines per flush. The binomial sampling plan was based on a closely fitting model of the functional relationship between mean density and proportion of infested flushes. Functional relationships using the parameters determined from Iwao's patchiness regression and Taylor's power law were equally satisfactory, and one based on the negative binomial model also fitted well, but the Poisson model did not. The three best fitting models indicated that a decision threshold of 1.2 mines per flush was equivalent to 50% of flushes infested. From a practical point of view, the transition from 25% infestation of flushes through 50% is so rapid that it may be prudent to take action when the 25% level is reached; otherwise, the 50% may be passed before the crop is checked again. For valuable nursery stock should infestation be detected in spring, it may be advisable to apply prophylactic treatment as the midseason flush starts. [source] Distribution and sampling of adults of Rhabdoscelus obscurus (Boisduval) (Coleoptera: Curculionidae) and their damage in sugarcaneAUSTRALIAN JOURNAL OF ENTOMOLOGY, Issue 3 2001Mohamed N Sallam Abstract Sampling statistics and spatial distribution were determined for adults of the sugarcane weevil borer, Rhabdoscelus obscurus, and for their damage in cane fields. Insect counts were obtained from split-cane traps and pheromone-baited traps. Counts of damaged internodes per stalk were also obtained from the same plots. Density and variance estimates of the three variables were fitted to Taylor's power law, which provided significant regression in all three cases (R2 > 0.86). Spatial distributions of weevil borers as well as damage symptoms were clumped, which may explain the patchy nature of infestation in cane. Analysis of within-plant distribution of damage showed that older internodes at the base of the stalk were more frequently infested than younger ones. Optimal sample sizes were determined for split-cane and pheromone traps and damaged stalks. Sequential sampling plans and fixed-precision level stop lines for the three parameters were also determined. [source] | ||||||||||