Protocols for sampling weeds in fields generally consist of selecting a given number of quadrats of a certain size, randomly located in the field, and counting the number of weeds of each type within each quadrat. Such a procedure is appropriate if weeds are distributed randomly in the field. However, it has been documented that weeds tend to cluster in fields so that the spatial distribution can often be described by a negative binomial. This research was conducted to identify an appropriate scouting protocol for use when weed populations are clumped in such a manner. Binomial, censored, and presence/absence sampling plans were compared through simulated sampling from negative binomial distributions of varying degrees of clustering and varying mean weed densities. Plans were compared in terms of bias and root mean square error. Study results indicate that binomial and presence/absence sampling offer reasonable alternatives to traditional sampling methods, except when there is extreme clumping. There is a trade-off between sampling effort needed per quadrat and number of quadrats needed for the sample. Traditional methods require intensive weed counting in each quadrat sampled, whereas binomial and presence/absence sampling protocols require less effort per quadrat, but more quadrats sampled for comparable results. Censored sampling displayed no advantage over binomial sampling in terms of bias and root mean square error, and is somewhat more difficult to do.

Mesoplatys ochroptera Stål, Exosoma and Ootheca spp. seriously damage sesbania, Sesbania sesban (L.) Merril, a multipurpose leguminous tree widely used in tropical agroforestry. This is discouraging farmers from expanding the planting of sesbania in various agroforestry systems in eastern and south-central Africa. Rapid methods are needed for estimation of population densities of these beetles for decisionmaking in pest management. A study was conducted with the objectives of determining the existence of any positive relationship between the occupancy and abundance of Mesoplatys, Exosoma and Ootheca and determining the model that best predicts abundance from occupancy for rapid estimation of population densities. The Poisson model assuming spatial randomness, the negative binomial distribution (NBD) model assuming spatial aggregation, the Nachman model without any distribution assumption, and a General model incorporating spatial variance-abundance and occupancy-abundance relationships were fitted to data on adult M. ochroptera, Exosoma and Ootheca from western Kenya, southern Malawi and eastern Zambia. Very strong variance to abundance relationships were observed in the spatial pattern of all three beetles. The occupancy-abundance relationships were also positive and strong in all beetles. The occupancy and abundance predicted by the four models were closest to the observed at lower densities compared with higher beetle densities. At higher population densities, the NBD and the General model gave better fit for M. ochroptera and Exosoma. For Ootheca populations, the Poisson and NBD models gave better fit at higher population densities. The relationships established here can be used as guide to estimate beetle densities for decision-making in pest management.

For every hth member of a two-state Markov chain the value of a random variable Y is observed where the distribution of Y is conditional on the state of the corresponding member of the chain. A recursive set of equations is derived giving the posterior probabilities for both the observed and unobserved members. The use of this recursive solution to investigate the optimality of certain simple classification rules is discussed, and a “classification by runs” is also presented.