In spite of the usefulness of codominant markers in population genetics, the existence of null alleles raises challenging estimation issues in natural populations that are characterized by positive inbreeding coefficients (F > 0). Disregarding the possibility of F > 0 in a population will generally lead to overestimates of null allele frequencies. Conversely, estimates of inbreeding coefficients (F) may be strongly biased upwards (excess homozygotes), in the presence of nontrivial frequencies of null alleles. An algorithm has been presented for the estimation of null allele frequencies in inbred populations (van Oosterhout method), using external estimates of the F-statistics. The goal of this study is to introduce a modification of this method and to provide a formal comparison with an alternative likelihood-based method (Chybicki-Burczyk). Using simulated data, we illustrate the strengths and limitations of these competing methods. Under most circumstances, the likelihood method is preferable, but for highly inbred organisms, a modified van Oosterhout method offers some advantages.

A B S T R A C TThe International Centre of Insect Physiology and Ecology (icipe), undertook a biological control (BC) programme for control of stemborers from 1993 to 2008, to reduce cereal yield losses due to stemborer attack in East and Southern Africa. The programme released four biological control agents-the larval parasitoids Cotesia flavipes and Cotesia sesamiae, the egg parasitoid Telenomus isis and the pupal parasitoid Xanthopimpla stemmator-to control the economically important stemborer pests Busseola fusca, Chilo partellus and Sesamia calamistis. Two of the natural enemies that were released got established and spread to many localities in the region. This study adopted the economic surplus model based on production, market and GIS data to evaluate the economic benefits and cost-effectiveness of the programme in three countries-Kenya, Mozambique and Zambia. Findings show that the biological control intervention has contributed to an aggregate monetary surplus of US$ 1.4 billion to the economies of the three countries with 84% from maize production and the remaining 16% from sorghum production. The net present value over the twenty years period was estimated at US$ 272 million for both crops and ranged from US$ 142 million for Kenya to US$ 39 million for Zambia. The attractive internal rate of return (IRR) of 67% compared to the considered discount rate of 10%, as well as the estimated benefit-cost ratio (BCR) of 33:1, illustrate the efficiency of investment in the BC research and intervention. The estimated number of people lifted out of poverty through the BC-programme was on average 57,400 persons (consumers and producers) per year in Kenya, 44,120 persons in Mozambique, and 36,170 persons in Zambia, representing an annual average reduction of poor populations, respectively of 0.35, 0.25 and 0.20% in each of the three countries. These findings underscore the need for increased investment in BC research to sustain cereal production and improve poor living conditions.