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A methodology is presented to facilitate a declaration that an area is 'pest-free' following an eradication campaign against an insect pest. This involves probability models to assess null trapping results and also growth models to help verify, following a waiting period, that pests were not present when control was stopped. Two probability models are developed to calculate the probability of negative trapping results if in fact insects were present. If this probability is sufficiently low, then the hypothesis that insects are present is rejected. The models depend on knowledge of the efficiency and the area of attractiveness of the traps. To verify the results of the probability model, a waiting period is required to see if a rebound occurs. If an incipient but non-detectable population remains after control measures are discontinued, then a rebound should occur. Using a growth model, the rate of increase of an insect population is examined starting from one gravid female or one male and a female. An example is given for tsetse in which both means and confidence limits are calculated for a period of 24 reproductive periods after control is terminated. If no rebound is detected, then a declaration of eradication can be made.

The effects of thinning (two-thirds of basal area removed) and N fertilization (448 kg N/ha as urea) on biomass and nutrition of a 24-year-old Douglas-fir (Pseudotsugamenziesii (Mirb.) Franco) stand at Shawnigan Lake were studied over 18 years. At years 0, 9, and 18 after treatments, the aboveground biomass and N, P, K, Ca, and Mg contents of stemwood, stem bark, foliage, and dead and live branches were determined (kg/ha), and increments in these properties (kg•ha−1•year−1) were calculated for the 0–9 and 9–18 year periods. Foliar biomass was increased by both treatments during the first period and also by thinning in the second period. Aboveground net primary production (ANPP) per unit of foliage biomass (foliage efficiency) was increased by treatments in the 0–9 year period. The combined effects of increased foliage mass and foliage efficiency resulted in increased total biomass production. Thinning and fertilization increased the uptake of all elements except for P with fertilization. This increase may have contributed to the long-term increase in stem growth. Retranslocation of elements before foliage shedding was important for tree nutrition, but was not improved by fertilization during the 9–18 year measurement period. The efficiency of N use in dry matter production (ANPP/unit of N uptake) was decreased by fertilization. This implied that poor sites would respond better to fertilization than rich sites.

Controlling pest insects is a challenge of main importance to preserve crop production. In the context of Integrated Pest Management (IPM) programs, we develop a generic model to study the impact of mating disruption control using an artificial female pheromone to confuse males and adversely affect their mating opportunities. Consequently the reproduction rate is diminished leading to a decline in the population size. For more efficient control, trapping is used to capture the males attracted to the artificial pheromone. The model, derived from biological and ecological assumptions, is governed by a system of ODEs. A theoretical analysis of the model without control is first carried out to establish the properties of the endemic equilibrium. Then, control is added and the theoretical analysis of the model enables to identify threshold values of pheromone which are practically interesting for field applications. In particular, we show that there is a threshold above which the global asymptotic stability of the trivial equilibrium is ensured, i.e. the population goes to extinction. Finally we illustrate the theoretical results via numerical experiments.

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Models were constructed for control of a pest species by the release of sterile insects and these models explored the consequences of incomplete sterility. This feature was then coupled with the lack of competitive ability of released insects, the immigration of insects from outside the control area, and the mode of population regulation (density independent vs. density dependent). Using the density‐independent models, it was seen that the limits on residual fertility of treated insects become much more stringent when incomplete sterilization is combined with a lack of competitive ability and immigration of insects into the control area. Strong density dependence in the system has a marked moderating effect on the requirements for sterility, competitive ability, and immigration. However, if the density‐independent limits on these factors are exceeded, then suppression is possible, but collapse of the pest population is impossible using sterile releases alone. Even suppression might not be satisfactory if these three detrimental factors are prominent. It is suggested that one remedy is the use of the sterile release method in combination with other control methods.