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The performance of discrete mathematical models to describe the population dynamics of diamondback moth (DBM) (Plutella xylostella L.) and its parasitoid Diadegma semiclausum was investigated. The parameter values for several well-known models (Nicholson¿Bailey, Hassell and Varley, Beddington, Free and Lawton, May, Holling type 2, 3 and Getz and Mills functional responses) were estimated. The models were tested on 20 consecutive sets of time series data collected at 14 days interval for pest and parasitoid populations obtained from a highland cabbage growing area in eastern Kenya. Model parameters were estimated from minimized squared difference between the numerical solution of the model equations and the empirical data using Powell's method. Maximum calculated DBM growth rates varied between 0.02 and 0.07. The carrying capacity determined at 16.5 DBM/plant by the Beddington et al. model was within the range of field data. However, all the estimated parameter values relating to the parasitoid, including the instantaneous searching rate (0.07¿0.28), per capita searching efficiency (0.20¿0.27), search time (5.20¿5.33), handling time (0.77¿0.90), and parasitism aggregation index (0.33), were well outside the range encountered empirically. All models evaluated for DBM under Durbin¿Watson criteria, except the May model, were not autocorrelated with respect to residuals. In contrast, the criteria applied to the parasitoid residuals showed strong autocorrelations. Thus, these models failed to estimate parasitoid dynamics. We conclude that the interactions of the DBM with its parasitoid cannot be explained by any of the models tested. Two factors may be associated with this failure. First, the parasitoid in this integrated biological control system may not be playing a major role in regulating DBM population. Second, and perhaps more likely, poor correlations reflect gross inadequacies in the theoretical assumptions that underlie the existing models. [Copyright &y& Elsevier]

Abstract: The Lotka–Volterra model was applied to the population densities of diamondback moth (DBM), Plutella xylostella (L.) and its exotic larval parasitoid Diadegma semiclausum (Hellen) data that was collected earlier by icipe’s DBM biological control team. The collections were done for 15 months before the release and 36 months after release of the parasitoid in two areas; in Werugha, Coast Province of Kenya and Tharuni, Central Province of Kenya, respectively. For each area in pre- and post-release periods, we estimated Lotka–Volterra model parameters from the minimization of the loss function between the theoretical and experimental time-series datasets following the Nelder-Mead multidimensional method. The model estimated a reduction in the value of the steady state of DBM population from 4.86 to 2.17 in Werugha and from 6.11 to 3.76 and 3.45 (with and without exclusion of the time before D. semiclausum recovery) in Tharuni when transiting from the pre- and post-release periods, respectively. This change was a consequence of the newly introduced parasitoid, in the areas. The study presented a successful and detailed technique for non-linear model parameters restoration which was demonstrated by the correct mimicking of empirical datasets from the classical biological control with D. semiclausum, in different areas of Kenya. The applied model has measured the parasitoids impact on the DBM biological control through a quantitative estimate of the effectiveness of the newly introduced species D. semiclausum. These equations may therefore be used as tool for decision making in the implementation for such pests’ management system strategy. [Copyright &y& Elsevier]

• Fruit fly infestation data was modelled using Artificial Neural Network. • Fuzzy logic was used to transform plant physiology stages to numeric variable. • Fuzzy Neural Network can be used as a predictive tool for fruit fly population. • Prediction of insect pest infestation can allow for timely control of the pests. Avocado (Persea americana) production is increasing in Kenya, with both small and largeholder farming for domestic and export markets. However, one of main challenges that limit production is infestation by insect pests, notably the oriential fruit fly Bactocera dorsalis and Ceratitis spp. fruit flies, which cause direct crop losses and are indirectly responsible for non-tariff trade barriers due to stringent export requirements. Data on weekly pest trap counts were collected between September 2017 and December 2020 within orchards in avocado plantations. Fuzzy neural network (FNN) were used to model the population dynamics of B. dorsalis and Ceratitis spp. Weekly pest counts, rainfall, average temperature, relative humidity and avocado plant physiological stages were used for predictive modeling in different orchards. The performance of the resulting models was evaluated using coefficient of determination (R2), mean absolute error (MAE), mean relative approximation error (MRAE) and root mean squared error (RMSE). FNN models achieved satisfactory results in predicting the dynamics of the pests in the orchards, with most of the models obtaining R2 > 0.85. We demonstrated how FNN models can be used as predictive tools for managing and controlling fruit fly pest populations in these plantations, and how they may be suitable to predict fruit fly or other pests in similar cropping systems. Once the input variables are known, they can be loaded into the FNN models to predict field pest populations, and based on threshold values, allow for implementation of timely and adequate control measures such as the use of biopesticides. [ABSTRACT FROM AUTHOR]