Relationship of total height and diameter at breast height (hereafter diameter) of the trees is generally nonlinear, and therefore has complex characteristics, which can be accurately described by the height-diameter model developed using the back propagation (BP) neural network approach. The multiple hidden layered-BP neural network has several hidden layers and neurons, and is therefore considered more appropriate modeling approach compared to the single hidden layered-BP neural network approach. However, the former approach is not widely applied for tree height prediction due to absence of the effective optimization method, but it can be done using the BP neural network modeling approach. The poplar (Populus spp. L.) plantation data acquired from Guangdong province of China were used for evaluating the BP neural network modeling approach and compared its results with those obtained from the traditional regression modeling and mixed-effects modeling approaches. We determined the best BP neural network structure with two hidden layers and five neurons in each layer, and logistic sigmoid transfer functions. Relative to the Mitscherlich height-diameter model that had the highest fitting precision among the six traditional height-diameter models evaluated, coefficient of determination (R²) of the neural network height-diameter model increased by 10.3%, root mean squares error (RMSE) and mean absolute error (MAE) decreased by 12% and 13.5%, respectively. The BP neural network height-diameter model also appeared more accurate than the mixed-effects height-diameter model. Our study proposes the method of determining the optimal numbers of hidden layers, neurons of each layer, and transfer functions in the BP neural network structure. This method can be useful for other modeling studies of similar or different types, such as tree crown modeling, height, and diameter increments modeling, and so on.

The simulation of landscape pattern optimization allocation (LPOA) to achieve ecological security is an important issue when constructing regional ecological security patterns. In this study, an LPOA model was developed by integrating a binary logistic regression model and a nonlinear programming model with a particle swarm optimization algorithm in order to consider the complexity of landscape pattern optimization in terms of the quantitative structure and spatial layout optimization, integrating the landscape suitability and factors that influence landscape patterns, and under constraints to maximize the economic, ecological, and comprehensive benefits of landscape patterns. The model was employed to simulate the LPOA in the Longquanyi District of Chengdu City, Sichuan Province, China. The model successfully obtained an appropriate combination of the landscape quantitative structure and spatial layout, as well as effectively integrating the landscape suitability and factors that influence the landscape pattern. Thus, the model addressed the problems of previous studies, such as neglecting the coupling between quantitative structure optimization and spatial layout optimization, ignoring the macrofactors that affect landscape patterns during optimization modeling, and initializing particles without considering the suitability of the landscape. Furthermore, we assessed and analyzed the accuracy and feasibility of the landscape pattern spatial layout optimization results, where the results showed that the overall accuracy of the optimization results was 84.98% with a Kappa coefficient of 0.7587, thereby indicating the good performance of the model. Moreover, the simulated optimization allocation scheme for the landscape pattern was consistent with the actual situation. Therefore, this model can provide support and a scientific basis for regional landscape pattern planning, land use planning, urban planning, and other related spatial planning processes.