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Fig. 2. Functional responses of female C. lividipennis adult populations to BPH eggs on rice plants with different N regimes. A: 0NF2 C. lividipennis on 0N rice plants. B: 200NF2 C. lividipennis on 200N rice plants.
this characteristic does not make the mirid bug an excellent biological agent because it contributes to lower predatory effectiveness on target eggs in the field and in nochoice experiments with a high N regime. The bigger size and more sources of cues could mislead the orienting, foraging, accessing, and locating of mirid bugs in nontargets or it could extend the range to find targets. Based on this study, the predatory capacity of mirid bugs can be enhanced on host plants treated with high-N fertilizers. ○
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References
Shepard MB, Barrion AT, Litsinger JA. 1987. Friends of the rice farmer: helpful insects, spiders, and pathogens. Manila (Philippines): International Rice Research Institute. Yu XP, Heong KL, Hu C. 1996. Effect of various nonrice hosts on the growth, reproduction, and predation of mirid bug, Cyrtorhinus lividipennis Reuter. In: Heong et al, editors. Rice IPM Conferenceintegrating science and people in rice pest management. Manila (Philippines): International Rice Research Institute. p 56-63.
Boethel DJ, Eikenbary RD. 1986. Interactions of plant resistance and parasitoids and predators of insects. Chichester (UK): Ellis Horwood Limited. 224 p. Heong KL, Aquino GB, Barrion AT. 1991. Arthropod community structures of rice ecosystems in the Philippines. Bull. Entomol. Res. 81:407-416. Laba IW, Heong KL. 1996. Predation of Cyrtorhinus lividipennis on eggs of planthoppers in rice. Indonesian J. Crop Sci. 11(2):40-50. Meerzainudeen M, Kareem AA. 1999. Effect of biofertilizers on BPH (Nilaparvata lugens) and its biocontrol agents in rice ecosystem. In: Vistas of rice research. Tamil Nadu Agricultural University, India. p 469-474. ○
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Neural network approximation of sampling yield-effort curves of rice invertebrates Wenjun Zhang and Yanhong Qi, Research Institute of Entomology, Zhongshan University, Guangzhou 510275, Peoples Republic of China; and A.T. Barrion, formerly of the Entomology and Plant Pathology Division, IRRI E-mail:
[email protected]
Biodiversity studies in ecology and agriculture often begin with the analysis of sampling curves. To measure the completeness of sampling, a sampling yield-effort curve 40
can be drawn that plots the number of taxa sampled against the sample size (Colwell and Coddington 1994, Zhang and Schoenly 1999a,b). This curve is a step
function with a slope that should decrease as sample size increases and as fewer taxa remain to be sampled. Many models or methods were developed to fit these December 2004
functions. Most of these models, however, yielded fixed errors. Neural network methods, always with any desired accuracy, were widely used to fit functions in engineering and related research (Bian and Zhang 2000, Hagan et al 1996, Zhang and Qi 2002). Therefore, we expect a better goodness of fit for sampling yieldeffort curves with neural networks. The back propagation (BP) neural network and the radial basis function (RBF) neural network algorithms are introduced and tested in this study to provide an effective tool to fit the sampling yield-effort curves and to document the sampling information, based on data sets of invertebrates sampled in tropical irrigated rice fields. Some conclusions on rice invertebrates are obtained from the fitted functions of neural networks. Four sampling data sets of rice invertebrates were sampled on the IRRI farm at different dates, which were represented as Mar18, Apr15, Sep17, and Oct08, each with 60 suction samples. The taxabased data sets were lumped into families using biodiversity software LUMP (Schoenly and Zhang 1999) and bootstrapped with bootstrap methods (Colwell and Coddington 1994, Zhang and Schoenly 1999a,b). The BP neural network is a multilayer architecture (Bian and Zhang 2000, Hagan et al 1996). For the two-layer BP network, as used in this report, the transfer function of the neuron in the hidden layer is a sigmoid functionuj = 1/ (1 + exp (Bx)), j = 1,2,
,N IRRN 29.2
and the transfer function of the neuron in the output layer is a linear function. The Levenberg-Marquardt rule was used to train the twolayer BP network. It was developed and trained to fit function and make pattern recognition and extrapolation. Two learning procedures are included in BP network training. The first one is the positive propagation process in which the input signal is transferred layer by layer and practical outputs of every neuron are computed. The second is the back propagation in which the errors between practical and expected outputs are progressively computed layer by layer, and weights are adjusted according to the errors. The RBF network is made up of two layers, a hidden layer of radial basis neurons and an output layer of linear neurons (Bian and Zhang 2000, Hagan et al 1996). The transfer functions of neurons in the hidden layer are radial basis functions, typically Gaussian kernel functions: u j = exp((x c j ) 2 /(2 V j 2 )), j = 1,2,
,N, where u j is the output of the jth hidden neuron, x is the input, cj is the centralized value of the Gaussian function, V j is the standardized constant, and N is the number of neurons in the hidden layer. The weights and biases of each neuron in the hidden layer define the position and width of a radial basis function. The linear output neuron forms a weighted sum of these radial basis functionse.g., linear output y is the linear combination of outputs of hidden neurons: y = Nj
w j u j T . With the correct weight and bias values for each layer and enough hidden neurons, a radial basis network can fit any function with any desired accuracy. There are two stages in the learning procedure of the RBF network. The first step is determining the centralized values c j and standardized constants V j according to inputs, and the second step is solving the weights w j of the output layer based on the least square sum principle. The BP and RBF networks are trained with bootstrapped taxon data of four sampling sets. Results revealed that both networks fit the taxa richness-sample size curves well (Fig. 1). The BP architecture with five neurons is enough to fit these functions, but a longer time was required to reach the desired accuracy. An asymptote was ideally obtained by extrapolation of the trained BP network. RBF networks were quickly trained with the desired accuracy, but more neurons (60) were required, although the number of neurons was automatically produced by the RBF network. The required extrapolation of taxa richness-sample size function cannot be obtained from the trained RBF network. Similar results were produced for family richness-sample size relationships. The total number of rice invertebrate taxa for the four sampling sets Zmar18, Zapr15, Zoct08, and Zsep17, extrapolated from the asymptote of the trained BP network function, was 140, 149, 147, and 144, respectively, while the observed taxa rich-
= 1
41
ness was 126, 141, 140, and 131, when sample size was 60. The total number of invertebrate families was 69, 73, 80, and 77, extrapolated from the asymptote of the BP network function, as compared with the observed family richness of 66, 71, 75, and 75 in a sample size of 60. For comparison, we tested the neural network algorithms with a mathematical function, the Arrhenius b model, N = aS , where N is the number of taxa when sample size is S. The results showed that, with the least square sum error and mean square error, the BP network and RBF network fit the curves much better than did the mathematical function (see table). Similar results were obtained in the analysis of family richness. The BP network and RBF network can fit a nonlinear function with any desired accuracy. In addition to the interpolation, the BP network can extrapolate the function and thus the asymptote of the yield-effort curve can be drawn. It will take longer for the BP network to train the network and the results will always be less stable than those of the RBF network. The RBF network will require more neurons to fit the functions and, generally, it cannot be used to extrapolate the function. Compared with mathematical functions, both networks are much better in fitting the sampling curves and documenting sampling information. The total numbers of rice invertebrate taxa for the four sampling sets, extrapolated from the trained BP network, were between 42
References
Comparison of goodness of fit to taxa richness-sample size curves derived using various methods.
Mar18 Apr15 Oct08 Sep17
BP extrapolated taxa
BP fitted MSEa
RBF fitted SSEb
Arrhenius fitted MSEa
140 149 147 144
0.0220 0.3270 0.0090 0.0110
0 0 0 0
5.2722 25.5010 17.4749 15.4121
Bian ZQ, Zhang XG. 2000. Pattern recognition. 2nd ed. Beijing: Tsinghua University Press. Colwell RK, Coddington JA. 1994. Estimating terrestrial biodiversity through extrapolation. Phil. Trans. Roy. Soc. London B 345:101-108. Hagan MT, Demuth HB, Beale MH. 1996. Neural network design. PWS Publishing Company. Zhang WJ, Schoenly KG. 1999a. IRRI Biodiversity Software Series. II. COLLECT1 and COLLECT2: programs for calculating statistics of collectors curves. IRRI Technical Bulletin No. 2. Manila (Philippines): International Rice Research Institute. 15 p. Zhang WJ, Schoenly KG. 1999b. IRRI Biodiversity Software Series. IV. EXTSPP1 and EXTSPP2: programs for comparing and performancetesting eight extrapolation-based estimators of total taxonomic richness. IRRI Technical Bulletin No. 4. Manila (Philippines): International Rice Research Institute. 13 p. Zhang WJ, Qi YH. 2002. Functional link artificial neural network and agribiodiversity analysis. Biodivers. Sci. 10(3):345-350.
MSE = mean square error. bSSE = square sum error.
a
140 and 149. Numbers of invertebrate families extrapolated from the BP network are between 69 and 80. An appropriate number of neurons should be specified in training the BP network. Excessive neurons will make the BP network overlearned; thus, the resultant extrapolation will not be reliable. However, function approximation with the desired accuracy will not be achieved when fewer neurons are used in the BP network. Unlike most other models with the property of self-learning, which allows the network to find any intrinsic mechanism (which is invisibly stored in the trained network) uncovered in sampling data, no assumptions are needed to fit sampling yield-effort curves using the BP network and RBF network. ○
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Acknowledgments This project was supported by the National Natural Science Foundation of China, through 30170184, and the Asian Development Bank, through RETA 5711. We thank the following people who participated in the rice invertebrate investigation, identification, and data sheet processing: I. Domingo, V. Magalit, L. Datoon, A. Rivera, E. Hernandez, E. Revilla, E. Rico, R. Abuyo, J. Reyes, B. Aquino, and A. Pulpulaan. ○
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December 2004
