Dynamical system and nonlinear regression for estimate host-parasitoid relationship. (English) Zbl 1211.37103

Cabrera, Ileana Miranda; Díaz, Heyker Lellanis Baños; De Los Ángeles Martínez, María

J. Appl. Math. 2010, Article ID 851037, 10 p. (2010).

The authors presents a dynamical system for studying the relationship host-parasitoid which permits the estimation of the parasite nymphs using nymphs healthy as the known variable. The model shows the functional answer of the parasitoid, in which a point arrives that its density is not augmented although the number host increases, and it becomes necessary to intervene in the ecosystem. By using a simple algorithm, the authors estimate the parasitoids level using the priori relationship between the host and the climate factors and then the nonlinear model. They study the relation host-parasitoid and use the random sequential samples to do regression models to estimate the parasitoid percent knowing the density host in the crop.

Reviewer: Xueyong Zhou (Xinyang)

MSC:

37N25	Dynamical systems in biology
91D25	Spatial models in sociology
92D40	Ecology

Keywords:

host-parasitoid relationship; nonlinear regression; stability

References:

[1]	L. Vázquez, “La conservación de los enemigos naturales de plagas en el contexto de la fitoprotección,” Boletín Técnico, vol. 5, no. 4, pp. 1-75, 1999.
[2]	V. Volterra, “Variazioni e fluttuazioni del numero d índividui in specie animal conviveri,” Memorie della R. Accademia dei Lincei, vol. 2, pp. 31-113, 1928. · JFM 52.0450.06
[3]	L. Beitschinger, E. R. Kelle, and C. Gessder, “Development of EPIVIT a simulation model for contact and aphidem-transmitted potato viruses,” Phytopathology, vol. 85, pp. 801-814, 1995.
[4]	I. Miranda Cabrera and M. Ramos Lima, “Mathematical study of the growth of tetranichidae mites under-field conditions: relationship prey-predator,” Applied Numerical Mathematics, vol. 40, no. 1-2, pp. 137-142, 2002. · Zbl 0988.92030
[5]	Sharov. Quantitative Ecology Population, 1999, http://www.ento.vt.edu/ sharov/PopEcol/.
[6]	F. W. Thiongo, H. Madsen, J. H. Ouma, J. Andreassen, and N. O. Christensen, “Host-parasite relationships in infections with two Kenyan isolates of Schistosoma mansoni in NMRI mice,” Journal of Parasitology, vol. 83, no. 2, pp. 330-332, 1997.
[7]	I. Miranda, H. L. Baños, M. Martínez, and J. Alemán, “Modelo teórico de la interacción de Diaphorina citri Kuwayana (Hemiptera:Psyllidae) con sus enemigos naturales,” Revista de Protección Vegetal, vol. 23, no. 2, pp. 126-130, 2008.
[8]	C. Chatterjee and R. R. Sarkar, “Multi-step polynomial regression method to model and forecast malaria incidence,” PLoS One, vol. 4, no. 3, Article ID e4726, 2009.
[9]	R. Levins and I. Miranda, “Mathematical model in crop protection,” Revista de Protección Vegetal, vol. 22, no. 1, pp. 1-17, 2007.
[10]	J. Alemán and J. Ravelo, “Diaphorina citri y la enfermedad Huanglogbing: una combinación destructiva para la producción citrícola,” Revista de Protección Vegetal, vol. 22, no. 3, pp. 154-165, 2007.
[11]	I. Miranda, Estudio Poblacional y modelación de Tetranychus urticae Koch, Ph.D. thesis, Centro Nacional de Sanidad Agropecuaria, La Habana, Cuba, thesis presenta en opción al título de Doctor en Ciencias Agrícolas, 2003.
[12]	R. L. Borrelli and C. S. Coleman, Differential Equations: A Modeling Perpective, John Wiley & Sons, New York, NY, USA, 1998. · Zbl 0895.34001
[13]	A. Scott and K. Lawrence, “Dynamical systems analysis of a five-dimensional trophic food web model in the Southern Oceans,” Journal of Applied Mathematics, vol. 2009, Article ID 5775047, 17 pages, 2009. · Zbl 1196.37125
[14]	S. E. Halbert and K. L. Manjunath, “Asian citrus psyllids (Sternorrhyncha: Psyllidae) and greening disease of citrus: a literature review and assessment of risk in Florida,” Florida Entomologist, vol. 87, no. 3, pp. 330-353, 2004.
[15]	V. Resco De Dios, C. Fischer, and C. Colinas, “Climate change effects on mediterranean forests and preventive measures,” New Forests, vol. 33, no. 1, pp. 29-40, 2007.
[16]	J. Etienne, S. Quilici, D. Marival, and A. Frank, “Biological control of Diaphorina citri (Hemiptera:Psyllidae) in Guadeloupe by imported Tamarixia radiata (Hymenoptera:Eulophidae),” Fruits, vol. 56, no. 5, pp. 307-315, 2001.
[17]	M. Fernández and I. Miranda, “Comportamiento de Diaphorina citri Kuwayana (Hemiptera:Psyllidae). Parte III. Relación entre el ciclo de vida y el brote vegetativo foliar,” Revista de Protección Vegetal, vol. 20, no. 3, pp. 161-164, 2005.