Asymptotic Behavior of an Age-Structured Population Model and Optimal Maturation Age

AbstractA continuous age-structured population model with two population groups, juveniles and adults, and with a dynamics for the resource, is considered. The only density dependence is through a uniform increase of the death rates. A complete description of the asymptotic behavior of the population dynamics system is obtained showing under natural hypotheses the existence of a nontrivial (“ecological”) equilibrium which attracts any initial nonzero population with nonzero initial amount of resources. Assuming that the offspring production rate is an increasing function of the maturation age, the evolutionarily stable value of this variable is briefly discussed

Positive Steady States of Evolution Equations with Finite Dimensional Nonlinearities

We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are generators of strongly continuous semigroups; and a xed point problem. In case of irreducible governing semigroups we consider evolution equations with non-monotone nonlinearities of dimension two, and we establish a new xed point theorem for set-valued maps. In case of reducible governing semigroups we establish results for monotone nonlinearities of any nite dimension n. In addition, we establish a non-quasinilpotency result for a class of strictly positive operators, which are neither irreducible nor compact, in general. We illustrate our theoretical results with examples of partial dierential equations arising in structured population dynamics. In particular, we establish existence of positive steady states of a size-structured juvenile- adult and a structured consumer-resource population model, as well as for a selection-mutation model with distributed recruitment process

Steady states in a structured epidemic model with Wentzell boundary condition

We introduce a nonlinear structured population model with diffusion in the state space. Individuals are structured with respect to a continuous variable which represents a pathogen load. The class of uninfected individuals constitutes a special compartment that carries mass, hence the model is equipped with generalized Wentzell (or dynamic) boundary conditions. Our model is intended to describe the spread of infection of a vertically transmitted disease, for example Wolbachia in a mosquito population. Therefore the (infinite dimensional) nonlinearity arises in the recruitment term. First we establish global existence of solutions and the Principle of Linearised Stability for our model. Then, in our main result, we formulate simple conditions, which guarantee the existence of non-trivial steady states of the model. Our method utilizes an operator theoretic framework combined with a fixed point approach. Finally, in the last section we establish a sufficient condition for the local asymptotic stability of the positive steady state

A simple mathematical model of gradual Darwinian evolution: Emergence of a Gaussian trait distribution in adaptation along a fitness gradient

We consider a simple mathematical model of gradual Darwinian evolution in continuous time and continuous trait space, due to intraspecific competition for common resource in an asexually reproducing population in constant environment, while far from evolutionary stable equilibrium. The model admits exact analytical solution. In particular, Gaussian distribution of the trait emerges from generic initial conditions.Comment: 21 pages, 2 figures, as accepted to J Math Biol 2013/03/1

Direct competition results from strong competiton for limited resource

We study a model of competition for resource through a chemostat-type model where species consume the common resource that is constantly supplied. We assume that the species and resources are characterized by a continuous trait. As already proved, this model, although more complicated than the usual Lotka-Volterra direct competition model, describes competitive interactions leading to concentrated distributions of species in continuous trait space. Here we assume a very fast dynamics for the supply of the resource and a fast dynamics for death and uptake rates. In this regime we show that factors that are independent of the resource competition become as important as the competition efficiency and that the direct competition model is a good approximation of the chemostat. Assuming these two timescales allows us to establish a mathematically rigorous proof showing that our resource-competition model with continuous traits converges to a direct competition model. We also show that the two timescales assumption is required to mathematically justify the corresponding classic result on a model consisting of only finite number of species and resources (MacArthur, R. Theor. Popul. Biol. 1970:1, 1-11). This is performed through asymptotic analysis, introducing different scales for the resource renewal rate and the uptake rate. The mathematical difficulty relies in a possible initial layer for the resource dynamics. The chemostat model comes with a global convex Lyapunov functional. We show that the particular form of the competition kernel derived from the uptake kernel, satisfies a positivity property which is known to be necessary for the direct competition model to enjoy the related Lyapunov functional

Effects of Goat Manure Fertilization on Grain Nutritional Value in Two Contrasting Quinoa (Chenopodium quinoa Willd.) Varieties Cultivated at High Altitudes

In this study, the effects of goat manure fertilization (2, 4, 8, and 12 Tn/ha) on the grain yield, organic compounds, and mineral composition of two quinoa varieties (CICA-17 and Regalona Baer) were evaluated under field conditions in Northwest Argentina. The results indicate that fertilization improved the quinoa grain yield and total protein content. Low manure doses positively affected the fatty acid (FA) profile, and significant changes were determined for the monounsaturated (MUFA) and polyunsaturated (PUFA) fatty acid contents of CICA-17 and on the saturated fatty acid (SFA) contents of R. Baer seeds. The amino acid contents were positively affected in CICA-17 and negatively in R. Baer. Soluble sugars (glucose, fructose, and sucrose), major elements (K, Si, P, Mg, Ca, and Na), minor elements (Fe, Mn, Al, Zn, and Cu), and ultratrace elements (Cr and Li) were detected and discussed in terms of their impact on human nutrition and health. Conclusively, manure addition affected some essential amino acids, the desaturase activity, the n6:n3 and SFA/UFA ratios, the atherogenic index, soluble sugars, and mineral content, and the fatty acid metabolism of each variety was differently affected, especially the C16 and C18 desaturase activity, which responded differently to various manure doses. Manure addition is a promising alternative to improve the nutritional quality and functionality of quinoa grains, but the response is not linear.EEA FamailláFil: González, Juan A. Fundación Miguel Lillo. Instituto de Ecología, Comportamiento y Conservación; ArgentinaFil: Yousif, Sawsan K.M. Al-Baha University. College of Arts and Science in Baljurashi. Department of Chemistry; Arabia SauditaFil: Erazzu, Luis Ernesto. Instituto Nacional de Tecnología Agropecuaria (INTA). Estación Experimental Agropecuaria Famaillá; ArgentinaFil: Erazzu, Luis Ernesto. Universidad Nacional de Tucumán. Facultad de Agronomía y Zootecnia; ArgentinaFil: Martinez Calsina, Luciana. Instituto Nacional de Tecnología Agropecuaria (INTA). Estación Experimental Agropecuaria Famaillá; ArgentinaFil: Lizarraga, Emilio. Fundación Miguel Lillo. Instituto de Fisiología Animal; ArgentinaFil: Lizarraga, Emilio. Universidad Nacional de Tucumán. Facultad de Ciencias Naturales e Instituto Miguel Lillo; ArgentinaFil: Omer, Rihab M. Al-Baha University. College of Arts and Science in Baljurashi. Department of Chemistry; Arabia SauditaFil: Bazile, D. CIRAD, UMR SENS; FranciaFil: Bazile, D. University Paul Valery Montpellier 3. CIRAD, IRD; FranciaFil: Fernandez-Turiel, J.L. CSIC. Geosciences Barcelona; EspañaFil: Buedo, Sebastián E. Fundación Miguel Lillo. Instituto de Ecología, Comportamiento y Conservación; ArgentinaFil: Rejas, M. CSIC. Geosciences Barcelona; EspañaFil: Fontana, Paola Daniela. Instituto Nacional de Tecnología Agropecuaria (INTA). Estación Experimental Agropecuaria Famaillá; ArgentinaFil: González, D.A. Universidad Nacional de Tucumán. Facultad de Ciencias Naturales e Instituto Miguel Lillo. Instituto de Bioprospección y Fisiología Vegetal (INBIOFIV); ArgentinaFil: González, D.A. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Bioprospección y Fisiología Vegetal (INBIOFIV); ArgentinaFil:Oviedo, A. Fundación Miguel Lillo. Instituto de Fisiología Animal; ArgentinaFil: Alzuaibr, Fahad Mohammed. University of Tabuk. Faculty of Science. Department of Biology; Arabia SauditaFil: Al-Qahtani, Salem Mesfer. University of Tabuk. University College of Tayma. Biology Department; Arabia SauditaFil: Al-Harbi, Nadi Awad. University of Tabuk. University College of Tayma. Biology Department; Arabia SauditaFil: Ibrahim, Mohamed F.M. Ain Shams University. Faculty of Agriculture. Department of Agricultural Botany; EgiptoFil: Van Nieuwenhove, Carina. Universidad Nacional de Tucumán. Facultad de Ciencias Naturales e Instituto Miguel Lillo; ArgentinaFil: Van Nieuwenhove, Carina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tucumán. Centro de Referencia para Lactobacilos. Laboratorio de Ecofisiología Tecnológica; Argentin

Effects of Goat Manure Fertilization on Grain Nutritional Value in Two Contrasting Quinoa (Chenopodium quinoa Willd.) Varieties Cultivated at High Altitudes

In this study, the effects of goat manure fertilization (2, 4, 8, and 12 Tn/ha) on the grain yield, organic compounds, and mineral composition of two quinoa varieties (CICA-17 and Regalona Baer) were evaluated under field conditions in Northwest Argentina. The results indicate that fertilization improved the quinoa grain yield and total protein content. Low manure doses positively affected the fatty acid (FA) profile, and significant changes were determined for the monounsaturated (MUFA) and polyunsaturated (PUFA) fatty acid contents of CICA-17 and on the saturated fatty acid (SFA) contents of R. Baer seeds. The amino acid contents were positively affected in CICA-17 and negatively in R. Baer. Soluble sugars (glucose, fructose, and sucrose), major elements (K, Si, P, Mg, Ca, and Na), minor elements (Fe, Mn, Al, Zn, and Cu), and ultratrace elements (Cr and Li) were detected and discussed in terms of their impact on human nutrition and health. Conclusively, manure addition affected some essential amino acids, the desaturase activity, the n6:n3 and SFA/UFA ratios, the atherogenic index, soluble sugars, and mineral content, and the fatty acid metabolism of each variety was differently affected, especially the C16 and C18 desaturase activity, which responded differently to various manure doses. Manure addition is a promising alternative to improve the nutritional quality and functionality of quinoa grains, but the response is not linear

Benign Orbital Tumors with Bone Destruction in Children

Purpose: To present rare benign orbital tumors with bone destruction in children who could not be diagnosed presurgically and may simulate malignant ones. Methods: A retrospective review of cases. Clinical, operative and pathological records in all children with a diagnosis of benign orbital tumors who showed remarkable bone destruction at a tertiary Ophthalmic Center in China between Jan 1, 2000 and Dec 31, 2009 were reviewed. All patients had definitive histopathologic diagnosis. Results: Eight patients with benign orbital tumors showed obvious bone destruction, including six cases of eosinophilic granuloma, one case of leiomyoma and one case of primary orbital intraosseous hemangioma. Among them, three patients were females and five patients were males. Tumors were unilateral in all cases, with both the right and left side affected equally. Age ranged from 3 to 7 years (mean 4.1 years). Symptom duration ranged from 1 to 5 weeks (mean 4.8 weeks). Eyelid swelling and palpable mass were the most common complaint. There was no evidence for multifocal involvement in cases with eosinophilic granuloma. Among six patients with eosinophilic granuloma, two were treated with low dose radiation (10 Gy), three received systemic corticosteroid and one was periodically observed only after incisional biopsy or subtotal curettage. There was no postoperative therapeutic intervention in the two patients with leiomyoma and intraosseous hemangioma. All eight patients regained normal vision without local recurrence after a mean follow-up time o