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The effects of demographic and environmental noise on the vital dynamics and spatial pattern formation are studied for a predator-prey system with strong Allee effect in the prey species. Time and space are taken discrete. It is shown that noise can promote extinction depending on the growth and interaction parameters as well as the noise type and amplitude. The extinction risk increases with the noise amplitude; however, the environmental and demographic noise can have different effects on the risk of extinction. In space, the spatial structures obtained are blurred versions of the deterministic ones in most scenarios. In particular, the complex spatial structures that appear in the parameter domains where the deterministic local dynamics leads to extinction are robust to the density-dependent stochastic fluctuations but are disrupted with environmental noise.

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Understanding of spatiotemporal patterns arising in invasive species spread is necessary for successful management and control of harmful species, and mathematical modeling is widely recognized as a powerful research tool to achieve this goal. The conventional view of the typical invasion pattern as a continuous population traveling front has been recently challenged by both empirical and theoretical results revealing more complicated, alternative scenarios. In particular, the so-called patchy invasion has been a focus of considerable interest; however, its theoretical study was restricted to the case where the invasive species spreads by predominantly short-distance dispersal. Meanwhile, there is considerable evidence that the long-distance dispersal is not an exotic phenomenon but a strategy that is used by many species. In this paper, we consider how the patchy invasion can be modified by the effect of the long-distance dispersal and the effect of the fat tails of the dispersal kernels.

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O presente estudo é caracterizado como descritivo-exploratório e teve como objetivo geral verificar a relação entre a prática do Goalball e a orientação e mobilidade das pessoas com deficiência visual. Foram aplicados 79 questionários com os atletas de Goalball participantes da Copa Brasil de Goalball, no ano de 2007. A contribuição do Goalball na orientação e mobilidade, sob a perspectiva dos atletas, foi positiva, sendo de suma importância para o desenvolvimento motor e também para a reabilitação da pessoa com deficiência visual, pois desenvolve percepções sensório-motoras como audição e tato, além de aguçar a noção espacial e aumentar os níveis de concentração.

The present study is characterized as descriptiveexploratory and have theobjective to investigate the relationship between the practice of goalball andorientation and mobility for people with visual impairments. 79 questionnaireswere administered to goalball athletes participants of Goalball Brazil Cup, in2007. The contribution of goalball orientation and mobility from the perspective of the athletes was positive, which is extremely important for motor development and also for the rehabilitation of the person with visual impairments, because it develops motor sensory perceptions such as hearing and touching, as well asimproves the concept space and increase levels of concentration.

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Understanding of population dynamics in a fragmented habitat is an issue of considerable importance. A natural modelling framework for these systems is spatially discrete. In this paper, we consider a predator-prey system that is discrete both in space and time, and is described by a Coupled Map Lattice (CML). The prey growth is assumed to be affected by a weak Allee effect and the predator dynamics includes intra-specific competition. We first reveal the bifurcation structure of the corresponding non-spatial system. We then obtain the conditions of diffusive instability on the lattice. In order to reveal the properties of the emerging patterns, we perform extensive numerical simulations. We pay a special attention to the system properties in a vicinity of the Turing-Hopf bifurcation, which is widely regarded as a mechanism of pattern formation and spatiotemporal chaos in space-continuous systems. Counter-intuitively, we obtain that the spatial patterns arising in the CML are more typically stationary, even when the local dynamics is oscillatory. We also obtain that, for some parameter values, the system's dynamics is dominated by long-term transients, so that the asymptotical stationary pattern arises as a sudden transition between two different patterns. Finally, we argue that our findings may have important ecological implications.

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O estudo avaliou a qualidade de vida e sobrecargade cuidadores informais de pessoas com deficiênciaintelectual da grande Florianópolis. Material e Métodos:Utilizou-se o WHOQOL-Bref para avaliação da qualidade devida e para a sobrecarga o “Burden Interview”. Os dadosforam tratados por meio de estatística descritiva eposteriormente foi aplicado o teste de Mann-Whitney paracomparação entre os grupos e verificou-se a correlaçãoentre os componentes da qualidade de vida e a sobrecargacom o teste de Spearman. Os dados foram analisados noprograma estatístico SPSS 17.0, com nível de significânciap<0,05. Resultados: A amostra (n=66) apresentou média de50,29±14,91 anos, sendo constituída, em sua maioria, pormulheres (83,3%), mães (56,1%), casadas (54,5%) eaposentadas (53%). Os cuidadores apresentaram pior escorede qualidade de vida no domínio meio ambiente, seguido dosdomínios psicológico e físico. Os resultados apontaram adependência e a responsabilidade pelo cuidado com maioresvalores de sobrecarga. Conclusão: Os dados mostram quequanto maior a sobrecarga relatada, pior a qualidade de vidaavaliada, apontando uma relação direta da sobrecarga naqualidade de vida dos cuidadores. Os cuidadores atribuíramà falta de dinheiro o excesso de responsabilidade e adependência como principais fatores do desgaste...

The study evaluated the quality of life and burdenof informal caregivers of people with intellectual disabilitiesof Florianópolis. Materials and Methods: Were used theWHOQOL-Bref to assess quality of life and the “BurdenInterview” to evaluate burden. The data were processed bydescriptive statistics and Mann-Whitney test was later appliedfor comparison between groups. Correlation between thecomponents of quality of life and burden was investigatedthrough the Spearman test. Data were analyzed with SPSS17.0, with significance level of p <0.05. Results: The sample(n = 66) had a mean of 50.29 ± 14.91 years, being composedmostly by women (83.3%), mothers (56.1%), married (54.5%)and retired (53%). Caregivers have showed poorer scoreson quality of life in the environment domain, followed bypsychological and physical domains. The results have alsoshowed the dependence and responsibility for the care withhigher burden values. Conclusion: The data have showedthat the higher the burden reported, the worse is the qualityof life measured, indicating a direct relationship betweenquality of life and burden of caregivers. It has been attributedto lack of money, exceeded liability and dependence as keyfactors for fret...

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A Coupled Map Lattice (CML) model, for host-parasitoid Nicholson-Bailey interactions, with an explicit spatial distribution of partial refuge areas, is presented by considering the parasitoid attack rate as a patch dependent parameter. The effect of habitat heterogeneity on the dynamics of both populations, that is, on their spatial distribution and temporal behavior is analyzed. Our results show that depending on many features such as position, size, and fragmentation of a refuge, as well as the dispersal parameters of hosts and parasitoids, together with the parasitoid attack rate, the inclusion of refuges may as well stabilize as destabilize the host-parasitoid dynamics. The results are analyzed for the local and the global scales. Spatial patterns resulting from such heterogeneous patchy environments are also obtained.

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The use of a mathematical model applied to biological science helps to predict the specific data. Based on biological data (weight and age) of silver catfish, Rhamdia quelen, a mathematical model was elaborated based on a nonlinear difference equation to demonstrate the relationship between age and growth in weight. Silver catfish growth was described following the Beverton-Holt model Pt+1 = (r Pt) / (1+ a Pt ), where r > 0 is the maximum growth rate and a > 0 is a constant of growth inhibition. The solution of this equation is Pt= 1 /{[1/P0 - a / (r-1)] 1/r t + a/ (r-1)}, were P0 is the initial weight of the fish. Through this model it was observed that the female reaches the theoretical maximum weight approximately at the age of 18 years and the male at the age of 12 years in a natural environment.

A formulação de modelos matemáticos aplicado às ciências biológicas auxilia na previsão de dados específicos. Fundamentado em dados biológicos (peso e idade) de jundiá, Rhamdia quelen, elaborou-se um modelo matemático com base em equações a diferenças não lineares para demonstrar a relação entre idade e crescimento em peso. O crescimento do jundiá foi descrito segundo o modelo de Beverton-Holt Pt+1 = (r Pt) / (1+ a Pt), onde r > 0 é a taxa de crescimento máxima e a > 0 é uma constante de inibição do crescimento. A solução dessa equação é Pt= 1 / {[1/P0 - a / (r-1)] 1/r t + a/ (r-1)}, onde P0 é o peso inicial do peixe. Por esse modelo foi observado que fêmeas alcançam o peso máximo aproximadamente aos 18 anos e os machos aos 12 anos, em ambiente natural.

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A general mathematical model for population dispersal featuring long range taxis is presented and exemplified by the dispersal episode of the Africanized honey bees (Apis mellifera adansonii) throughout the American Continent. The mathematical model is a discrete-time and nonlocal model represented by an integrodifference recursion. A new taxis concept is defined and introduced into the mathematical model by an appropriate modification of the redistribution kernel. The model is capable of predicting the natural barrier for the expansion of the Africanized honey bees in the southern part of the Continent due to low winter temperatures. It also describes a sensitive expansion velocity with respect to the quality of resources, which can explain the AHB's astounding spread rate, by using two different kinds of population dynamics strategies, one for a resourceful environment and the other for poor regions.

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