Linear Models for Functional Responses

SUMMARYHost-parasite interactions generally involve communities of parasites. Within these communities, species will co-exist and/or interact with one another in a manner either benefiting the species involved or to the detriment of one or more of the species. At the level of helminth infracommunities, evidence for intra- and inter-specific competition includes numerical responses, i.e. those regulating helminth intensity of infection, and functional responses, i.e. where the presence of competitors modifies the realised niche of infrapopulations. The objectives of this study are to assess the numerical and functional responses of helminths in infracommunities from 3 rajid skates using general linear models. Despite a lack of numerical responses, functional responses to intra- and inter-specific interactions were observed. A positive correlation between the number of individuals in an infrapopulation and its niche breadth (functional response) was observed for the tapewormsPseudanthobothriumspp. andEcheneibothriumspp., in all their respective hosts, and for the nematodePseudanisakissp. in the little skate. Evidence for inter-specific competition includes niche shifts inPseudanthobothrium purtoni(exlittle skate) andPseudanisakissp. (exthorny skate) in the presence ofPseudanisakissp. and the tapewormGrillotiasp., respectively. These results are consistent with other studies in providing evidence for competition between helminths of skates.

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Statistical inferences for linear models with functional responses

Statistica Sinica ◽

10.5705/ss.2009.302 ◽

2011 ◽

Vol 21 (3) ◽

pp. 1431-1451 ◽

Cited By ~ 11

Author(s):

Jin-Ting Zhang

Keyword(s):

Linear Models ◽

Functional Responses ◽

Statistical Inferences

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Estimation of Causal Functional Linear Regression Models

Journal of Mathematics Research ◽

10.5539/jmr.v9n6p106 ◽

2017 ◽

Vol 9 (6) ◽

pp. 106

Author(s):

J.C.S. De Miranda

Keyword(s):

Linear Regression ◽

Tensor Product ◽

Linear Regression Model ◽

Regression Models ◽

Linear Models ◽

Linear Regression Models ◽

Functional Responses ◽

Functional Linear Models ◽

Triangular Region ◽

Functional Linear Regression

We present a methodology for estimating causal functional linear models using orthonormal tensor product expansions. More precisely, we estimate the functional parameters $\alpha$ and $\beta$ that appear in the causal functional linear regression model:$$\mathcal{Y}(s)=\alpha(s)+\int_a^b\beta(s,t)\mathcal{X}(t)\mathrm{d}t+\mathcal{E}(s),$$ where $\mbox{supp } \beta \subset \mathfrak{T},$ and $\mathfrak{T}$ is the closed triangular region whose vertexes are $(a,a) , (b,a)$ and $(b,b).$ We assume we have an independent sample $\{ (\mathcal{Y}_k,\mathcal{X}_k) : 1\le k \le N, k\in \mathbb{N}\}$ of observations where the $\mathcal{X}_k $'s are functional covariates, the $\mathcal{Y}_k$'s are time order preserving functional responses and $\mathcal{E}_k,$ $1\le k \le N,$ is i.i.d. zero mean functional noise.

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Functional linear models for functional responses

Springer Series in Statistics - Functional Data Analysis ◽

10.1007/0-387-22751-2_16 ◽

2006 ◽

pp. 279-296

Keyword(s):

Linear Models ◽

Functional Responses ◽

Functional Linear Models

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Differential responses of marsh predators to rainfall-induced habitat loss and subsequent variations in prey availability

Canadian Journal of Zoology ◽

10.1139/z08-007 ◽

2008 ◽

Vol 86 (5) ◽

pp. 407-418 ◽

Cited By ~ 15

Author(s):

A. D. Canepuccia ◽

A. A. Farias ◽

A. H. Escalante ◽

O. Iribarne ◽

A. Novaro ◽

...

Keyword(s):

Habitat Use ◽

Habitat Loss ◽

Structural Equation ◽

Linear Models ◽

Prey Availability ◽

Equation Modeling ◽

Negative Effects ◽

Functional Responses ◽

Rainy Period ◽

Native Grasslands

Rainfall has increased in many regions during recent decades, but most information is from dryland ecosystems, which precludes generalizations about its ecological consequences. We explored the effects of increased flooding on the Geoffroy’s cat, Leopardus geoffroyi (d’Orbigny and Gervais, 1844), and pampas fox, Pseudalopex gymnocercus (G. Fischer, 1814), exposed to an abnormally rainy period in marshes at Mar Chiquita, Argentina. In particular, we assessed the effects of flooding on (i) habitat use by L. geoffroyi and P. gymnocercus, (ii) abundance of their main prey, and (iii) functional responses of predators to variations in prey abundance. Overall, simple regression analysis identified negative effects of flooding on abundance of prey (rodents, waterbirds, and arthropods), but structural-equation modeling and logistic generalized linear models identified differential effects of rainfall on habitat use by and functional responses of predators, respectively. Habitat use by L. geoffroyi was more negatively affected by interannual variability in flooding-induced habitat loss, particularly through its effect on waterbirds. At the same time, habitat use by P. gymnocercus was less affected, likely because this species was less dependent on prey from flooded areas and used higher elevation habitats. Given that most native grasslands in elevated areas have been converted to agriculture, the more specialized L. geoffroyi faces a greater threat if current trends of climate change persist in this region.

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