Low-rank scale-invariant tensor product smooths for generalized additive mixed models

A general method for constructing low-rank tensor product smooths for use as components of generalized additive models or generalized additive mixed models is presented. A penalized regression approach is adopted in which tensor product smooths of several variables are constructed from smooths of each variable separately, these "marginal" smooths being represented using a low-rank basis with an associated quadratic wiggliness penalty. The smooths offer several advantages: (i) they have one wiggliness penalty per covariate and are hence invariant to linear rescaling of covariates, making them useful when there is no "natural" way to scale covariates relative to each other; (ii) they have a useful tuneable range of smoothness, unlike single-penalty tensor product smooths that are scale invariant; (iii) the relatively low rank of the smooths means that they are computationally efficient; (iv) the penalties on the smooths are easily interpretable in terms of function shape; (v) the smooths can be generated completely automatically from any marginal smoothing bases and associated quadratic penalties, giving the modeler considerable flexibility to choose the basis penalty combination most appropriate to each modeling task; and (vi) the smooths can easily be written as components of a standard linear or generalized linear mixed model, allowing them to be used as components of the rich family of such models implemented in standard software, and to take advantage of the efficient and stable computational methods that have been developed for such models. A small simulation study shows that the methods can compare favorably with recently developed smoothing spline ANOVA methods.     

Habitat models of wood-inhabiting fungi along a decay gradient of Norway spruce logs

Information on the habitat requirements of wood-inhabiting fungi is needed to understand the factors that affect their diversity. We applied culture-free DNA extraction and 454-pyrosequencing to study the mycobiota of decaying Norway spruce (Picea abies) logs in five unmanaged boreal forests. Fungal habitat preferences in respect of wood density gradient were then estimated with generalized additive mixed models. Fungal diversity and wood density were inversely related, i.e., OTU richness generally increased as the log became increasingly decomposed. White-rot fungi (e.g., Phellinus nigrolimitatus) and members of Hyphodontia did not show a clear response to the wood-density gradient, whereas abundance of Phellinus viticola and brown-rot fungi (e.g., Fomitopsis pinicola, Antrodia serialis, Coniophora olivaceae) peaked during intermediate decay and mycorrhizal fungi (e.g., Piloderma, Tylospora, Russula) increased in the later stages. This information on fungal habitat requirements facilitates the development of management practices that preserve fungal diversity in managed forests.     

Predicting species interactions from edge responses: mongoose predation on hawksbill sea turtle nests in fragmented beach habitat

Because species respond differently to habitat boundaries and spatial overlap affects encounter rates, edge responses should be strong determinants of spatial patterns of species interactions. In the Caribbean, mongooses (Herpestes javanicus) prey on hawksbill sea turtle (Eretmochelys imbricata) eggs. Turtles nest in both open sand and vegetation patches, with a peak in nest abundance near the boundary between the two microhabitats; mongooses rarely leave vegetation. Using both artificial nests and hawksbill nesting data, we examined how the edge responses of these species predict the spatial patterns of nest mortality. Predation risk was strongly related to mongoose abundance but was not affected by nest density or habitat type. The product of predator and prey edge response functions accurately described the observed pattern of total prey mortality. Hawksbill preference for vegetation edge becomes an ecological trap in the presence of mongooses. This is the first study to predict patterns of predation directly from continuous edge response functions of interacting species, establishing a link between models of edge response and species interactions.