Generalized time-independent correlation transport equation with static background: influence of anomalous transport on the field autocorrelation function.

A generalized time-independent correlation transport equation (GCTE) is proposed for the field autocorrelation function. The GCTE generalizes various models for anomalous transport of photons and takes into account the possible presence of a static background. In a tutorial example, the GCTE is solved for a homogeneous semi-infinite medium in reflectance configuration through Monte Carlo simulations. The chosen anomalous photon transport model also includes the classic and the "generalized" Lambert-Beer's law (depending on the choice of parameters). A numerical algorithm allowing generation of the related anomalous random photon steps is also given. The clear influence of anomalous transport on the field autocorrelation function is shown and discussed for the proposed specific examples by comparing the general results with the classical case (Lambert-Beer's law).

The global distribution of diet breadth in insect herbivores.

Understanding variation in resource specialization is important for progress on issues that include coevolution, community assembly, ecosystem processes, and the latitudinal gradient of species richness. Herbivorous insects are useful models for studying resource specialization, and the interaction between plants and herbivorous insects is one of the most common and consequential ecological associations on the planet. However, uncertainty persists regarding fundamental features of herbivore diet breadth, including its relationship to latitude and plant species richness. Here, we use a global dataset to investigate host range for over 7,500 insect herbivore species covering a wide taxonomic breadth and interacting with more than 2,000 species of plants in 165 families. We ask whether relatively specialized and generalized herbivores represent a dichotomy rather than a continuum from few to many host families and species attacked and whether diet breadth changes with increasing plant species richness toward the tropics. Across geographic regions and taxonomic subsets of the data, we find that the distribution of diet breadth is fit well by a discrete, truncated Pareto power law characterized by the predominance of specialized herbivores and a long, thin tail of more generalized species. Both the taxonomic and phylogenetic distributions of diet breadth shift globally with latitude, consistent with a higher frequency of specialized insects in tropical regions. We also find that more diverse lineages of plants support assemblages of relatively more specialized herbivores and that the global distribution of plant diversity contributes to but does not fully explain the latitudinal gradient in insect herbivore specialization.