Global leaf-trait mapping based on optimality theory

Aim Leaf traits are central to plant function, and key variables in ecosystem models. However recently published global trait maps, made by applying statistical or machine-learning techniques to large compilations of trait and environmental data, differ substantially from one another. This paper aims to demonstrate the potential of an alternative approach, based on eco-evolutionary optimality theory, to yield predictions of spatio-temporal patterns in leaf traits that can be independently evaluated. Innovation Global patterns of community-mean specific leaf area (SLA) and photosynthetic capacity (Vcmax) are predicted from climate via existing optimality models. Then leaf nitrogen per unit area (Narea) and mass (Nmass) are inferred using their (previously derived) empirical relationships to SLA and Vcmax. Trait data are thus reserved for testing model predictions across sites. Temporal trends can also be predicted, as consequences of environmental change, and compared to those inferred from leaf-level measurements and/or remote-sensing methods, which are an increasingly important source of information on spatio-temporal variation in plant traits. Main conclusions Model predictions evaluated against site-mean trait data from > 2,000 sites in the Plant Trait database yielded R2 = 73% for SLA, 38% for Nmass and 28% for Narea. Declining species-level Nmass, and increasing community-level SLA, have both been recently reported and were both correctly predicted. Leaf-trait mapping via optimality theory holds promise for macroecological applications, including an improved understanding of community leaf-trait responses to environmental change

Fluctuations of time averages for Langevin dynamics in a binding force field

We derive a simple formula for the fluctuations of the time average around the thermal mean for overdamped Brownian motion in a binding potential U(x). Using a backward Fokker-Planck equation, introduced by Szabo, et al. in the context of reaction kinetics, we show that for ergodic processes these finite measurement time fluctuations are determined by the Boltzmann measure. For the widely applicable logarithmic potential, ergodicity is broken. We quantify the large non-ergodic fluctuations and show how they are related to a super-aging correlation function.Comment: 5 pages, 3 figure

Machine-learning a virus assembly fitness landscape

Realistic evolutionary fitness landscapes are notoriously difficult to construct. A recent cutting-edge model of virus assembly consists of a dodecahedral capsid with 12 corresponding packaging signals in three affinity bands. This whole genome/phenotype space consisting of 312 genomes has been explored via computationally expensive stochastic assembly models, giving a fitness landscape in terms of the assembly efficiency. Using latest machine-learning techniques by establishing a neural network, we show that the intensive computation can be short-circuited in a matter of minutes to astounding accuracy

Superaging correlation function and ergodicity breaking for Brownian motion in logarithmic potentials

We consider an overdamped Brownian particle moving in a confining asymptotically logarithmic potential, which supports a normalized Boltzmann equilibrium density. We derive analytical expressions for the two-time correlation function and the fluctuations of the time-averaged position of the particle for large but finite times. We characterize the occurrence of aging and nonergodic behavior as a function of the depth of the potential, and support our predictions with extensive Langevin simulations. While the Boltzmann measure is used to obtain stationary correlation functions, we show how the non-normalizable infinite covariant density is related to the super-aging behavior.Comment: 16 pages, 6 figure

Machine Learning Clifford Invariants of ADE Coxeter Elements

There has been recent interest in novel Clifford geometric invariants of linear transformations. This motivates the investigation of such invariants for a certain type of geometric transformation of interest in the context of root systems, reflection groups, Lie groups and Lie algebras: the Coxeter transformations. We perform exhaustive calculations of all Coxeter transformations for A8, D8 and E8 for a choice of basis of simple roots and compute their invariants, using high-performance computing. This computational algebra paradigm generates a dataset that can then be mined using techniques from data science such as supervised and unsupervised machine learning. In this paper we focus on neural network classification and principal component analysis. Since the output—the invariants—is fully determined by the choice of simple roots and the permutation order of the corresponding reflections in the Coxeter element, we expect huge degeneracy in the mapping. This provides the perfect setup for machine learning, and indeed we see that the datasets can be machine learned to very high accuracy. This paper is a pump-priming study in experimental mathematics using Clifford algebras, showing that such Clifford algebraic datasets are amenable to machine learning, and shedding light on relationships between these novel and other well-known geometric invariants and also giving rise to analytic results

EFFECTS OF MANAGEMENT PRACTICES ON GRASSLAND BIRDS: LESSER PRAIRIE-CHICKEN

Information on the habitat requirements and effects of habitat management on grassland birds were summarized from information in more than 4,000 published and unpublished papers. A range map is provided to indicate the breeding distribution of Lesser Prairie-Chicken in the United States and southern Canada. Although birds frequently are observed outside the breeding range indicated, the maps are intended to show areas where managers might concentrate their attention. It may be ineffectual to manage habitat at a site for a species that rarely occurs in an area. The species account begins with a brief capsule statement, which provides the fundamental components or keys to management for the species. A section on breeding range outlines the current breeding distribution of the species in North America. The suitable habitat section describes the breeding habitat and occasionally microhabitat characteristics of the species, especially those habitats that occur in the Great Plains. Details on habitat and microhabitat requirements often provide clues to how a species will respond to a particular management practice. A table near the end of the account complements the section on suitable habitat, and lists the specific habitat characteristics for the species by individual studies. A special section on prey habitat is included for those predatory species that have more specific prey requirements. The area requirements section provides details on territory and home range sizes, minimum area requirements, and the effects of patch size, edges, and other landscape and habitat features on abundance and productivity. It may be futile to manage a small block of suitable habitat for a species that has minimum area requirements that are larger than the area being managed. The Brown-headed Cowbird (Molothrus ater) is an obligate brood parasite of many grassland birds. The section on cowbird brood parasitism summarizes rates of cowbird parasitism, host responses to parasitism, and factors that influence parasitism, such as nest concealment and host density. The impact of management depends, in part, upon a species’ nesting phenology and biology. The section on breeding-season phenology and site fidelity includes details on spring arrival and fall departure for migratory populations in the Great Plains, peak breeding periods, the tendency to renest after nest failure or success, and the propensity to return to a previous breeding site. The duration and timing of breeding varies among regions and years. Species’ response to management summarizes the current knowledge and major findings in the literature on the effects of different management practices on the species. The section on management recommendations complements the previous section and summarizes specific recommendations for habitat management provided in the literature. If management recommendations differ in different portions of the species’ breeding range, recommendations are given separately by region. The literature cited contains references to published and unpublished literature on the management effects and habitat requirements of the species. This section is not meant to be a complete bibliography; a searchable, annotated bibliography of published and unpublished papers dealing with habitat needs of grassland birds and their responses to habitat management is posted at the Web site mentioned below

Effects of Management Practices on Grassland Birds: Grasshopper Sparrow

Grasshopper Sparrow (Ammodramus savannarum): Breeding range Suitable habitat Area requirements Brown-headed Cowbird brood parasitism Breeding-season phenology and site fidelity Species’ response to management Management Recommendations Habitat Characteristic

Effects of Management Practices on Grassland Birds: Sprague’s Pipit

Sprague’s Pipit (Anthus spragueii): Breeding range Suitable habitat Area requirements Brown-headed Cowbird brood parasitism Breeding-season phenology and site fidelity Species’ response to management Management Recommendations Habitat Characteristic

Effects of Management Practices on Grassland Birds: Sprague’s Pipit

Sprague’s Pipit (Anthus spragueii): Breeding range Suitable habitat Area requirements Brown-headed Cowbird brood parasitism Breeding-season phenology and site fidelity Species’ response to management Management Recommendations Habitat Characteristic

Effects of Management Practices on Grassland Birds: Grasshopper Sparrow

Grasshopper Sparrow (Ammodramus savannarum): Breeding range Suitable habitat Area requirements Brown-headed Cowbird brood parasitism Breeding-season phenology and site fidelity Species’ response to management Management Recommendations Habitat Characteristic