Correcting for missing and irregular data in home-range estimation.

Home-range estimation is an important application of animal tracking data that is frequently complicated by autocorrelation, sampling irregularity, and small effective sample sizes. We introduce a novel, optimal weighting method that accounts for temporal sampling bias in autocorrelated tracking data. This method corrects for irregular and missing data, such that oversampled times are downweighted and undersampled times are upweighted to minimize error in the home-range estimate. We also introduce computationally efficient algorithms that make this method feasible with large data sets. Generally speaking, there are three situations where weight optimization improves the accuracy of home-range estimates: with marine data, where the sampling schedule is highly irregular, with duty cycled data, where the sampling schedule changes during the observation period, and when a small number of home-range crossings are observed, making the beginning and end times more independent and informative than the intermediate times. Using both simulated data and empirical examples including reef manta ray, Mongolian gazelle, and African buffalo, optimal weighting is shown to reduce the error and increase the spatial resolution of home-range estimates. With a conveniently packaged and computationally efficient software implementation, this method broadens the array of data sets with which accurate space-use assessments can be made.

Mathematical model of Zika virus with vertical transmission.

Zika is a flavivirus transmitted to humans through either the bites of infected Aedes mosquitoes or sexual transmission. Zika has been linked to congenital anomalies such as microcephaly. In this paper, we analyze a new system of ordinary differential equations which incorporates human vertical transmission of Zika virus, the birth of babies with microcephaly and asymptomatically infected individuals. The Zika model is locally and globally asymptotically stable when the basic reproduction number is less than unity. Our model shows that asymptomatic individuals amplify the disease burden in the community, and the most important parameters for ZIKV spread are the death rate of mosquitoes, the mosquito biting rate, the mosquito recruitment rate, and the transmission per contact to mosquitoes and to adult humans. Scenario exploration indicates that personal-protection is a more effective control strategy than mosquito-reduction strategy. It also shows that delaying conception reduces the number of microcephaly cases, although this does little to prevent Zika transmission in the broader community. However, by coupling aggressive vector control and personal protection use, it is possible to reduce both microcephaly and Zika transmission. 2000 Mathematics Subject Classifications: 92B05, 93A30, 93C15.

Estimating where and how animals travel: an optimal framework for path reconstruction from autocorrelated tracking data.

An animal's trajectory is a fundamental object of interest in movement ecology, as it directly informs a range of topics from resource selection to energy expenditure and behavioral states. Optimally inferring the mostly unobserved movement path and its dynamics from a limited sample of telemetry observations is a key unsolved problem, however. The field of geostatistics has focused significant attention on a mathematically analogous problem that has a statistically optimal solution coined after its inventor, Krige. Kriging revolutionized geostatistics and is now the gold standard for interpolating between a limited number of autocorrelated spatial point observations. Here we translate Kriging for use with animal movement data. Our Kriging formalism encompasses previous methods to estimate animal's trajectories--the Brownian bridge and continuous-time correlated random walk library--as special cases, informs users as to when these previous methods are appropriate, and provides a more general method when they are not. We demonstrate the capabilities of Kriging on a case study with Mongolian gazelles where, compared to the Brownian bridge, Kriging with a more optimal model was 10% more precise in interpolating locations and 500% more precise in estimating occurrence areas.

Rigorous home range estimation with movement data: a new autocorrelated kernel density estimator.

Quantifying animals' home ranges is a key problem in ecology and has important conservation and wildlife management applications. Kernel density estimation (KDE) is a workhorse technique for range delineation problems that is both statistically efficient and nonparametric. KDE assumes that the data are independent and identically distributed (IID). However, animal tracking data, which are routinely used as inputs to KDEs, are inherently autocorrelated and violate this key assumption. As we demonstrate, using realistically autocorrelated data in conventional KDEs results in grossly underestimated home ranges. We further show that the performance of conventional KDEs actually degrades as data quality improves, because autocorrelation strength increases as movement paths become more finely resolved. To remedy these flaws with the traditional KDE method, we derive an autocorrelated KDE (AKDE) from first principles to use autocorrelated data, making it perfectly suited for movement data sets. We illustrate the vastly improved performance of AKDE using analytical arguments, relocation data from Mongolian gazelles, and simulations based upon the gazelle's observed movement process. By yielding better minimum area estimates for threatened wildlife populations, we believe that future widespread use of AKDE will have significant impact on ecology and conservation biology.

Biological stoichiometry of plant production: metabolism, scaling and ecological response to global change.

Biological stoichiometry theory considers the balance of multiple chemical elements in living systems, whereas metabolic scaling theory considers how size affects metabolic properties from cells to ecosystems. We review recent developments integrating biological stoichiometry and metabolic scaling theories in the context of plant ecology and global change. Although vascular plants exhibit wide variation in foliar carbon:nitrogen:phosphorus ratios, they exhibit a higher degree of 'stoichiometric homeostasis' than previously appreciated. Thus, terrestrial carbon:nitrogen:phosphorus stoichiometry will reflect the effects of adjustment to local growth conditions as well as species' replacements. Plant stoichiometry exhibits size scaling, as foliar nutrient concentration decreases with increasing plant size, especially for phosphorus. Thus, small plants have lower nitrogen:phosphorus ratios. Furthermore, foliar nutrient concentration is reflected in other tissues (root, reproductive, support), permitting the development of empirical models of production that scale from tissue to whole-plant levels. Plant stoichiometry exhibits large-scale macroecological patterns, including stronger latitudinal trends and environmental correlations for phosphorus concentration (relative to nitrogen) and a positive correlation between nutrient concentrations and geographic range size. Given this emerging knowledge of how plant nutrients respond to environmental variables and are connected to size, the effects of global change factors (such as carbon dioxide, temperature, nitrogen deposition) can be better understood.

Brucellosis, botflies, and brainworms: the impact of edge habitats on pathogen transmission and species extinction.

Ecological interactions between species that prefer different habitat types but come into contact in edge regions at the interfaces between habitat types are modeled via reaction-diffusion systems. The primary sort of interaction described by the models is competition mediated by pathogen transmission. The models are somewhat novel because the spatial domains for the variables describing the population densities of the interacting species overlap but do not coincide. Conditions implying coexistence of the two species or the extinction of one species are derived. The conditions involve the principal eigenvalues of elliptic operators arising from linearizations of the model system around equilibria with only one species present. The conditions for persistence or extinction are made explicit in terms of the parameters of the system and the geometry of the underlying spatial domains via estimates of the principal eigenvalues. The implications of the models with respect to conservation and refuge design are discussed.

How predator incursions affect critical patch size: the role of the functional response.

Understanding the impact of habitat edges provides a key to deciphering how community dynamics change as functions of habitat structure and spatial scale. Motivated by studies of predation on bird nests in forest fragments and other cases of "cross-boundary subsidies," we present results from a partial differential equation model in which a patch-resident prey species suffers incidental mortality from a generalist predator species residing in the surrounding matrix habitat. We demonstrate that predator intrusions have the potential to induce critical patch size effects for the prey species, even when the prey's dynamics would otherwise preclude such effects. We also demonstrate that the existence of critical patch size effects depends on the functional response of the predator, with Lotka-Volterra and Type II functional responses generating the effect (but not Type III). We conclude by discussing how predator-induced critical patch size effects can influence opportunities for regionwide persistence of the prey by altering the fraction and spatial distribution of meaningful patches within a metapopulation.

Nutritional constraints in terrestrial and freshwater food webs.

Biological and environmental contrasts between aquatic and terrestrial systems have hindered analyses of community and ecosystem structure across Earth's diverse habitats. Ecological stoichiometry provides an integrative approach for such analyses, as all organisms are composed of the same major elements (C, N, P) whose balance affects production, nutrient cycling, and food-web dynamics. Here we show both similarities and differences in the C:N:P ratios of primary producers (autotrophs) and invertebrate primary consumers (herbivores) across habitats. Terrestrial food webs are built on an extremely nutrient-poor autotroph base with C:P and C:N ratios higher than in lake particulate matter, although the N:P ratios are nearly identical. Terrestrial herbivores (insects) and their freshwater counterparts (zooplankton) are nutrient-rich and indistinguishable in C:N:P stoichiometry. In both lakes and terrestrial systems, herbivores should have low growth efficiencies (10-30%) when consuming autotrophs with typical carbon-to-nutrient ratios. These stoichiometric constraints on herbivore growth appear to be qualitatively similar and widespread in both environments.

Umbrellas and flagships: efficient conservation surrogates or expensive mistakes?

The use of umbrella and flagship species as surrogates for regional biota whose spatial distributions are poorly known is a popular conservation strategy. Yet many assumptions underlying the choice of surrogate species remain untested. By using biodiversity databases containing spatial incidence data for species of concern for (i) the southern California coastal sage scrub habitat, (ii) the Columbia Plateau ecoregion, and (iii) the continental United States, we evaluate the potential effectiveness of a range of conservation surrogate schemes (e.g., big carnivores, charismatic species, keystone species, wide-ranging species), asking how many species potentially are protected by each scheme and at what cost in each habitat area. For all three databases, we find that none of the surrogate schemes we evaluated performs significantly better than do a comparable number of species randomly selected from the database. Although some surrogate species may have considerable publicity value, based on the databases we analyzed, representing diverse taxa on three different geographic scales, we find that the utility of umbrella and flagship species as surrogates for regional biodiversity may be limited.

Competitive reversals inside ecological reserves: the role of external habitat degradation.

Habitat degradation is the slow--and often subtle--deterioration in habitat quality that accompanies human activities through increases in road density, pesticide use, hunting pressure, etc. Such degradation is of particular concern in fragmented habitats where economic or jurisdictional boundaries rather than ecological ones determine the level of exploitation adjoining habitat patches endure. To examine the consequences habitat degradation might have on species interactions, we posited a patch of pristine habitat surrounded by "matrix" habitat whose degradation level was variable. Using a coupled pair of diffusive Lotka-Volterra competition equations with Robin (mixed) boundary conditions, we modeled the dynamics of two competing species inhabiting the pristine patch and incorporated matrix degradation through a tunable "hostility" parameter representing species' mortality rates in the matrix. We found that the numerical range of competition coefficients over which one species is the competitive dominant and the other inferior may grow or shrink as matrix quality deteriorates. In some cases, degradation of the exterior habitat would bring about a complete competitive reversal inside the preserve. This result, wherein a formerly inferior species supplants a formerly dominant one--even inside the "protected" remnant patch itself--has policy implications for both nature reserve design and management of human activities outside park boundaries.

Omnivory as a stabilizing feature of natural communities.

Omnivory-defined broadly as feeding on more than one trophic level-occupies a prominent position in discussions of food web architecture and dynamics, due in large part to an enduring conflict regarding omnivory's role in community dynamics. According to classical results from mathematical food web theory, omnivory destabilizes ecological communities, whereas more recent conceptual syntheses suggest that omnivory should be a strongly stabilizing factor in food webs. Working with an arthropod assemblage at Mount Saint Helens, I experimentally addressed this controversy using a two-way factorial design that crossed a manipulation of the degree of omnivory with another "disturbance" manipulation that targeted a specific component of the assemblage. In this statistical design, significant interaction effects (i.e., how the community impacts of the disturbance varied with the degree of omnivory) identified key stabilizing or destabilizing influences of omnivory. Overall, my experimental results indicated that increasing the degree of omnivory stabilized community dynamics, in keeping with recent conceptual syntheses.

Cursorial spiders and succession: age or habitat structure?

The structure of cursorial spider assemblages was examined along a gradient of four temperature successional communities. Species diversity (H'), richness (S), and evenness (J') exhibited a dichotomy between herbaceous and woody communities rather than a progressive change with community age: all three parameters were higher in the two younger fields than in the two older woodlands, which is contrary to conventional successional theory. Species importance curves were steeper in the two woody communities. The breadth of the distribution of adult body lengths was greater in the two herbaceous communities. Indices of community similarity revealed neither a successional trend nor the vegetative dichotomy. We suggest the hypothesis that habitat structure is a more important determinant of cursorial spider diversity than successional age per se, and that the switch in dominance from herbaceous to woody vegetation is the critical change. We further suggest that competition for prey is more important to cursorial spiders in early successional (herbaceous) communities, because of a switch in the limiting resource from prey in these communities to the amount of accumulating litter (a spatial resource) in older woody stands. This may explain the greater variation in adult body size of these generalist predators in the two younger communities.