Spatial statistical models that use flow and stream distance

We develop spatial statistical models for stream networks that can estimate relationships between a response variable and other covariates, make predictions at unsampled locations, and predict an average or total for a stream or a stream segment. There have been very few attempts to develop valid spatial covariance models that incorporate flow, stream distance, or both. The application of typical spatial autocovariance functions based on Euclidean distance, such as the spherical covariance model, are not valid when using stream distance. In this paper we develop a large class of valid models that incorporate flow and stream distance by using spatial moving averages. These methods integrate a moving average function, or kernel, against a white noise process. By running the moving average function upstream from a location, we develop models that use flow, and by construction they are valid models based on stream distance. We show that with proper weighting, many of the usual spatial models based on Euclidean distance have a counterpart for stream networks. Using sulfate concentrations from an example data set, the Maryland Biological Stream Survey (MBSS), we show that models using flow may be more appropriate than models that only use stream distance. For the MBSS data set, we use restricted maximum likelihood to fit a valid covariance matrix that uses flow and stream distance, and then we use this covariance matrix to estimate fixed effects and make kriging and block kriging predictions.

Impacts of Plant Size, Density, Herbivory, and Desease on Native Platte Thistle (Cirsium Canescens)

Abstract. Based on prior field observations, we hypothesized that individual and interacting effects of plant size, density, insect herbivory, and especially fungal disease, influenced seedling and juvenile plant growth in native Platte thistle populations (Cirsium canescens Nutt.). We worked at Arapaho Prairie in the Nebraska Sandhills (May - August 2007), monitoring plant growth, insect damage, and fungal infection within different density thistle patches. In the main experiment, we sprayed half of test plants in different density patches with fungicide (Fungonil© Bonide, containing chlorothalonil) and half with a water control. Fungal infection rates were very low, so we found no difference in fungal attack between these treatments. However, plants that received the fungicide treatment had significantly faster growth over the season than did the control plants. At the same time, plants in the fungicide treatment had significantly reduced insect herbivory. These results strongly suggest that the fungicide had insecticidal effects and that insect herbivory significantly decreases juvenile Platte thistle growth. Further, damage by insect herbivores tended to be higher for larger plants, and herbivory was variable among different patches. However, plant density did not appear to have a large effect on the amount of insect herbivory that individual juvenile Platte thistle plants received. In the second experiment, we examined germination and survival success in relationship to seed density, and found that germination success was higher in areas of lower seed density. In the third experiment, we tested germination for filled seeds categorized primarily by color variation and size, and found no difference in germination related to either color or seed weight. We conclude that seed density, but not seed quality as estimated by color or size, affects germination success. Further, although herbivory was not significantly affected by plant density at any of the scales examined, insect herbivory significantly reduces the growth and success of juveniles of this characteristic native sand prairie plant.