Tile Number and Space-Efficient Knot Mosaics

In this paper we introduce the concept of a space-efficient knot mosaic. That is, we seek to determine how to create knot mosaics using the least number of non-blank tiles necessary to depict the knot. This least number is called the tile number of the knot. We determine strict bounds for the tile number of a knot in terms of the mosaic number of the knot. In particular, if $t$ is the tile number of a prime knot with mosaic number $m$, then $5m-8 \leq t \leq m^2-4$ if $m$ is even and $5m-8 \leq t \leq m^2-8$ if $m$ is odd. We also determine the tile number of several knots and provide space-efficient knot mosaics for each of them.Comment: The original version of this article was split into two articles during refereein

Climatic signals in growth and its relation to ENSO events of two Prosopis species following a latitudinal gradient in South America

Semiarid environments throughout the world have lost a major part of their woody vegetation and biodiversity due to the effects of wood cutting, cattle grazing and subsistence agriculture. The resulting state is typically used for cattle production, but the productivity of these systems is often very low, and erosion of the unprotected soil is a common problem. Such dry-land degradation is of great international concern, not only because the resulting state is hardly productive but also because it paves the way to desertification. The natural distribution of the genus Prosopis includes arid and semiarid zones of the Americas, Africa and Asia, but the majority of the Prosopis species are, however, native to the Americas. In order to assess a likely gradient in the response of tree species to precipitation, temperature and their connection to El Niño southern oscillation (ENSO) events, two Prosopis species were chosen along a latitudinal gradient in Latin America, from northern Peru to central Chile: Prosopis pallida from a semi-arid land in northern and southern Peru and P. chilensis from a semiarid land in central Chile. Growth rings of each species were crossdated at each sampling site using classical dendrochronological techniques. Chronologies were related with instrumental climatic records in each site, as well as with SOI and N34 series. Cross-correlation, spectral and wavelet analysis techniques were used to assess the relation of growth with precipitation and temperature. Despite the long distance among sites, the two Prosopis species presented similar responses. Thus, the two species' growth is positively correlated to precipitation, while with temperature it is not. In northern Peru, precipitation and growth of P. pallida present a similar cyclic pattern, with a period of around 3 years. On the other hand, P. pallida in southern Peru, and P. chilensis also present this cyclic pattern, but also another one with lower frequency, coinciding with the pattern of precipitation. Both cycles are within the range of the ENSO band

Riparian thermal conditions across a mixed rural and urban landscape

Riparian corridors have the potential to function as thermal refuges, moderating extremes of local temperature variation. However, although demonstrated at individual sites, and over short periods, the consistency of this effect at wider temporal and spatial scales is poorly understood. The aim of this study is to assess the temperature differences between riparian corridors and adjacent non-riparian habitats and to explore the influence of environmental characteristics on these differences. Air temperature was monitored hourly at 20 paired locations (riparian and non-riparian) for two consecutive years. Urban index and canopy cover were characterised by calculating the percentage of impervious surface area and tree canopy cover within a 100 m radius from the centre of each sampling site. Canopy cover reduced summer thermal stresses in both urban and rural areas whereas high urban index tended to increase the daily thermal indices. Rivers had a significant mitigating effect on the urban riparian thermal condition, particularly in extreme hot weather. Riparian corridors were generally 1 °C cooler than non-riparian locations in summer and could be up to 3 °C cooler at some sites in extreme hot weather. Furthermore, riparian corridors at some sites were warmer than non-riparian locations in winter. These findings suggest that the proximity of rivers can modify riparian thermal environments, potentially reducing the heat stress of riparian corridors across landscapes

Predicting understory maximum shrubs cover using altitude and overstory basal area in different Mediterranean forests

In some areas of the Mediterranean basin where the understory stratum represents a critical fire hazard, managing the canopy cover to control the understory shrubby vegetation is an ecological alternative to the current mechanical management techniques. In this study, we determine the relationship between the overstory basal area and the cover of the understory shrubby vegetation for different dominant canopy species (Pinaceae and Fagaceae species) along a wide altitudinal gradient in the province of Catalonia (Spain). Analyses were conducted using data from the Spanish National Forest Inventory. At the regional scale, when all stands are analysed together, a strong negative relationship between mean shrub cover and site elevation was found. Among the Pinaceae species, we found fairly good relationships between stand basal area and the maximum development of the shrub stratum for species located at intermediate elevations (Pinus nigra, Pinus sylvestris). However, at the extremes of the elevationclimatic gradient (Pinus halepensis and Pinus uncinata stands), stand basal area explained very little of the shrub cover variation probably because microsite and topographic factors override its effect. Among the Fagaceae species, a negative relationship between basal area and the maximum development of the shrub stratum was found in Quercus humilis and Fagus sylvatica dominated stands but not in Quercus ilex. This can be due to the particular canopy structure and management history of Q. ilex stands. In conclusion, our study revealed a marked effect of the tree layer composition and the environment on the relationship between the development of the understory and overstory tree structure. More fine-grained studies are needed to provide forest managers with more detailed information about the relationship between these two forest strata

A Benchmark of Lidar-Based Single Tree Detection Methods Using Heterogeneous Forest Data from the Alpine Space

In this study, eight airborne laser scanning (ALS)-based single tree detection methods are benchmarked and investigated. The methods were applied to a unique dataset originating from different regions of the Alpine Space covering different study areas, forest types, and structures. This is the first benchmark ever performed for different forests within the Alps. The evaluation of the detection results was carried out in a reproducible way by automatically matching them to precise in situ forest inventory data using a restricted nearest neighbor detection approach. Quantitative statistical parameters such as percentages of correctly matched trees and omission and commission errors are presented. The proposed automated matching procedure presented herein shows an overall accuracy of 97%. Method based analysis, investigations per forest type, and an overall benchmark performance are presented. The best matching rate was obtained for single-layered coniferous forests. Dominated trees were challenging for all methods. The overall performance shows a matching rate of 47%, which is comparable to results of other benchmarks performed in the past. The study provides new insight regarding the potential and limits of tree detection with ALS and underlines some key aspects regarding the choice of method when performing single tree detection for the various forest types encountered in alpine regions.The European Commissio

Factors influencing modern wildfire occurrence in the Mark Twain National Forest, Missouri

Understanding relative influences of ecological and anthropogenic factors on wildfire occurrence can assist decisionmakers in allocating fire management resources. We examined the influences of ecological and anthropogenic variables on probability of modern fire occurrence in the Mark Twain National Forest (MTNF), Missouri, using classification and regression free (CART) and logistic regression analyses. Models were developed for five classes of fire size. Although CART distinguished some effects of fire size on results, logistic regression indicated a single model developed for all fires was sufficient for predictions. Ecological subsection was a dominating influence on fire occurrence for final CART and logistic models, highlighting the potential usefulness of ecosystem classification as a framework for considering factors influencing modern wildfires. Other influential predictors included ecosystem fire resistance; distance to roads, cities, and railroads; road density; mean October precipitation; elevation; median house value; and population density. Wildfires in the MTNF are caused overwhelmingly by arson, which, when combined with our results, suggests that arsonists may seek out flammable fuel types in remote areas With easy access. Within this general anthropogenic fire regime, we found a more subordinate effect of specific human variables (e.g., population density) on modern fire occurrence than did similar studies in the Upper Midwest, perhaps because our study area encompassed primarily federal forestlands with low population density. Copyright © 2007 by the Society of American Foresters

A review of methods for mapping and prediction of inventory attributes for operational forest management

Forest inventory attributes are an important source of information for a variety of strategic and tactical forest management purposes. However, it is not possible or feasible for field inventories to be conducted contiguously across large areas, especially at a resolution fine enough to be useful for operational management. Therefore, a large number of quantitative modeling and prediction methods have been and are being developed and applied to predict and map forest attributes, with the goal of providing an accurate, spatially continuous, and detailed information base for practitioners of forestry and ecosystem management. This article reviews the most commonly used prediction techniques in the context of a comprehensive modeling framework that includes a discussion of methods, data sources, variable selection, and model validation. The methods discussed include regression, nearest neighbor, artificial neural networks, decision trees, and ensembles such as random forest. No single technique is revealed as universally superior for predicting forest inventory attributes; the ideal approach depends on goals, available training and ancillary data, and the modeler\u27s interest in tradeoffs between realism and statistical considerations. Useful ancillary data included in the models tend to include climate and topographic variables as well as vegetation indices derived from optical remote sensing systems such as Landsat. However, the use of airborne LiDAR in modeling of forest inventory attributes is increasing rapidly and shows promise for operational forest management applications. Different considerations are encapsulated within a generalized model development framework that provides a structure against which tradeoffs can be evaluated

Modelling air temperature gradients across managed small streams in western Washington

Leaving riparian strips on both sides of a stream is widely accepted to be an effective management approach in sustaining the valuable functions of stream and riparian ecosystems. The authors\u27 overall objective is to provide microclimatic information for assessing the effectiveness of these strips. During the summer of 1993 and 1994, air temperatures were collected across 20 small, buffered streams in western Washington, USA, including five streams sampled before and after harvesting of the forest. These data were statistically analysed to examine the effects of adjacent harvesting with preservation of 16-72 m riparian forest strips. Regression models were developed to predict air temperatures at the stream and buffer edges, the difference between two locations, and seasonal changes. The authors found: (1) clearcutting in winter 1993/94 increased air temperature on the stream by up to 4°C, and changes in temperature variability from the stream to the upland, measured by coefficient of variation (CV), were significantly higher after harvesting; (2) forest buffers provided minimal protection for stream air temperature during the middle of summer (July) but were more effective early and late in the season; (3) buffer width was not a significant variable in predicting stream air temperature, suggesting that even a 72 m buffer was not sufficient to maintain a stream environment because of greater depth of edge influences

Effects of Forest Roads on Understory Plants in a Managed Hardwood Landscape

The effect of forest roads on species distribution and dispersal is an important conservation and management issue. We examined distributions of understory plants and their relationships to unpaved forest roads in a northern hardwood landscape in the Chequamegon National Forest, Wisconsin (U.S.A.). At six different sites, we recorded species cover, canopy cover, litter depth and cover, and bare ground at 11 distances (0, 5, 10, 15, 20, 30, 45, 60, 90, 120, and 150 m) from the road edge. At each of the 11 distances, we established a 60-m transect parallel to the road edge, within which we sampled 10 randomlyplaced 1 X 1 m plots (660 plots). We examined changes in species abundance (percent species cover per plot), richness, and Shannon-Wiener diversity (H′) with distance from the roads in an effort to determine the degree and magnitude of road effects on plant distribution. The species richness and H′ of native plants and the abundance of exotic species were clearly related to distance from the roads. Exotic species were most prevalent within 15 m of roads, occurring infrequently in the interior forest. The richness and H′ of native species were lower on the roadsides but reached interior-forest levels within a short distance (5 m) from the roads. The roads appeared to be associated with a disturbance corridor that affected site variables up to 15 m into the hardwood stands. At our six sites we detected 117 species, 25% of which occurred more frequently near the road, with only 12% having a 90% or greater preference for the forest interior. Our results suggest that roads have associated effects that alter interior-forest conditions and thus plant species composition and abundance; however, these effects are limited in depth of penetration into managed forests