Different responses to changes in phosphorus,P, among lakes. A study of slopes in chl-a = f(P) graphs

The least squares estimator of a linear regression coefficient _L will give an overall expression for the change in with x. In fresh water ecology, however, subgroups, % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuaSGaci% 4Aaaaa!37BE!\[P\operatorname{k}\], of a parent population may have slopes which differ from the overall slope, _L. By constructing frequency histograms for the set of angles: Arctang % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4uaSGaam% yAaiaadQgaaaa!38AE!\[\operatorname{S} ij\],% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4uaSGaam% yAaiaadQgaaaa!38AE!\[\operatorname{S} ij\]= para sa y and x% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaadM% faliaadMgakiabgkHiTiaadMfaliaadQgakiaacMcacaGGVaGaaiik% aiaadIhaliaadMgakiabgkHiTiaadIhaliaadQgakiaacMcaaaa!42F0!\[(Yi - Yj)/(xi - xj)\], i < j, % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaSGaam% yAaOGaeyiyIKRaamiEaSGaamOAaaaa!3BAB!\[xi \ne xj\], peaks in the distribution may be identified and related to ecological phenomenon. To identify peaks we fit Gaussian distributions to the frequency histograms. For a set consisting of 142 observations of chlorophyll-a and total phosphorus (nutrient) concentrations (TP) from 16 lakes we found four Gaussian peaks corresponding to four subgroups, % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuaSGaci% 4Aaaaa!37BE!\[P\operatorname{k}\]k = 1,4. One group identified a response of chl-a to changes in TP which correspond approximately to the average slope found by least square regression (the slope was 0.49). The second group consisted of steeper response than the average (1.28). A third group showed that there is an enhanced proportion of cases where chl-a does not respond to TP (zero slope, all the three deep lakes > 10 m, included in the date set contributed to this group). The size of the last group, spanning a wide range of slopes, suggested that about 30% of the inter annual changes in chl-a is unrelated to TP. The results are compared to result obtained by simple least squares regression and to the Theil non-parametric slope estimator.     

Statistical torsion angle potential energy functions for protein structure modeling: A bicubic interpolation approach

A set of grid type knowledge‐based energy functions is introduced for ?–χ₁, ψ–χ₁, ?–ψ, and χ₁–χ₂ torsion angle combinations. Boltzmann distribution is assumed for the torsion angle populations from protein X‐ray structures, and the functions are named as statistical torsion angle potential energy functions. The grid points around periodic boundaries are duplicated to force periodicity, and the remedy relieves the derivative discontinuity problem. The devised functions rapidly improve the quality of model structures. The potential bias in the functions and the usefulness of additional secondary structure information are also investigated. The proposed guiding functions are expected to facilitate protein structure modeling, such as protein structure prediction, protein design, and structure refinement. Proteins 2013. Proteins 2013; 81:1156–1165. © 2013 Wiley Periodicals, Inc.     

An evaluation of transferability of ecological niche models

Ecological niche modeling (ENM) is used widely to study species’ geographic distributions. ENM applications frequently involve transferring models calibrated with environmental data from one region to other regions or times that may include novel environmental conditions. When novel conditions are present, transferability implies extrapolation, whereas, in absence of such conditions, transferability is an interpolation step only. We evaluated transferability of models produced using 11 ENM algorithms from the perspective of interpolation and extrapolation in a virtual species framework. We defined fundamental niches and potential distributions of 16 virtual species distributed across Eurasia. To simulate real situations of incomplete understanding of species’ distribution or existing fundamental niche (environmental conditions suitable for the species contained in the study area; N* _F ), we divided Eurasia into six regions and used 1–5 regions for model calibration and the rest for model evaluation. The models produced with the 11 ENM algorithms were evaluated in environmental space, to complement the traditional geographic evaluation of models. None of the algorithms accurately estimated the existing fundamental niche (N* _F ) given one region in calibration, and model evaluation scores decreased as the novelty of the environments in the evaluation regions increased. Thus, we recommend quantifying environmental similarity between calibration and transfer regions prior to model transfer, providing an avenue for assessing uncertainty of model transferability. Different algorithms had different sensitivity to completeness of knowledge of N* _F , with implications for algorithm selection. If the goal is to reconstruct fundamental niches, users should choose algorithms with limited extrapolation when N* _F is well known, or choose algorithms with increased extrapolation when N* _F is poorly known. Our assessment can inform applications of ecological niche modeling transference to anticipate species invasions into novel areas, disease emergence in new regions, and forecasts of species distributions under future climate conditions.     

Spatial heterogeneity in the determinants of woody plant invasion of lowland heath

Questions: 1. What is the scale and extent of spatial variability in factors affecting Betula invasion of heaths? 2. How much effect does each factor have on within‐patch patterns of invasion? 3. How can this understanding aid in managing Betula invasions? Location: Lowland heath of southern England. Methods: Determinants of Betula (both B. pubescens and B. pendula) invasion: biomass density, necromass density, mean vegetation height, P‐availability, soil water content and total Betula seed bank density, were measured at two sites on a 5‐ha sampling grid. Spatial pattern was assessed using geostatistics. Contributions of each determinant to within‐site heterogeneity in predicted Betula seedling densities were estimated by varying variables over their full and interquartile ranges in a statistical model derived from experimental data. Results: Salient spatial trends were revealed: strong autocorrelation over distances of < 50 m for soil factors and more extensive autocorrelation (0 to > 150 m) in vegetation variables and Betula seed bank densities. The latter resulted in single across‐site gradients, the former small, distinct patches. All patterns were overlain with variance that was present at distances of < 17.6 m. Variables displaying spatial pattern also accounted for within‐site heterogeneity in predicted Betula seedling densities but their relative contribution to this varied between sites. Conclusions: Identifiable spatial autocorrelation in factors controlling patch‐scale invasion patterns allows managers to target invasion prone patches, potentially reducing management intensities. Furthermore, management effort may be optimised by spatially de‐coupling Betula seed from safe‐sites. This plan may adaptable to the management of other weeds and open‐land ecosystems.     

Cubic-spline interpolation to estimate effects of inbreeding on milk yield in first lactation Holstein cows

Milk yield records (305d, 2X, actual milk yield) of 123,639 registered first lactation Holstein cows were used to compare linear regression (y = β(0) + β(1)X + e), quadratic regression, (y = β(0) + β(1)X + β(2)X(2) + e) cubic regression (y = β(0) + β(1)X + β(2)X(2) + β(3)X(3) +e) and fixed factor models, with cubic-spline interpolation models, for estimating the effects of inbreeding on milk yield. Ten animal models, all with herd-year-season of calving as fixed effect, were compared using the Akaike corrected-Information Criterion (AICc). The cubic-spline interpolation model with seven knots had the lowest AICc, whereas for all those labeled as "traditional", AICc was higher than the best model. Results from fitting inbreeding using a cubic-spline with seven knots were compared to results from fitting inbreeding as a linear covariate or as a fixed factor with seven levels. Estimates of inbreeding effects were not significantly different between the cubic-spline model and the fixed factor model, but were significantly different from the linear regression model. Milk yield decreased significantly at inbreeding levels greater than 9%. Variance component estimates were similar for the three models. Ranking of the top 100 sires with daughter records remained unaffected by the model used.     

Volume interpolation of CT images from tree trunks

Computerized tomography as a non-destructive scanning method to analyze wood structures has become an important technique in tree research. The possibility to reconstruct three-dimensional volumes based on a number of slices of two-dimensional data from CT scans is strongly dependent on the number of measured slices. Radial basis function methods can be successfully used to interpolate CT images with the aim of obtaining a satisfactory reconstruction of tree trunks. In contrast to standard interpolation techniques, our method takes into account that wood structures differ more in the radial than in the longitudinal direction. Therefore we obtain better interpolation results for wood structures.