Numerical Biases Research Articles

Contrasting Nutritional Acclimation of Sugar Maple (Acer saccharum Marsh.) and Red Maple (Acer rubrum L.) to Increasing Conifers and Soil Acidity as Demonstrated by Foliar Nutrient Balances

Sugar maple (Acer saccharum Marshall, SM) is believed to be more sensitive to acidic and nutrient-poor soils associated with conifer-dominated stands than red maple (Acer rubrum L., RM). Greater foliar nutrient use efficiency (FNUE) of RM is likely the cause for this difference. In the context of climate change, this greater FNUE could be key in favouring northward migration of RM over SM. We used the concept of foliar nutrient balances to study the nutrition of SM and RM seedlings along an increasing gradient in forest floor acidity conditioned by increasing proportions of conifers (pH values ranging from 4.39 under hardwoods, to 4.29 under mixed hardwood-conifer stands and 4.05 under conifer-dominated stands). Nutrients were subjected to isometric log-ratio (ilr) transformation, which views the leaf as one closed system and considers interactions between nutrients. The ilr method eliminates numerical biases and weak statistical inferences based on raw or “operationally’’ log-transformed data. We analyzed foliar nutrients of SM and RM seedlings and found that the [Ca,Mg,K|P,N] and [Ca,Mg|K] balances of SM seedlings were significantly different among soil acidity levels, whereas they did not vary for RM seedlings. For SM seedlings, these differences among soil acidity levels were due to a significant decrease in foliar Ca and Mg concentrations with increasing forest floor acidity. Similar differences in foliar balances were also found between healthy and declining SM stands estimated from literature values. Conversely, foliar balances of RM seedlings did not differ among soil acidity levels, even though untransformed foliar nutrient concentrations were significantly different. This result highlights the importance of using ilr transformation, since it provides more sensitive results than standard testing of untransformed nutrient concentrations. The lower nutrient requirements of RM and its greater capacity to maintain nutrient equilibrium are factors that could explain its competitive success and recent northward expansion. This study underscores the importance of using nutrient balances to study the redistribution of plant species in natural ecosystems under climate change.

Toward Energetically Consistent Ocean Models

Abstract Possibilities to construct a realistic quasi-global ocean model in Boussinesq approximation with a closed energy cycle are explored in this study. In such a model, the energy related to the mean variables would interact with all parameterized forms of energy without any spurious energy sources or sinks. This means that the energy available for interior mixing in the ocean would be only controlled by external energy input from the atmosphere and the tidal system and by internal exchanges. In the current implementation of such a consistent model, however, numerical biases and sources due to the nonlinear equation of state violate energy conservation, resulting in an overall residual up to several percent. In three (approximately) consistent model versions with different scenarios of mesoscale eddy dissipation, the parameterized internal wave field provides between 2 and 3 TW for interior mixing from the total external energy input of about 4 TW, such that a transfer between 0.3 and 0.4 TW into mean potential energy contributes to drive the large-scale circulation in the model. In contrast, the wind work on the mean circulation contributes by about 1.8 TW to the large-scale circulation in all model versions. It is shown that the consistent model versions are more energetic than standard and inconsistent model versions and in better agreement with hydrographic observations.

Applicability analysis of the TRMM precipitation data in the Sichuan-Chongqing region

Precipitation data is often needed for hydrological, meteorological, ecological, and other environmental and geographic applications. Currently there are mainly two sources of precipitation estimates: observation at meteorological stations and remote sensing data. However, a large number of studies has demonstrated that measurements at conventional meteorological stations are point data and they cannot reflect the spatial variation of precipitation effectively, especially in areas of more complex terrain. Remote sensing technology, on the other hand, is able to produce reasonably high resolution gridded precipitation fields. Precipitation products obtained by satellites have been widely used in previous studies in the world. The Sichuan-Chongqing region is a typical area with complicated terrain and climate characteristics. The meteorological stations are very unevenly distributed in this region, especially in the western area. Precipitation estimation using satellite data provides potential alternatives to precipitation measurements in this region. In this study,the performance of the TRMM(Tropical Rainfall Measurement Mission) 3B43 monthly precipitation data over 2000-2011 was evaluated in the SichuanChongqing region with rainfall records from 72 meteorological stations at different time intervals. The influence of elevation and slope on the verification result was analyzed at the monthly scale. Finally, principal component analysis was used to compare the effects of elevation and slope on the accuracy of TRMM 3B43 precipitation estimates. The results show that:(1) Regional average annual precipitation estimated by TRMM 3B43 is higher than the observed data from meteorological stations by 5.38%, and the eastern area estimation results are less accurate than the western plateau. Goodness of fit of seasonal precipitation between TRMM 3B43 estimates and observed data is high, but varies between the seasons—the goodness of fit of spring precipitation is higher than other seasons. Correlation between observations at the 72 stations and TRMM 3B43 estimates is high and shows little numerical biases in the whole study area at the monthly scale.(2) For individual stations, at most stations the correlation coefficients are reasonably high and the estimation biases are small, but the correlation coefficient at the Xuyong Station is comparatively low and the estimation biases at the Xiaojin Station, Yaan Station, Leibo Station, Yanyuan Station, and Panzhihua Station are comparatively high.(3) Compared with slope, elevation has greater influence on the accuracy of TRMM 3B43 estimates, which can be characterized by a cubic nonlinear relationship. With the increase of Elevation, R shows an increasing trend and |Bias(%)| increases-decreases-increases.(4) The influence of slope on the accuracy of TRMM 3B43 estimates is more complicated. Generally speaking, slope significantly affects the accuracy of TRMM 3B43 estimates

Doing arithmetic by hand: hand movements during exact arithmetic reveal systematic, dynamic spatial processing.

Mathematics requires precise inferences about abstract objects inaccessible to perception. How is this possible? One proposal is that mathematical reasoning, while concerned with entirely abstract objects, nevertheless relies on neural resources specialized for interacting with the world-in other words, mathematics may be grounded in spatial or sensorimotor systems. Mental arithmetic, for instance, could involve shifts in spatial attention along a mental "number-line", the product of cultural artefacts and practices that systematically spatialize number and arithmetic. Here, we investigate this hypothesized spatial processing during exact, symbolic arithmetic (e.g., 4 + 3 = 7). Participants added and subtracted single-digit numbers and selected the exact solution from responses in the top corners of a computer monitor. While they made their selections using a computer mouse, we recorded the movement of their hand as indexed by the streaming x, y coordinates of the computer mouse cursor. As predicted, hand movements during addition and subtraction were systematically deflected toward the right and the left, respectively, as if calculation involved simultaneously simulating motion along a left-to-right mental number-line. This spatial-arithmetical bias, moreover, was distinct from-but correlated with-individuals' spatial-numerical biases (i.e., spatial-numerical association of response codes, SNARC, effect). These results are the first evidence that exact, symbolic arithmetic prompts systematic spatial processing associated with mental calculation. We discuss the possibility that mathematical calculation relies, in part, on an integrated system of spatial processes.

Sets within sets: The influence of set membership on numerical estimates.

Navigating the world requires attention to number; however, sets in real-world contexts are rarely homogeneous or presented in isolation, thus the task of determining what constitutes a relevant set for enumeration can be a difficult one. This contextual ambiguity increases the likelihood that irrelevant sets may bias our ability to accurately track number. In the current study, we investigated whether numerical estimates are influenced by irrelevant set information, such as the size of other present subsets or the number of subsets composing the set. Adult observers were shown brief arrays of dots containing 1 or 2 intermixed subsets, differentiated by color, and were asked to estimate the number of either: (1) 1 of the subsets or (2) the superset (total number of dots). When estimating the size of a subset, numerical estimates were greatly influenced by the size of the other, irrelevant subset, suggesting that the presence of extraneous sets may hinder accurate number judgments. Furthermore, when asked to judge the total number of items (the superset), observers judged supersets comprising 2 subsets as more numerous compared to those comprising only a single subset. Importantly, both trends were apparent even when observers had prior information about the identity of the target set, suggesting adults preattentively parse the world into sets, causing numerical biases that are not under conscious control. Potential explanations for this pattern of results, including simultaneous numerical contrast effects and superset summation, are discussed.

Nutrient signature of Quebec (Canada) cranberry (Vaccinium macrocarpon Ait.)

Fertilizer recommendations for cranberry crops are guided by plant and soil tests. However, critical tissue concentration ranges used for diagnostic purposes are inherently biased by nutrient interactions and physiological age. Compositional data analysis using isometric log ratios (ilr) of nutrients as well as time detrending can avoid numerical biases. The objective was to derive unbiased nutrient signature standards for cranberry in Quebec and compare those standards to literature data. Field trials were conducted during 3 consecutive years with varying P treatments at six commercial sites in Quebec. Leaf tissues were analyzed for N, P, K, Ca, Mg, B, Cu, Zn, Mn and Fe. The analytical results were transformed into ilr nutrient balances of parts and groups of parts. High-yield reference ilr values were computed for cranberry yielding greater than 35 Mg ha-1. Many cranberry fields appeared to be over-supplied with K and either under-supplied with Mn or over-supplied with Fe as shown by their imbalanced [K | Ca, Mg] and [Mn | Fe] ratios. Nutrient concentration ranges from Maine and Wisconsin, USA, were combined into ilr values to generate ranges of balances. It was found that these nutrient ranges were much too broad for application in Quebec or outside the Quebec ranges for the [Ca | Mg] and the [Mn | Fe] balances, that were lower compared to those of high yielding cranberry crops in Quebec.

Balancing guava nutrition with liming and fertilization

Guava response to liming and fertilization can be monitored by tissue testing. Tissue nutrient signature is often diagnosed against nutrient concentration standards. However, this approach has been criticized for not considering nutrient interactions and to generate numerical biases as a result of data redundancy, scale dependency and non-normal distribution. Techniques of compositional data analysis can control those biases by balancing groups of nutrients, such as those involved in liming and fertilization. The sequentially arranged and orthonormal isometric log ratios (ilr) or balances avoid numerical bias inherent to compositional data. The objectives were to relate tissue nutrient balances with the production of "Paluma" guava orchards differentially limed and fertilized, and to adjust the current patterns of nutrient balance with the range of more productive guava trees. It was conducted one experiment of 7-yr of liming and three experiments of 3-yr with N, P and K trials in 'Paluma' orchards on an Oxisol. Plant N, P, K, Ca and Mg were monitored yearly. It was selected the [N, P, K | Ca, Mg], [N, P | K], [N | P] and [Ca | Mg] balances to set apart the effects of liming (Ca-Mg) and fertilizers (N-K) on macronutrient balances. Liming largely influenced nutrient balances of guava in the Oxisol while fertilization was less influential. The large range of guava yields and nutrient balances allowed defining balance ranges and comparing them with the critical ranges of nutrient concentration values currently used in Brazil and combined into ilr coordinates.

HOW WELL DO COSMOLOGICAL SIMULATIONS REPRODUCE INDIVIDUAL HALO PROPERTIES?

Cosmological simulations of galaxy formation often rely on prescriptions for star formation and feedback that depend on halo properties such as halo mass, central over-density, and virial temperature. In this paper we address the convergence of individual halo properties, based on their number of particles N, focusing in particular on the mass of halos near the resolution limit of a simulation. While it has been established that the halo mass function is sampled on average down to N~30 particles, we show that individual halo properties exhibit significant scatter, and some systematic biases, as one approaches the resolution limit. We carry out a series of cosmological simulations using the Gadget2 and Enzo codes with N_p=64^3 to N_p=1024^3 total particles, keeping the same large-scale structure in the simulation box. We consider boxes from l_{box} = 8 Mpc/h to l_{box} = 512 Mpc/h to probe different halo masses and formation redshifts. We cross-identify dark matter halos in boxes at different resolutions and measure the scatter in their properties. The uncertainty in the mass of single halos depends on the number of particles (scaling approximately as N^{-1/3}), but the rarer the density peak, the more robust its identification. The virial radius of halos is very stable and can be measured without bias for halos with N>30. In contrast, the average density within a sphere containing 25% of the total halo mass is severely underestimated (by more than a factor 2) and the halo spin is moderately overestimated for N<100. If sub-grid physics is implemented upon a cosmological simulation, we recommend that rare halos (~3sigma peaks) be resolved with N>100 particles and common halos (~1sigma peaks) with N>400 particles to avoid excessive numerical noise and possible systematic biases in the results.

Host and habitat preferences of polypore fungi in Micronesian tropical flooded forests

The distribution and ecological impacts of plant-associated fungi is determined in large part by their degree of specificity for particular host species or environmental conditions. Here we evaluate the host and habitat preferences among the Aphyllophorales, a guild of wood-decay basidiomycete fungi usually considered to be host generalists. We determined the patterns of host association in three well-defined, floristically distinct, tropical wetlands — freshwater forested wetlands, saltwater mangrove forests, and peatlands with scattered trees — on the islands of Kosrae and Pohnpei in the Federated States of Micronesia. Of 33 fungal species, 20 were locally rare. Of the 11 species sufficiently common to evaluate habitat specificity, nine showed significant habitat preferences. Of eight species common enough to evaluate within-habitat host specificity, six showed strong host preferences. All except one of the nine habitat-specialized fungi showed either statistically significant host specificity or strong numerical biases toward single host species. Our results suggest that host preferences may be important in shaping the assemblages of wood-decay fungi, and that the effect of environment on the distribution of susceptible plant species, rather on the fungi themselves, may ultimately drive the apparent habitat specificity of many fungi.

Numerical Biases on Initial Mass Function Determinations Created by Binning

We detect and quantify significant numerical biases in the determination of the slope of power laws with Salpeter (or similar) indices from uniformly binned data using χ2 minimization. The biases are caused by the correlation between the number of stars per bin and the assigned weights and are especially important when the number of stars per bin is small. This result implies the existence of systematic errors in the values of IMFs calculated in this way. We propose as an alternative using variable-size bins and dividing the stars evenly among them. Such variable-size bins yield very small biases that are only weakly dependent on the number of stars per bin. Furthermore, we show that they allow for the calculation of reliable IMFs with only a small total number of stars. Therefore, they are a preferred alternative to the standard uniform-size binning.

Denominational Biases in the American Press

Because biased religion coverage in the elite press affects the sociopolitical role denominations play in society, a study of the 1977 coverage of denominations in the NEW YORK TIMES and the WASHINGTON POST was conducted. The results show that numerical biases were present: establishment denominations tended to receive inordinate coverage and prominent placement, while evangelical groups were slighted. The numerical biases probably resulted to a large degree from the issues which were reported most often.

On the Freezing of Liquid Water in a Cloud

Abstract A technique due to Saunders is used to give quantitative information on the amount of heating to be realized from the freezing of liquid water in a cloud. The commonly accepted value of ⅓C per gram of water frozen per kilogram of air plus an additional amount due to saturation adjustment from water to ice is shown to be imprecise. The total heating is realized only after ice pseudo- or saturated-adiabatic ascent to higher levels in the atmosphere; less than one-half of the maximum temperature difference between liquid water and ice processes is realized at the time of freezing, if freezing of cloud contents of 7 gm kg−1 or less is done at −5C. The delay in the freezing of rainwater in operational, one-dimensional numerical models biases the results against natural clouds, leading to overestimates of “seedability.” Also the neglect of the temperature dependence of the latent heat of condensation (increasing with lower temperatures) in those models causes the same kind of bias.