On the Interpretation of the Normalization Constant in the Scaling Equation

The scaling equation, Y1 = βYα2, has been used empirically and explored theoretically primarily to determine the numerical value and meaning of the scaling exponent, α. The mathematical interpretation of α is clear—it is the quotient of the relative rate of change of Y1 with respect to the rate of change of Y2. In contrast, the interpretation of the normalization constant, β, is obscure, so much so that some workers have rejected the idea that it has any biological importance. With the notable exception of Steven J. Gould\u27s early work, Huxley\u27s dismissal of β largely relegated the study of its biological role to that of an academic afterthought. Here, we attempt to clarify the meaning of β by using examples from plant biology to illustrate the four primary difficulties that have obscured its importance: (1) the consistency of the units of measurement and the metric being measured (e.g., meters and body length, respectively), (2) the relationship between β and α, (3) the interpretation of scaling equations, and (4) detecting if the numerical value of β has changed and if the change is biologically meaningful. Using examples, we show that β is biologically interpretable and offers a way to quantitatively consider similarities of biological form if (1) it is expressed in terms of the relative magnitudes of Y1 or Y2 for corresponding data points in a set of Y1 = βYα2 equations, (2) the units of measurements are in the same scale, and (3) the corresponding dimensionless numbers are established based on the same units of measurement. We provide examples of where the numerical value of β or differences in the values of β are important, and we propose a research agenda examining the meaning of β values in terms of trait-based ecology

Optimising the analysis of transcript data using high density oligonucleotide arrays and genomic DNA-based probe selection

Background: Affymetrix GeneChip arrays are widely used for transcriptomic studies in a diverse range of species. Each gene is represented on a GeneChip array by a probe-set, consisting of up to 16 probe-pairs. Signal intensities across probe-pairs within a probe-set vary in part due to different physical hybridisation characteristics of individual probes with their target labelled transcripts. We have previously developed a technique to study the transcriptomes of heterologous species based on hybridising genomic DNA (gDNA) to a GeneChip array designed for a different species, and subsequently using only those probes with good homology. Results: Here we have investigated the effects of hybridising homologous species gDNA to study the transcriptomes of species for which the arrays have been designed. Genomic DNA from Arabidopsis thaliana and rice (Oryza sativa) were hybridised to the Affymetrix Arabidopsis ATH1 and Rice Genome GeneChip arrays respectively. Probe selection based on gDNA hybridisation intensity increased the number of genes identified as significantly differentially expressed in two published studies of Arabidopsis development, and optimised the analysis of technical replicates obtained from pooled samples of RNA from rice. Conclusion: This mixed physical and bioinformatics approach can be used to optimise estimates of gene expression when using GeneChip arrays

On the Interpretation of the Normalization Constant in the Scaling Equation

The scaling equation, Y1 = βY2α, has been used empirically and explored theoretically primarily to determine the numerical value and meaning of the scaling exponent, α. The mathematical interpretation of α is clear—it is the quotient of the relative rate of change of Y1 with respect to the rate of change of Y2. In contrast, the interpretation of the normalization constant, β, is obscure, so much so that some workers have rejected the idea that it has any biological importance. With the notable exception of Steven J. Gould's early work, Huxley's dismissal of β largely relegated the study of its biological role to that of an academic afterthought. Here, we attempt to clarify the meaning of β by using examples from plant biology to illustrate the four primary difficulties that have obscured its importance: (1) the consistency of the units of measurement and the metric being measured (e.g., meters and body length, respectively), (2) the relationship between β and α, (3) the interpretation of scaling equations, and (4) detecting if the numerical value of β has changed and if the change is biologically meaningful. Using examples, we show that β is biologically interpretable and offers a way to quantitatively consider similarities of biological form if (1) it is expressed in terms of the relative magnitudes of Y1 or Y2 for corresponding data points in a set of Y1 = βY2α equations, (2) the units of measurements are in the same scale, and (3) the corresponding dimensionless numbers are established based on the same units of measurement. We provide examples of where the numerical value of β or differences in the values of β are important, and we propose a research agenda examining the meaning of β values in terms of trait-based ecology

Using genomic DNA-based probe-selection to improve the sensitivity of high-density oligonucleotide arrays when applied to heterologous species

High-density oligonucleotide (oligo) arrays are a powerful tool for transcript profiling. Arrays based on GeneChip® technology are amongst the most widely used, although GeneChip® arrays are currently available for only a small number of plant and animal species. Thus, we have developed a method to improve the sensitivity of high-density oligonucleotide arrays when applied to heterologous species and tested the method by analysing the transcriptome of Brassica oleracea L., a species for which no GeneChip® array is available, using a GeneChip® array designed for Arabidopsis thaliana (L.) Heynh. Genomic DNA from B. oleracea was labelled and hybridised to the ATH1-121501 GeneChip® array. Arabidopsis thaliana probe-pairs that hybridised to the B. oleracea genomic DNA on the basis of the perfect-match (PM) probe signal were then selected for subsequent B. oleracea transcriptome analysis using a .cel file parser script to generate probe mask files. The transcriptional response of B. oleracea to a mineral nutrient (phosphorus; P) stress was quantified using probe mask files generated for a wide range of gDNA hybridisation intensity thresholds. An example probe mask file generated with a gDNA hybridisation intensity threshold of 400 removed > 68 % of the available PM probes from the analysis but retained >96 % of available A. thaliana probe-sets. Ninety-nine of these genes were then identified as significantly regulated under P stress in B. oleracea, including the homologues of P stress responsive genes in A. thaliana. Increasing the gDNA hybridisation intensity thresholds up to 500 for probe-selection increased the sensitivity of the GeneChip® array to detect regulation of gene expression in B. oleracea under P stress by up to 13-fold. Our open-source software to create probe mask files is freely available http://affymetrix.arabidopsis.info/xspecies/ webcite and may be used to facilitate transcriptomic analyses of a wide range of plant and animal species in the absence of custom arrays

Beyond a warming fingerprint: individualistic biogeographic responses to heterogeneous climate change in California.

Understanding recent biogeographic responses to climate change is fundamental for improving our predictions of likely future responses and guiding conservation planning at both local and global scales. Studies of observed biogeographic responses to 20th century climate change have principally examined effects related to ubiquitous increases in temperature - collectively termed a warming fingerprint. Although the importance of changes in other aspects of climate - particularly precipitation and water availability - is widely acknowledged from a theoretical standpoint and supported by paleontological evidence, we lack a practical understanding of how these changes interact with temperature to drive biogeographic responses. Further complicating matters, differences in life history and ecological attributes may lead species to respond differently to the same changes in climate. Here, we examine whether recent biogeographic patterns across California are consistent with a warming fingerprint. We describe how various components of climate have changed regionally in California during the 20th century and review empirical evidence of biogeographic responses to these changes, particularly elevational range shifts. Many responses to climate change do not appear to be consistent with a warming fingerprint, with downslope shifts in elevation being as common as upslope shifts across a number of taxa and many demographic and community responses being inconsistent with upslope shifts. We identify a number of potential direct and indirect mechanisms for these responses, including the influence of aspects of climate change other than temperature (e.g., the shifting seasonal balance of energy and water availability), differences in each taxon's sensitivity to climate change, trophic interactions, and land-use change. Finally, we highlight the need to move beyond a warming fingerprint in studies of biogeographic responses by considering a more multifaceted view of climate, emphasizing local-scale effects, and including a priori knowledge of relevant natural history for the taxa and regions under study

A Macroecological Analysis of SERA Derived Forest Heights and Implications for Forest Volume Remote Sensing

Individual trees have been shown to exhibit strong relationships between DBH, height and volume. Often such studies are cited as justification for forest volume or standing biomass estimation through remote sensing. With resolution of common satellite remote sensing systems generally too low to resolve individuals, and a need for larger coverage, these systems rely on descriptive heights, which account for tree collections in forests. For remote sensing and allometric applications, this height is not entirely understood in terms of its location. Here, a forest growth model (SERA) analyzes forest canopy height relationships with forest wood volume. Maximum height, mean, H100, and Lorey's height are examined for variability under plant number density, resource and species. Our findings, shown to be allometrically consistent with empirical measurements for forested communities world-wide, are analyzed for implications to forest remote sensing techniques such as LiDAR and RADAR. Traditional forestry measures of maximum height, and to a lesser extent H100 and Lorey's, exhibit little consistent correlation with forest volume across modeled conditions. The implication is that using forest height to infer volume or biomass from remote sensing requires species and community behavioral information to infer accurate estimates using height alone. SERA predicts mean height to provide the most consistent relationship with volume of the height classifications studied and overall across forest variations. This prediction agrees with empirical data collected from conifer and angiosperm forests with plant densities ranging between 102–106 plants/hectare and heights 6–49 m. Height classifications investigated are potentially linked to radar scattering centers with implications for allometry. These findings may be used to advance forest biomass estimation accuracy through remote sensing. Furthermore, Lorey's height with its specific relationship to remote sensing physics is recommended as a more universal indicator of volume when using remote sensing than achieved using either maximum height or H100

A Freeze Frame View of Vesicular Stomatitis Virus Transcription Defines a Minimal Length of RNA for 5′ Processing

The RNA synthesis machinery of vesicular stomatitis virus (VSV) comprises the genomic RNA encapsidated by the viral nucleocapsid protein (N) and associated with the RNA dependent RNA polymerase, the viral components of which are a large protein (L) and an accessory phosphoprotein (P). The 241 kDa L protein contains all the enzymatic activities necessary for synthesis of the viral mRNAs, including capping, cap methylation and polyadenylation. Those RNA processing reactions are intimately coordinated with nucleotide polymerization such that failure to cap results in termination of transcription and failure to methylate can result in hyper polyadenylation. The mRNA processing reactions thus serve as a critical check point in viral RNA synthesis which may control the synthesis of incorrectly modified RNAs. Here, we report the length at which viral transcripts first gain access to the capping machinery during synthesis. By reconstitution of transcription in vitro with highly purified recombinant polymerase and engineered templates in which we omitted sites for incorporation of UTP, we found that transcripts that were 30-nucleotides in length were uncapped, whereas those that were 31-nucleotides in length contained a cap structure. The minimal RNA length required for mRNA cap addition was also sufficient for methylation since the 31-nucleotide long transcripts were methylated at both ribose-2′-O and guanine-N-7 positions. This work provides insights into the spatial relationship between the active sites for the RNA dependent RNA polymerase and polyribonucleotidyltransferase responsible for capping of the viral RNA. We combine the present findings with our recently described electron microscopic structure of the VSV polymerase and propose a model of how the spatial arrangement of the capping activities of L may influence nucleotide polymerization