Biological similarity relative to allometric quantities

It is an empirical finding that an allometric quantity with dimensional exponents α, β and γ relative to mass, length, and time, respectively, has a value for its allometric exponentb satisfying the relation

$$\tfrac{1}{3}(3\alpha + \beta + {\gamma \mathord{\left/ {\vphantom {\gamma 2}} \right. \kern-\nulldelimiterspace} 2}) \leqslant b \leqslant \tfrac{1}{3}(3\alpha + \beta + \gamma ).$$

A theoretical derivation is given of this double inequality using only the fact of constant density and the plausible assumption that metabolic rate is a dominant allometric quantity.

     

Techniques for estimating allometric equations.

Morphologists have long been aware that differential size relationships of variables can be fo great value when studying shape. Allometric patterns have been the basis of many interpretations of adaptations, biomechanisms, and taxonomies. It is of importance that the parameters of the allometric equation be as accurate estimates as possible since they are so commonly used in such interpretations. Since the error term may come into the allometric relation either exponentially or additively, there are at least two methods of estimating the parameters of the allometric equation. That most commonly used assumes exponentiality of the error term, and operates by forming a linear function by a logarithmic transformation and then solving by the method of ordinary least squares. On the other hand, if the rrror term comes into the equation in an additive way, a nonlinear method may be used, searching the parameter space for those parameters which minimize the sum of squared residuals. Study of data on body weight and metabolism in birds explores the issues involved in discriminating between the two models by working through a specific example and shows that these two methods of estimation can yield highly different results. Not only minimizing the sum of squared residuals, but also the distribution and randomness of the residuals must be considered in determing which model more precisely estimates the parameters. In general there is no a priori way to tell which model will be best. Given the importance often attached to the parameter estimates, it may be well worth considerable effort to find which method of solution is appropriate for a given set of data.     

Estimation of parameters of allometric equations.

Accurate parameter estimation of allometric equations is a question of considerable interest. Various techniques that address this problem exist. In this paper it is assumed that the measured values are normally distributed and a maximum likelihood estimation approach is used. The computations involved in this procedure are reducible to relatively simple forms, and an efficient numerical algorithm is used. A listing of the computer program is included as an appendix.     

A comparison of methods for fitting allometric equations to field metabolic rates of animals

We re-examined data for field metabolic rates of varanid lizards and marsupial mammals to illustrate how different procedures for fitting the allometric equation can lead to very different estimates for the allometric coefficient and exponent. A two-parameter power function was obtained in each case by the traditional method of back-transformation from a straight line fitted to logarithms of the data. Another two-parameter power function was then generated for each data-set by non-linear regression on values in the original arithmetic scale. Allometric equations obtained by non-linear regression described the metabolic rates of all animals in the samples. Equations estimated by back-transformation from logarithms, on the other hand, described the metabolic rates of small species but not large ones. Thus, allometric equations estimated in the traditional way for field metabolic rates of varanids and marsupials do not have general importance because they do not characterize rates for species spanning the full range in body size. Logarithmic transformation of predictor and response variables creates new distributions that may enable investigators to perform statistical analyses in compliance with assumptions underlying the tests. However, statistical models fitted to transformations should not be used to estimate parameters of equations in the arithmetic domain because such equations may be seriously biased and misleading. Allometric analyses should be performed on values expressed in the original scale, if possible, because this is the scale of interest.     

Theoretical and empirical derivation of cardiovascular allometric relationships in children.

Basic fluid dynamic principles were used to derive a theoretical model of optimum cardiovascular allometry, the relationship between somatic and cardiovascular growth. The validity of the predicted models was then tested against the size of 22 cardiovascular structures measured echocardiographically in 496 normal children aged 1 day to 20 yr, including valves, pulmonary arteries, aorta and aortic branches, pulmonary veins, and left ventricular volume. Body surface area (BSA) was found to be a more important determinant of the size of each of the cardiovascular structures than age, height, or weight alone. The observed vascular and valvar dimensions were in agreement with values predicted from the theoretical models. Vascular and valve diameters related linearly to the square root of BSA, whereas valve and vascular areas related to BSA. The relationship between left ventricular volume and body size fit a complex model predicted by the nonlinear decrease of heart rate with growth. Overall, the relationship between cardiac output and body size is the fundamental driving factor in cardiovascular allometry.     

Some theoretical consequences of the allometric growth equations

The rate of growth of an organism may be described as a function of both its mass and of the time. In particular, if the rate of growth is described as a function of mass alone, one derives the so-called principle of “equifinality”, according to which the final mass achieved is independent of any interruption of the growth process. Since this phenomenon is observed in many instances, the assumption that the rate of growth is a function of mass alone has some theoretical justification. On the other hand, it is obvious that in many instances irreversible effects can be achieved by interrupting the growth process, thus indicating that the rate of growth may depend on variables other than mass. The consequences of some of these alternative assumptions are examined. A growth factorG is postulated, which is supposed to decay with time, and whose concentration determines the over-all rate of growth per unit mass. The rate of decay ofG is calculated from the postulated growth equation under two alternative assumptions, (1) thatG is a constituent of all the cells of the organism and (2) thatG is produced separately and distributed through the organism. It is shown that in each case the concentration ofG satisfies a simple differential equation. While in normal growth the results deduced from these hypotheses are indistinguishable from those deduced from the assumption that the rate of growth depends on mass alone, widely different results are obtained in the case of interrupted growth. In particular, the rate at which growth is resumed after interruption and the final mass achieved depend on the time and on the duration of interruption. It appears, therefore, that various assumptions about the nature of the “aging” of the organism lead to various quantitative relations between growth and the times of interruption and resumption of growth.     

Wanted: new allometric equations for large lianas and African lianas

Liana abundance appears to be increasing, possibly to the detriment of trees, but methods for measuring liana biomass are undependable. We show that five commonly used allometric equations produce disparate results and discuss two large information gaps—Central African lianas and large lianas—that currently preclude accurate liana biomass estimation.     

Biological nonlocality and the mind-brain interaction problem: comments on a new empirical approach

Up to now, we have been faced with an age old fundamental dilemma posed by the mind-brain interaction problem, i.e. how is it that the mind which is subjective and immaterial, can interact with the brain which is objective and material? Analysis of recent experiments appears to indicate that quantum mechanics may have a role to play in the resolution of the mind-brain interaction problem in the form of biological entanglement and nonlocality. In addition to this analysis, when coupled with ongoing and proposed experiments, may help us to simultaneously resolve related issues such as whether mental events can initiate neural events, the transference of conscious subjective experience, the measurement problem and the binding problem.     

A comparison of several similarity indices used in the classification of protein sequences: a multivariate analysis.

The present work describes an attempt to identify reliable criteria which could be used as distance indices between protein sequences. Seven different criteria have been tested: i and ii) the scores of the alignments as given by the BESTFIT and the FASTA programs; iii) the ratio parameter, i.e. the BESTFIT score divided by the length of the aligned peptides; iv and v) the statistical significance (Z-scores) of the scores calculated by BESTFIT and FASTA, as obtained by comparison with shuffled sequences; vi) the Z-scores provided by the program RELATE which performs a segment-by-segment comparison of 2 sequences, and vii) an original distance index calculated by the program DOCMA from all the pairwise dotplots between the sequences. These 7 criteria have been tested against the aminoacid sequences of 39 globins and those of the 20 aminoacyl-tRNA synthetases from E. coli. The distances between the sequences were analyzed by the multivariate analysis techniques. The results show that the distances calculated from the scores of the pairwise alignments are not adequately sensitive. The Z-score from RELATE is not selective enough and too demanding in computer time. Three criteria gave a classification consistent with the known similarities between the sequences in the sets, namely the Z-scores from BESTFIT and FASTA and the multiple dotplot comparison distance index from DOCMA.     

A comparison of variant theories of intact biochemical systems. II. Flux-oriented and metabolic control theories

In the past two decades, several theories, all ultimately based upon the same power-law formalism, have been proposed to relate the behavior of intact biochemical systems to the properties of their underlying determinants. Confusion concerning the relatedness of these alternatives has become acute because the implications of these theories have never been compared. In the preceding paper we characterized a specific system involving enzyme-enzyme interactions for reference in comparing alternative theories. We also analyzed the reference system by using an explicit variant that involves the S-system representation within biochemical systems theory (BST). We now analyze the same reference system according to two other variants within BST. First, we carry out the analysis by using an explicit variant that involves the generalized mass action representation, which includes the flux-oriented theory of Crabtree and Newsholme as a special case. Second, we carry out the analysis by using an implicit variant that involves the generalized mass action representation, which includes the metabolic control theory of Kacser and his colleagues as a special case. The explicit variants are found to provide a more complete characterization of the reference system than the implicit variants. Within each of these variant classes, the S-system representation is shown to be more mathematically tractable and accurate than the generalized mass action representation. The results allow one to make clear distinctions among the variant theories.     

Pitfalls and challenges of estimating population growth rate from empirical data: consequences for allometric scaling relations

The intrinsic rate of increase is a fundamental concept in population ecology, and a variety of problems require that estimates of population growth rate be obtained from empirical data. However, depending on the extent and type of data available (e.g. time series, life tables, life history traits), several alternative empirical estimators of population growth rate are possible. Because these estimators make different assumptions about the nature of age‐dependent mortality and density‐dependence of population dynamics, among other factors, these quantities capture fundamentally different aspects of population growth and are not interchangeable. Nevertheless, they have been routinely commingled in recent ecoinformatic analyses relating to allometry and conservation biology. Here we clarify some of the confusion regarding the empirical estimation of population growth rate and present separate analyses of the frequency distributions and allometric scaling of three alternative, non‐interchangeable measures of population growth. Studies of allometric scaling of population growth rate with body size are additionally sensitive to the statistical line fitting approach used, and we find that different approaches yield different allometric scaling slopes. Across the mix of population growth estimators and line fitting techniques, we find scattered and limited support for the key allometric prediction from the metabolic theory of ecology, namely that log₁₀(population growth rate) should scale as ?0.25 power of log₁₀(body mass). More importantly, we conclude that the question of allometric scaling of population growth rate with body size is highly sensitive to previously unexamined assumptions regarding both the appropriate population growth parameter to be compared and the line fitting approach used to examine the data. Finally, we suggest that the ultimate test of allometric scaling of maximum population growth rates with body size has not been done and, moreover, may require data that are not currently available.     

The evolution of genomic imprinting: theories,predictions and empirical tests

The epigenetic phenomenon of genomic imprinting has motivated the development of numerous theories for its evolutionary origins and genomic distribution. In this review, we examine the three theories that have best withstood theoretical and empirical scrutiny. These are: Haig and colleagues'' kinship theory; Day and Bonduriansky''s sexual antagonism theory; and Wolf and Hager''s maternal–offspring coadaptation theory. These theories have fundamentally different perspectives on the adaptive significance of imprinting. The kinship theory views imprinting as a mechanism to change gene dosage, with imprinting evolving because of the differential effect that gene dosage has on the fitness of matrilineal and patrilineal relatives. The sexual antagonism and maternal–offspring coadaptation theories view genomic imprinting as a mechanism to modify the resemblance of an individual to its two parents, with imprinting evolving to increase the probability of expressing the fitter of the two alleles at a locus. In an effort to stimulate further empirical work on the topic, we carefully detail the logic and assumptions of all three theories, clarify the specific predictions of each and suggest tests to discriminate between these alternative theories for why particular genes are imprinted.The discovery of genomic imprinting, where the expression of an allele depends on its parental origin, motivated a diversity of theories attempting to explain its existence (Spencer and Clark, 2014). Three main theories have withstood scrutiny and are the focus of this review: Haig and colleagues'' kinship theory (Haig and Westoby, 1989; Haig, 2000a, 2004); Day and Bonduriansky''s (2004) sexual antagonism theory (see also Bonduriansky, 2007); and Wolf and Hager''s (2006) maternal–offspring coadaptation theory (see also Wolf and Hager, 2009; Wolf, 2013). Although these theories rest on different logic and fundamental assumptions, they share a critical common feature: some process creates a selective asymmetry between the maternally and paternally inherited allelic copies at a locus that causes selection to favor differential expression of the alleles (typically silencing of one of the copies) (Figures 1, ​,2,2, ​,33).Open in a separate windowFigure 1The kinship theory of genomic imprinting has two prerequisites: first, epigenetic marks that differentiate matrigenes from patrigenes; second, a difference in the relatedness of matrigenes and patrigenes to the social group. (a) The social group in the example depicted is a single litter of offspring, and multiple mating produces a relatedness asymmetry between half-siblings. The relatedness for matrigenes is ½ and the relatedness for patrigenes is 0. (Other sources of relatedness asymmetry are possible—e.g., sex-biased dispersal or high fitness variance in one sex—and social interactions are not limited to the juvenile period only). (b) The kinship theory envisions kin selection acting independently on genes of maternal and paternal origin and solves for the evolutionarily stable gene expression strategy for matrigenes and patrigenes. (c) For genes where the matrigenic allele''s optimum expression level is higher than that of the patrigene''s (e.g., a fetal growth inhibitor), the kinship theory predicts silencing of the patrigenic allele; for genes with the opposite effect (e.g., a fetal growth enhancer), the prediction is for patrigenic expression.Open in a separate windowFigure 2(a, b) The sexual antagonism theory of genomic imprinting starts with sexually antagonistic selection, which produces different allele frequencies, shown as pie charts, for genes of maternal and paternal origin. (c, d) Natural selection favors individuals that are able to express the fitter of the two alleles at a locus, which for males will be the patrigenic allele and for females will be the matrigenic allele. (In addition, the sexual antagonism theory may predict matrigenic or patrigenic expression in both sexes, such that the expressed allele derives from the parental sex that experiences stronger selection pressure. This scenario is not depicted).Open in a separate windowFigure 3(a) The maternal–offspring coadaptation theory of genomic imprinting relies on the correlation of genes in the mother and genes of maternal origin in the offspring (shown in light blue). (b) Fitness of offspring is determined by the interaction (shown in dark purple) between the phenotypes of mothers and offspring. (c) Imprinted silencing of the patrigenic allele can be favored for either of two reasons, depending on the genetic architecture of the interacting phenotypes. First, when a single gene governs the interaction and phenotypic matching between mothers and their offspring produces high fitness, then silencing of the patrigenic allele is beneficial to offspring because it raises the probability of producing a match. Second, if different loci are involved in the phenotypic interaction, past correlational selection will have produced a covariance between them, generating haplotypes with combinations of alleles that interact well together. (N.B. This multi-locus interaction is not depicted in the figure.) The offspring is more likely to inherit from its mother an allele that interacts well with the alleles in the mother''s genotype. This also favors the imprinted silencing of the patrigenic allele because it raises the probability that the offspring expresses an allele that makes for a good interaction with the maternal phenotype.Here we provide an overview of the fundamental logic and critical assumptions of these models. We then derive predictions that can be used to distinguish between theories. In doing so, we also highlight ambiguities in and overlap between the predictions they make, with a goal of motivating further research. In addition, we suggest some areas for future work that will test some of these predictions.     

How to derive biological information from the value of the normalization constant in allometric equations

Allometric equations are widely used in many branches of biological science. The potential information content of the normalization constant b in allometric equations of the form Y = bX(a) has, however, remained largely neglected. To demonstrate the potential for utilizing this information, I generated a large number of artificial datasets that resembled those that are frequently encountered in biological studies, i.e., relatively small samples including measurement error or uncontrolled variation. The value of X was allowed to vary randomly within the limits describing different data ranges, and a was set to a fixed theoretical value. The constant b was set to a range of values describing the effect of a continuous environmental variable. In addition, a normally distributed random error was added to the values of both X and Y. Two different approaches were then used to model the data. The traditional approach estimated both a and b using a regression model, whereas an alternative approach set the exponent a at its theoretical value and only estimated the value of b. Both approaches produced virtually the same model fit with less than 0.3% difference in the coefficient of determination. Only the alternative approach was able to precisely reproduce the effect of the environmental variable, which was largely lost among noise variation when using the traditional approach. The results show how the value of b can be used as a source of valuable biological information if an appropriate regression model is selected.     

岷江上游干旱河谷引种番麻的生态适应性及生物量预测模型

以岷江上游干旱河谷地区引种的番麻为研究对象,通过对不同海拔番麻的株高、冠幅、单株叶片数以及萌芽数等生长指标的调查研究结果,了解其在干旱河谷区的生长分布上限,为该地区与类似地区引种该品种相关物种提供理论依据;同时,利用株高等简单生长指标与番麻生物量的关系进行拟合,建立预测方程.通过高度、冠幅、单株叶片数、萌芽数(株/100m2)等生长指标比较表明,番麻的最适生长区为海拔1400～1500m.在干旱河谷阳坡的生长上限为海拔1800m,往上仅能成活,不能自身繁殖.根据番麻的株高、冠幅、叶片数等简单生长指标与生物量呈显著相关(P＜0.01),分别建立了相应的回归模型,其中地上生物量和单株生物量的最优回归模型R2值均在0.90以上,地下生物量的最优回归模型R2值也在0.75以上.     

Biological populations obeying difference equations: the effects of stochastic perturbation

We consider the effects of stochastic perturbation in various components of a finite difference model arising in population biology. In particular, we examine how fluctuation in the net reproductive rate can effect the population dynamics of the system. Computer simulation and some elementary analyses bear out the result that, in the mean, the stochastic dynamics will behave like the deterministic dynamics. This study also answers a currently unanswered conjecture published by the first author in 1977.     

An allometric comparison of the mitochondria of mammalian and reptilian tissues: The implications for the evolution of endothermy

Summary The effects of body size and phylogeny on metabolic capacities were examined by comparing the mitochondrial capacities of 6 mammalian and 4 reptilian species representing 100-fold body weight ranges. The mammals examined included 3 eutherian, 2 marsupial and a monotreme species and the reptiles 2 saurian, 1 crocodilian and 1 testudine species. The tissues examined were liver, kidney, brain, heart, lung and skeletal muscle. Allometric equations were derived for tissue weights, mitochondrial volume densities, internal mitochondrial membrane surface area densities, tissue mitochondrial membrane surface areas both per gram and per total tissue and summated tissue mitochondrial membrane surface areas. For the mammals and reptiles studied a 100% increase in body size resulted in average increases of 68% in internal organ size and 107% in skeletal muscle mass. Similarly, total organ mitochondrial membrane surface areas increase in mammals and reptiles by an average 54% and for skeletal muscle by an average 96%. These values are similar to increases in standard (54 and 71%) and maximum (73 and 77%) organismal metabolism values found by other authors for mammals and reptiles respectively. Although the allometric exponents (or rates of change with increasing body size) of the mitochondrial parameters in mammals and reptiles are statistically the same, in general the total amount of mitochondrial membrane surface area in the mammalian tissues are four times greater than found in the reptilian tissues. These differences were not the result of any single ‘quantum’ factor but are the result of the mammals having relatively larger tissues with a greater proportion of their volume occupied by mitochondria and to a lesser extent increases in the internal mitochondrial membrane surface area densities. Mitochondrial volume density from this present study would appear to be the major factor involved in changing weight specific metabolism of tissues both as a result of changes in body size and in the evolution of endothermy in mammals from reptiles.     

On the similarity of sets of permutations and its applications to genome comparison.

The comparison of genomes with the same gene content relies on our ability to compare permutations, either by measuring how much they differ, or by measuring how much they are alike. With the notable exception of the breakpoint distance, which is based on the concept of conserved adjacencies, measures of distance do not generalize easily to sets of more than two permutations. In this paper, we present a basic unifying notion, conserved intervals, as a powerful generalization of adjacencies, and as a key feature of genome rearrangement theories. We also show that sets of conserved intervals have elegant nesting and chaining properties that allow the development of compact graphic representations, and linear time algorithms to manipulate them.     

SIVcpz from a naturally infected Cameroonian chimpanzee: Biological and genetic comparison with HIV-1 N

Thus far, simian immunodeficiency virus from chimpanzees (SIVcpz) genomes have been characterized as Pan troglodytes troglodytes and show a strong relation with human immunodeficiency virus (HIV)-1 N in their env genes. We fully characterized another SIVcpz from P. t. troglodytes . This chimpanzee (Cam5) was, as was also the host of SIVcpz-cam3, wild born in Cameroon, a region where all three groups of HIV-1 (M, N and O) co-occur. In contrast to other SIVcpz, SIVcpz-cam5 was isolated immediately after the rescue of the animal. Our data demonstrate that SIVcpz-cam5, like SIVcpz-cam3, grows easily on human peripheral blood mononuclear cells (PBMCs) and uses CCR5 as a co-receptor similar to HIV-1 N YBF30. Phylogenetic analysis based on the entire env gene shows that SIVcpz-cam5 falls into the same unique subcluster as HIV-1 N YBF30, SIVcpz-cam3 and SIVcpz-US. A phylogenetic relationship was also found with the vif gene of HIV-1 N. This study provides proof that HIV-1 N related viruses circulate in wild P. t. troglodytes .