THE MICRO AND MACRO IN BODY SIZE EVOLUTION

The diversity of body sizes of organisms has traditionally been explained in terms of microevolutionary processes: natural selection owing to differential fitness of individual organisms, or to macroevolutionary processes: species selection owing to the differential proliferation of phylogenetic lineages. Data for terrestrial mammals and birds indicate that even on a logarithmic scale frequency distributions of body mass among species are significantly skewed towards larger sizes. We used simulation models to evaluate the extent to which macro- and microevolutionary processes are sufficient to explain these distributions. Simulations of a purely cladogenetic process with no bias in extinction or speciation rates for different body sizes did not produce skewed log body mass distributions. Simulations that included size-biased extinction rates, especially those that incorporated anagenetic size change within species between speciation and extinction events, regularly produced skewed distributions. We conclude that although cladogenetic processes probably play a significant role in body size evolution, there must also be a significant anagenetic component. The regular variation in the form of mammalian body size distributions among different-sized islands and continents suggests that environmental conditions, operating through both macro- and microevolutionary processes, determine to a large extent the diversification of body sizes within faunas. Macroevolution is not decoupled from microevolution.     

麻城黄山松天然林直径分布

为研究黄山松天然次生林直径分布特征,以麻城市黄山松天然次生林为研究对象,采用标准样地调查,计算林分直径的偏度、峰度,林分直径分布的Shannon-Weiner和Simpson指数,运用负指数分布、normal分布、lognormal分布、logistic分布和Weibull分布等5种概率密度函数对黄山松天然次生林林分直...     

Preference patterns for skewed gambles in rhesus monkeys

While standard models of risky choice account for the first and second statistical moments of reward outcome distributions (mean and variance, respectively), they often ignore the third moment, skewness. Determining a decision-maker''s attitude about skewness is useful because it can help constrain process models of the mental steps involved in risky choice. We measured three rhesus monkeys’ preferences for gambles whose outcome distributions had almost identical means and variances but differed in skewness. We tested five distributions of skewness: strong negative, weak negative, normal, weak positive and strong positive. Monkeys preferred positively skewed gambles to negatively skewed ones and preferred strongly skewed and normal (i.e. unskewed) gambles to weakly skewed ones. This pattern of preferences cannot be explained solely by monotonic deformations of the utility curve or any other popular single account, but can be accounted for by multiple interacting factors.     

Stochastic Models of Soil Denitrification

Soil denitrification is a highly variable process that appears to be lognormally distributed. This variability is manifested by large sample coefficients of variation for replicate estimates of soil core denitrification rates. Deterministic models for soil denitrification have been proposed in the past, but none of these models predicts the approximate lognormality exhibited by natural denitrification rate estimates. In this study, probabilistic (stochastic) models were developed to understand how positively skewed distributions for field denitrification rate estimates result from the combined influences of variables known to affect denitrification. Three stochastic models were developed to describe the distribution of measured soil core denitrification rates. The driving variables used for all the models were denitrification enzyme activity and CO₂ production rates. The three models were distinguished by the functional relationships combining these driving variables. The functional relationships used were (i) a second-order model (model 1), (ii) a second-order model with a threshold (model 2), and (iii) a second-order saturation model (model 3). The parameters of the models were estimated by using 12 separate data sets (24 replicates per set), and their abilities to predict denitrification rate distributions were evaluated by using three additional independent data sets of 180 replicates each. Model 2 was the best because it produced distributions of denitrification rate which were not significantly different (P > 0.1) from distributions of measured denitrification rates. The generality of this model is unknown, but it accurately predicted the mean denitrification rates and accounted for the stochastic nature of this variable at the site studied. The approach used in this study may be applicable to other areas of ecological research in which accounting for the high spatial variability of microbiological processes is of interest.     

Bayesian QTL mapping using skewed Student-t distributions

In most QTL mapping studies, phenotypes are assumed to follow normal distributions. Deviations from this assumption may lead to detection of false positive QTL. To improve the robustness of Bayesian QTL mapping methods, the normal distribution for residuals is replaced with a skewed Student-t distribution. The latter distribution is able to account for both heavy tails and skewness, and both components are each controlled by a single parameter. The Bayesian QTL mapping method using a skewed Student-t distribution is evaluated with simulated data sets under five different scenarios of residual error distributions and QTL effects.     

Diversity and Evolution of Body Size in Fishes

The diversity of body sizes observed among species of a clade is a combined result of microevolutionary processes (i.e. natural selection and genetic drift) that cause size changes within phylogenetic lineages, and macroevolutionary processes (i.e. speciation and extinction) that affect net rates of diversification among lineages. Here we assess trends of size diversity and evolution in fishes (non-tetrapod craniates), employing paleontological, macroecological, and phylogenetic information. Fishes are well suited to studies of size diversity and evolution, as they are highly diverse, representing more than 50% of all living vertebrate species, and many fish taxa are well represented in the fossil record from throughout the Phanerozoic. Further, the frequency distributions of sizes among fish lineages resemble those of most other animal taxa, in being right-skewed, even on a log scale. Using an approach that measures rates of size evolution (in darwins) within a formal phylogenetic framework, we interpret the shape of size distributions as a balance between the competing forces of diversification, pushing taxa away from ancestral values, and of conservation, drawing taxa closer to a central tendency. Within this context we show how non-directional mechanisms of evolution (i.e. passive diffusion processes) can produce an hitherto unperceived bias to larger size, when size is measured on the conventional log scale. These results demonstrate how the interpretation of macroecological datasets can be enriched from an historical perspective, and document the ways in which macroevolutionary and microevolutionary processes may be decoupled in the production of size diversity.     

Alternatives to the Wright-Fisher model: The robustness of mitochondrial Eve dating

Methods of calculating the distributions of the time to coalescence depend on the underlying model of population demography. In particular, the models assuming deterministic evolution of population size may not be applicable to populations evolving stochastically. Therefore the study of coalescence models involving stochastic demography is important for applications. One interesting approach which includes stochasticity is the O’Connell limit theory of genealogy in branching processes. Our paper explores how many generations are needed for the limiting distributions of O’Connell to become adequate approximations of exact distributions. We perform extensive simulations of slightly supercritical branching processes and compare the results to the O’Connell limits. Coalescent computations under the Wright-Fisher model are compared with limiting O’Connell results and with full genealogy-based predictions. These results are used to estimate the age of the so-called mitochondrial Eve, i.e., the root of the mitochondrial polymorphisms of the modern humans based on the DNA from humans and Neanderthal fossils.     

Normalization of high dimensional genomics data where the distribution of the altered variables is skewed

Genome-wide analysis of gene expression or protein binding patterns using different array or sequencing based technologies is now routinely performed to compare different populations, such as treatment and reference groups. It is often necessary to normalize the data obtained to remove technical variation introduced in the course of conducting experimental work, but standard normalization techniques are not capable of eliminating technical bias in cases where the distribution of the truly altered variables is skewed, i.e. when a large fraction of the variables are either positively or negatively affected by the treatment. However, several experiments are likely to generate such skewed distributions, including ChIP-chip experiments for the study of chromatin, gene expression experiments for the study of apoptosis, and SNP-studies of copy number variation in normal and tumour tissues. A preliminary study using spike-in array data established that the capacity of an experiment to identify altered variables and generate unbiased estimates of the fold change decreases as the fraction of altered variables and the skewness increases. We propose the following work-flow for analyzing high-dimensional experiments with regions of altered variables: (1) Pre-process raw data using one of the standard normalization techniques. (2) Investigate if the distribution of the altered variables is skewed. (3) If the distribution is not believed to be skewed, no additional normalization is needed. Otherwise, re-normalize the data using a novel HMM-assisted normalization procedure. (4) Perform downstream analysis. Here, ChIP-chip data and simulated data were used to evaluate the performance of the work-flow. It was found that skewed distributions can be detected by using the novel DSE-test (Detection of Skewed Experiments). Furthermore, applying the HMM-assisted normalization to experiments where the distribution of the truly altered variables is skewed results in considerably higher sensitivity and lower bias than can be attained using standard and invariant normalization methods.     

暴露评估中样本采集量的模拟研究

选择暴露评估常用的4种右偏分布,就评估关注的高百分位数估计与采样量的关系进行模拟研究;又以对数正态分布为代表,从分布形态和变异的角度做了细致探讨.结果表明：（1）对右偏分布来说,百分位数越高,准确估计所需的采样容量就越大.而其估计值都随采样量的增大而趋近理论值,精度也随之增大,采样量500时,本文考察的4种右偏分布除P99.9外的其它百分位数都得到了较为准确的估计.（2）估计相同的百分位数,对数正态分布所需的样本容量要比正态分布大得多;而其分布变异越大,所需的采样量也就越大.本研究可为暴露评估中数据的采样调查提供借鉴.     

Steady-state and limit cycle activity of mass of neurons forming simple feedback loops (II): Distributed parameter model

It is shown that there exist spatial distributions of nonzero steady state mean pulse rates of the periglomerular and mitraltufted neuron populations and of nonzero EEG in the mammalian olfactory bulb. Such distributions are stable, i.e., if there are small perturbations, the population state variables return to the equilibrium states. It is predicted that the sensory and centrifugal inputs to the neuron populations in the bulb determine existence of such active states.This research was supported by a grant from the National Institute of Mental Health, MH 06686 and by a Fellowship from the National Institute of Neurological Diseases and Strokes, 5F 102 NS 544 56-02.     

Competition and species diversity: removal of dominant species increases diversity in Costa Rican butterfly communities

Biological communities are usually dominated by a few species and show characteristically skewed species abundance distributions. Although niche apportionment and resource competition are sometimes implicated in such patterns, few experimental studies have shown direct links between resource limitation, competition with dominant species and their impacts on the overall diversity and composition of large natural communities. Here I report the results of an experiment in which I first studied species diversity and composition in two Costa Rican nectar-feeding butterfly communities numerically dominated by two species of Anartia butterflies. Then I removed Anartia from these communities to study changes in resource availability, species abundance relationships, community diversity and composition as an outcome of the removal of the dominant competitors. In the face of competition with Anartia , nectar was scarce, species abundance distributions were highly skewed, and species diversity was low in both communities. Within two weeks after the removal of Anartia , there were parallel changes in both communities: competition for nectar reduced and the nectar quantity increased substantially, which facilitated increase in community diversity and resulted in significantly less skewed species abundance distributions. Higher nectar quantity also enabled the distribution of body size and proboscis length of constituent species in the communities to expand at both ends. This study thus experimentally showed that resource competition with the dominant species was excluding many species from the communities, lowering their diversity and skewing relative species abundance relationships. These findings are of fundamental importance for competition theory and community ecology because they indicate ways in which diverse communities may be affected by and recover from competition with dominant species.     

Extending eco-evolutionary theory with oligomorphic dynamics

Understanding the interplay between ecological processes and the evolutionary dynamics of quantitative traits in natural systems remains a major challenge. Two main theoretical frameworks are used to address this question, adaptive dynamics and quantitative genetics, both of which have strengths and limitations and are often used by distinct research communities to address different questions. In order to make progress, new theoretical developments are needed that integrate these approaches and strengthen the link to empirical data. Here, we discuss a novel theoretical framework that bridges the gap between quantitative genetics and adaptive dynamics approaches. ‘Oligomorphic dynamics’ can be used to analyse eco-evolutionary dynamics across different time scales and extends quantitative genetics theory to account for multimodal trait distributions, the dynamical nature of genetic variance, the potential for disruptive selection due to ecological feedbacks, and the non-normal or skewed trait distributions encountered in nature. Oligomorphic dynamics explicitly takes into account the effect of environmental feedback, such as frequency- and density-dependent selection, on the dynamics of multi-modal trait distributions and we argue it has the potential to facilitate a much tighter integration between eco-evolutionary theory and empirical data.     

Selection on skewed characters and the paradox of stasis

Observed phenotypic responses to selection in the wild often differ from predictions based on measurements of selection and genetic variance. An overlooked hypothesis to explain this paradox of stasis is that a skewed phenotypic distribution affects natural selection and evolution. We show through mathematical modeling that, when a trait selected for an optimum phenotype has a skewed distribution, directional selection is detected even at evolutionary equilibrium, where it causes no change in the mean phenotype. When environmental effects are skewed, Lande and Arnold's (1983) directional gradient is in the direction opposite to the skew. In contrast, skewed breeding values can displace the mean phenotype from the optimum, causing directional selection in the direction of the skew. These effects can be partitioned out using alternative selection estimates based on average derivatives of individual relative fitness, or additive genetic covariances between relative fitness and trait (Robertson–Price identity). We assess the validity of these predictions using simulations of selection estimation under moderate sample sizes. Ecologically relevant traits may commonly have skewed distributions, as we here exemplify with avian laying date — repeatedly described as more evolutionarily stable than expected — so this skewness should be accounted for when investigating evolutionary dynamics in the wild.     

The Curious Anomaly of Skewed Judgment Distributions and Systematic Error in the Wisdom of Crowds

Judgment distributions are often skewed and we know little about why. This paper explains the phenomenon of skewed judgment distributions by introducing the augmented quincunx (AQ) model of sequential and probabilistic cue categorization by neurons of judges. In the process of developing inferences about true values, when neurons categorize cues better than chance, and when the particular true value is extreme compared to what is typical and anchored upon, then populations of judges form skewed judgment distributions with high probability. Moreover, the collective error made by these people can be inferred from how skewed their judgment distributions are, and in what direction they tilt. This implies not just that judgment distributions are shaped by cues, but that judgment distributions are cues themselves for the wisdom of crowds. The AQ model also predicts that judgment variance correlates positively with collective error, thereby challenging what is commonly believed about how diversity and collective intelligence relate. Data from 3053 judgment surveys about US macroeconomic variables obtained from the Federal Reserve Bank of Philadelphia and the Wall Street Journal provide strong support, and implications are discussed with reference to three central ideas on collective intelligence, these being Galton''s conjecture on the distribution of judgments, Muth''s rational expectations hypothesis, and Page''s diversity prediction theorem.     

A self-similarity model for the occupancy frequency distribution

The shapes of interspecific range-size distributions at scales finer than the geographic range are highly variable. However, no numerical model has been developed as a basis for understanding this variation. Using self-similarity conditions, we present an occupancy probability transition (OPT) model to investigate the effect of sampling scale (i.e. sample grain) and species saturation (strongly positively correlated with the fractal dimension) on the shape of occupancy frequency distributions (fine scale expression of range-size distributions). In accordance with empirical observations, the model showed that core-modes are likely to be rare in occupancy frequency distributions. The modal occupancy shifted from core to satellite with an increase in sample grain (from coarse scale to fine scale) at a linear rate after log-transformation of occupancy. Saturation coefficients above a particular threshold generated multimodality. Bimodal distributions arose from a combination of different occupancy probability distributions (OPDs), with species-specific saturation coefficients generating occupancy frequency distributions of the shape commonly observed empirically, i.e. bimodal with a dominant satellite mode. This is a consequence of the statistical properties of the OPD, and is also largely insensitive to species richness. The OPT model thus provides a null model for the shape of occupancy frequency distributions. Furthermore, it demonstrates that the sample grain of a study, sampling adequacy (based on a linear sampling assumption) and the distribution of species saturation coefficients in a community are together largely able to explain the patterns observed in empirical occupancy frequency distributions.     

Species range size distributions for some marine taxa in the Atlantic Ocean. Effect of latitude and depth

The range size distributions of 6643 species in ten different fish and invertebrate taxa dwelling in pelagic (latitudinal range sizes) and benthic (latitudinal and depth range sizes) habitats on both sides of the Atlantic Ocean (80°N−70°S) were studied. The objectives were to analyse: (1) the range size distribution patterns for the various taxa and whether they have right/left skewed or lognormal distributions; (2) the geographical species distributions, to ascertain whether the distribution ranges change with latitude (Rapoport's rule); and (3) the relationship between the depth ranges of benthic species and their maximum depth of occurrence and how depth range size distributions change with latitude. The pelagic taxa exhibited larger range sizes than did the benthic taxa, continental slope/rise species excepted. On the other hand, the boundaries between geographical provinces for both benthic taxa and pelagic taxa tended to occur in association with major oceanographic processes. The shape of the latitudinal range frequency distributions (LRFDs) of the pelagic organisms were distinctly left‐skewed, and the LRFDs for most taxa were significantly different from lognormal. There was no common pattern for the distributions of the benthic organisms, which were lognormal in Cephalopoda, Stomatopoda, and Crustacea Decapoda and tended to be left‐skewed and significantly different from lognormal in Pisces. The applicability of Rapoport's rule was not clearly inferable from the results, and the rule appears to be conditioned by the location of biogeographical boundaries and the endemism rate in the different biogeographical provinces. A clear increase in depth range size with maximum depth range was observable for benthic species, confirming previous studies. Species’ depth range distributions displayed a discernible latitudinal pattern, right‐skewed at high latitudes and left‐skewed at low latitudes. The location of biogeographical boundaries, and endemism rate by biogeographical province were considered to be the factors most useful in explaining species’ distribution patterns and their conformity or nonconformity to Rapoport's rule. © 2003 The Linnean Society of London, Biological Journal of the Linnean Society, 2003, 80 , 437–455.     

Invasion of a naticid predator and associated changes in death assemblages of bivalve prey in northern Japan: implications for palaeoecological studies

The recent invasion of a naticid predator (Laguncula pulchella) and associated changes in the death assemblages of bivalve prey (Ruditapes philippinarum) provide a baseline for interpreting predator–prey interactions in the fossil record. This article presents quantitative data on size‐frequency distributions (SFDs) of living and death assemblages, prey size selectivity and drillhole site selectivity from the Tona Coast, northern Japan. Before the appearance of the predator, the SFD of the death assemblage exhibited a right‐skewed platykurtic distribution, and there were very few predatory drillholes. Once the predator appeared, frequencies of predatory drillholes increased, particularly in the smallest size class (2–10 mm shell length). Furthermore, juvenile peaks in the SFDs of death assemblages sharpened, and thus, SFDs exhibited strongly right‐skewed leptokurtic distributions. These changes suggest that intense naticid predation precluded juvenile clams from growing to adulthood, and thus, many dead shells of juvenile clams were introduced into the sediment. The changes in SFDs may also indicate intensification of predation pressure in the fossil record. No temporal shifts in prey size selectivity and drillhole site selectivity were noted, despite substantial changes in the demographics of Ruditapes philippinarum. This suggests that lack of specific size classes of preferred prey species is unlikely to be a primary factor accounting for size mismatches between predator and prey, because, in such situations, naticid predators probably attack other prey species. Therefore, such a factor is unlikely to primarily explain the less stereotypical predatory behaviour (i.e. low prey size selectivity and low drillhole site selectivity), which has been frequently recognized in fossil assemblages. Such less stereotypical predatory behaviour in fossil assemblages is likely to be explained by other factors, such as the existence of multiple predator taxa and lack of specific size classes of all available prey.