Species-range size distributions in Britain

The detailed forms of species-range size distributions in Britain are determined and contrasted for ten taxonomic assemblages (liverworts, vascular plants, molluscs [aquatic and terrestrial], dragonflies, macro-moths. butterflies, birds [breeding and wintering], mammals). All are strongly right-skewed when range sizes are untransformed. A logarithmic transformation fails to normalise the distribution for all but one group, and the distributions for several groups are not readily normalised at all. Taxa with larger median range sizes have species-range size distributions that are less strongly right-skewed. The median observed range sizes of species in each of the taxonomic groups fall, in terms of decreasing range size, in the sequence wintering birds < breeding birds < mammals < butterflies < terrestrial molluscs < dragonflies < aquatic molluscs < vascular plants < moths < liverworts. Despite the difficulties in deriving a simple and sensible mechanistic model for range size distributions, this is likely to be the most important next step towards understanding their forms.     

Mortality rates from size distributions

Summary A population model explicitly describing the dynamics of an arbitrary population size distribution is presented. One consequence of the model is an equation for the exact shape of the size distribution of a stationary or steady-state population. The shape is expressed as a function of sizespecific mortality and growth rates. From the equation, various mortality estimation formulas can be derived, two of which are discussed in detail. One of the methods permits estimation of size-specific mortality rates without the assumption of a theoretical growth model.Supported by a National Research Council Research Associateship     

Species size distributions in Arctic benthic communities

In most subtidal soft-sediment faunal assemblages there is a trough in the species size distribution separating the macrofauna and meiofauna. To examine the hypothesis that this may be maintained by the avoidance of competition between macrofaunal adults and settling larvae, samples were taken from around Svalbard, an area where most macrofaunal species have either lecithotrophic or direct development. At three contrasting sites, bimodality of the species size spectrum was conserved. However, it is proposed that the adult-larval interaction hypothesis should not be rejected as low endemism in the fauna of the study area suggests its species size spectrum probably reflects evolutionary processes outside rather than within the Arctic. Received: 13 May 1996/Accepted: 26 July 1996     

Species size distributions in marine benthic communities

Summary Species body size distributions from eight temperate benthic communities show a highly conservative pattern with two separate lognormal distributions, corresponding to the traditional categories of meiofauna and macrofauna. The meiofaunal mode occurs at a dry body weight of 0.64 g and the macrofaunal mode at 3.2 mg, with a trough between them at 45 g. It is suggested that there is a particular body size at which meiofaunal life-history and feeding traits can be optimised, and another for macrofaunal traits. As size departs in either direction (larger or smaller) from these optima, fewer species of the same size are able to co-exist. The split occurs at 45 g because many life history and feeding characteristics switch more or less abruptly at about this body size, compromise traits being either non-viable or disadvantageous. Meiofauna and macrofauna therefore comprise two separate evolutionary units each with an internally coherent set of biological characteristics.The expression of this conservative pattern is modified by water depth: the proportion of macrofauna species increases from intertidal situations to deeper water, and it is suggested that mechanisms of resource partitioning and diversity maintainence in the meiofauna and macrofauna are affected differentially by sediment disturbance. Salinity does not affect this proportionality, and so does not differentially affect mechanisms for maintaining species diversity in any particular size category of animals. Meiofauna species size distributions may be modified in sandy sediments because of physical impositions on interstitial or burrowing lifestyles.Brief discussion of some implications of these observations includes speculations on the larval ecology of macrofauna, on gigantism in Antarctic invertebrates, and on the benthic Sheldon spectrum.     

Reducing liposome size with ultrasound: bimodal size distributions

Sonication is a simple method for reducing the size of liposomes. We report the size distributions of liposomes as a function of sonication time using three different techniques. Liposomes, mildly sonicated for just 30 sec, had bimodal distributions when surface-weighted with modes at about 140 and 750 nm. With extended sonication, the size distribution remains bimodal but the average diameter of each population decreases and the smaller population becomes more numerous. Independent measurements of liposome size using Dynamic Light Scattering (DLS), transmission electron microscopy (TEM), and the nystatin/ergosterol fusion assay all gave consistent results. The bimodal distribution (even when number-weighted) differs from the Weibull distribution commonly observed for liposomes sonicated at high powers over long periods of time and suggests that a different mechanism may be involved in mild sonication. The observations are consistent with the following mechanism for decreasing liposome size. During ultrasonic irradiation, cavitation, caused by oscillating microbubbles, produces shear fields. Large liposomes that enter these fields form long tube-like appendages that can pinch-off into smaller liposomes. This proposed mechanism is consistent with colloidal theory and the observed behavior of liposomes in shear fields.     

Tree size distributions in an old-growth temperate forest

Despite the wide variation in the structural characteristics in natural forests, tree size distribution show fundamental similarities that suggest general underlying principles. The metabolic ecology theory predicts the number of individual scales as the −2 power of tree diameter. The demographic equilibrium theory predicts tree size distribution starting from the relationship of size distributions with growth and mortality at demographic equilibrium. Several analytic predictions for tree size distributions are derived from the demographic equilibrium theory, based on different growth and mortality functions. In addition, some purely phenomenological functions, such as polynomial function, have been used to describe the tree size distributions. In this paper, we use the metabolic ecology theory, the demographic equilibrium theory and the polynomial function to predict the tree size distribution for both the whole community and each species in an old-growth temperate forest in northeastern China. The results show that metabolic ecology theory predictions for the scaling of tree abundance with diameter were unequivocally rejected in the studied forest. Although these predictions of demographic theory are the best models for most of the species in the temperate forest, the best models for some species ( Tilia amurensis , Quercus mongolica and Fraxinus mandshurica ) are compound curves (i.e. rotated sigmoid curves), best predicted by the polynomial function. Hence, the size distributions of natural forests were unlikely to be invariant and the predictive ability of general models was limited. As a result, developing a more sophisticated theory to predict tree size distributions remains a complex, yet tantalizing, challenge.     

Physiological constraints on body size distributions in Crocodyliformes

At least 26 species of crocodylian populate the globe today, but this richness represents a minute fraction of the diversity and disparity of Crocodyliformes. Fossil forms are far more varied, spanning from erect, fully terrestrial species to flippered, fully marine species. To quantify the influence of a marine habitat on the directionality, rate, and variance of evolution of body size in Crocodyliformes and thereby identify underlying selective pressures, we compiled a database of body sizes for 264 fossil and modern species of crocodyliform covering terrestrial, semi-aquatic, and marine habitats. We find increases in body size coupled with increases in strength of selection and decreases in variance following invasions of marine habitats but not of semiaquatic habitats. A model combining constraints from thermoregulation and lung capacity provides a physiological explanation for the larger minimum and average sizes of marine species. It appears that constraints on maximum size are shared across Crocodyliformes, perhaps through factors such as the allometric scaling of feeding rate versus basal metabolism with body size. These findings suggest that broad-scale patterns of body size evolution and the shapes of body size distributions within higher taxa are often determined more by physiological constraints than by ecological interactions or environmental fluctuations.     

Coalescent time distributions in trees of arbitrary size

The relationship between speciation times and the corresponding times of gene divergence is of interest in phylogenetic inference as a means of understanding the past evolutionary dynamics of populations and of estimating the timing of speciation events. It has long been recognized that gene divergence times might substantially pre-date speciation events. Although the distribution of the difference between these has previously been studied for the case of two populations, this distribution has not been explicitly computed for larger species phylogenies. Here we derive a simple method for computing this distribution for trees of arbitrary size. A two-stage procedure is proposed which (i) considers the probability distribution of the time from the speciation event at the root of the species tree to the gene coalescent time conditionally on the number of gene lineages available at the root; and (ii) calculates the probability mass function for the number of gene lineages at the root. This two-stage approach dramatically simplifies numerical analysis, because in the first step the conditional distribution does not depend on an underlying species tree, while in the second step the pattern of gene coalescence prior to the species tree root is irrelevant. In addition, the algorithm provides intuition concerning the properties of the distribution with respect to the various features of the underlying species tree. The methodology is complemented by developing probabilistic formulae and software, written in R. The method and software are tested on five-taxon species trees with varying levels of symmetry. The examples demonstrate that more symmetric species trees tend to have larger mean coalescent times and are more likely to have a unimodal gamma-like distribution with a long right tail, while asymmetric trees tend to have smaller mean coalescent times with an exponential-like distribution. In addition, species trees with longer branches generally have shorter mean coalescent times, with branches closest to the root of the tree being most influential.     

Measurement of size distributions of bacterial cells

Harvey, R. J. (University of California, Davis), and Allen G. Marr. Measurement of size distributions of bacterial cells. J. Bacteriol. 92:805-811. 1966.-Apparatus for the automatic determination of the volume distribution of particles by measurement of the amplitude of pulses generated in a Coulter transducer is described. Distributions of volume estimated by direct measurement of pulse amplitude are distorted by coincidence. Differentiation and integration of the pulses followed by automatic pulse-height analysis permit precise measurement of volume of latex spheres and of bacteria over a range of at least 0.25 to 20 mu(3). The apparatus is also capable of accurate determination of particle concentration over a wide range. Other advantages are the speed of both measurement and data processing.     

Domain size distributions can predict domain boundaries

MOTIVATION: The sizes of protein domains observed in the 3D-structure database follow a surprisingly narrow distribution. Structural domains are furthermore formed from a single-chain continuous segment in over 80% of instances. These observations imply that some choices of domain boundaries on an otherwise uncharacterized sequence are more likely than others, based solely on the size and segment number of predicted domains. This property might be used to guess the locations of protein domain boundaries. RESULTS: To test this possibility we enumerate putative domain boundaries and calculate their relative likelihood under a probability model that considers only the size and segment number of predicted domains. We ask, in a cross-validated test using sequences with known 3D structure, whether the most likely guesses agree with the observed domain structure. We find that domain boundary predictions are surprisingly successful for sequences up to 400 residues long and that guessing domain boundaries in this way can improve the sensitivity of threading analysis.     

Intraspecific body size frequency distributions of insects

Although interspecific body size frequency distributions are well documented for many taxa, including the insects, intraspecific body size frequency distributions (IaBSFDs) are more poorly known, and their variation among mass-based and linear estimates of size has not been widely explored. Here we provide IaBSFDs for 16 species of insects based on both mass and linear estimates and large sample sizes (n ≥ 100). In addition, we review the published IaBSFDs for insects, though doing so is complicated by their under-emphasis in the literature. The form of IaBSFDs can differ substantially between mass-based and linear measures. Nonetheless, in non-social insects they tend to be normally distributed (18 of 27 species) or in fewer instances positively skewed. Negatively skewed distributions are infrequently reported and log transformation readily removes the positive skew. Sexual size dimorphism does not generally cause bimodality in IaBSFDs. The available information on IaBSFDs in the social insects suggests that these distributions are usually positively skewed or bimodal (24 of 30 species). However, only c. 15% of ant genera are polymorphic, suggesting that normal distributions are probably more common, but less frequently investigated. Although only 57 species, representing seven of the 29 orders of insects, have been considered here, it appears that whilst IaBSFDs are usually normal, other distribution shapes can be found in several species, though most notably among the social insects. By contrast, the interspecific body size frequency distribution is typically right-skewed in insects and in most other taxa.     

A mathematical theory of size distributions in tissue culture

A model for growth of a tissue culture consisting of cell clumps is given. A set of equations for following the size distribution of clumps is used to determine total biomass accumulation. Existence and uniqueness of a solution to the equations is proved, and estimates of the biomass growth is given in a number of situations.     

Simulation study of territory size distributions in subterranean termites

In this study, on the basis of empirical data, we have simulated the foraging tunnel patterns of two subterranean termites, Coptotermes formosanus Shiraki and Reticulitermes flavipes (Kollar), using a two-dimensional model. We have defined a territory as a convex polygon containing a tunnel pattern and explored the effects of competition among termite territory colonies on the territory size distribution in the steady state that was attained after a sufficient simulation time. In the model, territorial competition was characterized by a blocking probability P_block that quantitatively describes the ease with which a tunnel stops its advancement when it meets another tunnel; higher P_block values imply easier termination. In the beginning of the simulation run, N=10, 20,…,100 territory seeds, representing the founding pair, were randomly distributed on a square area. When the territory density was less (N=20), the differences in the territory size distributions for different P_block values were small because the territories had sufficient space to grow without strong competitions. Further, when the territory density was higher (N>20), the territory sizes increased in accordance with the combinational effect of P_block and N. In order to understand these effects better, we introduced an interference coefficient γ. We mathematically derived γ as a function of P_block and N: γ(N,P_block)=a(N)P_block/(P_block+b(N)). a(N) and b(N) are functions of N/(N+c) and d/(N+c), respectively, and c and d are constants characterizing territorial competition. The γ function is applicable to characterize the territoriality of various species and increases with both the P_block values and N; higher γ values imply higher limitations of the network growth. We used the γ function, fitted the simulation results, and determined the c and d values. In addition, we have briefly discussed the predictability of the present model by comparing it with our previous lattice model that had been used to explain the territory size distributions of mangrove termites on the Atlantic coast of Panama.     

Multimodality in the individual size distributions of bird communities

Aim Body size often plays a significant role in community assembly through its impacts on the life history and ecological attributes of species. Insight into the importance of size in structuring communities can be gained by examining the distribution of sizes of individuals [i.e. the individual size distribution (ISD) or size spectrum] in a community. ISDs have been studied extensively in aquatic and tree communities, but have received little attention in terrestrial animal communities. Here, we conduct the first macroecological analysis of ISDs in terrestrial animal communities to determine whether they show broad‐scale consistency in shape. Location North America, north of Mexico. Methods Using likelihood‐based methods and Gaussian mixture modelling, coupled with data from the Breeding Bird Survey and Christmas Bird Count, we determine whether the ISDs for thousands of breeding and wintering North American bird communities are: (1) monotonically decreasing, (2) unimodal or (3) multimodal. Results We find that avian ISDs are consistently multimodal, with most characterized by more than five modes in both breeding and wintering communities from local to continental scales. In addition, the positions of these modes along the size axis are remarkably consistent. Main conclusions The striking consistency in the ISD within bird communities, as with tree and aquatic communities, indicates that the ISD is an important and informative characterization of resource utilization within an ecological assemblage. The differences in shape of the ISD among these groups also suggest that differences in body size‐related constraints affect interactions within a group and with the environment. Our results confirm that avian assemblages do exhibit structure along the body size axis, and therefore it will be fruitful to explore this pattern in greater detail.     

Connecting landscape structure and patterns in body size distributions

Understanding the interaction between community structure and landscape structure represents a pressing theoretical challenge of great applied importance considering the increasing structural modification of ecosystems through habitat loss and fragmentation. Dispersal ability and energetic demands coupled to body size determine the landscape structure experienced by an organism, which could essentially be fragmented for small individuals but continuous for large ones. Although discontinuities in species assemblages have been predicted and detected, no explicit association between habitat structure and body size distributions has been demonstrated. In this contribution, we propose that body size structure in local communities should reflect such different perceptions of landscape structure. To this end, we explore this association in a simple metacommunity located in the Atacama Desert, in northern Chile. Using graph theory we found that species of different size and trophic position (carnivores and herbivores) perceive the landscape at contrasting spatial scales. In each community (n = 31) we determined the observed and the expected body size distributions – in a random sample from the metacommunity of 18 727 individuals –, which allowed us to identify the body sizes at which an overrepresentation or underrepresentation of individuals occur. Such aggregations and discontinuities in body sizes were related, for carnivores, to patch location within the landscape, and to the internal banded vegetation pattern within patches for herbivores. Our study shows, for the first time, an empirical connection between the spatial distribution of communities, their local attributes, and the existence and locations of discontinuities and aggregations in body size distributions.     

Steady size distributions for cells in one-dimensional plant tissues

We consider a population of cells growing and dividing steadily without mortality, so that the total cell population is increasing, but the proportion of cells in any size class remains constant. The cell division process is non-deterministic in the sense that both the size at which a cell divides, and the proportions into which it divides, are described by probability density functions. We derive expressions for the steady size/birth-size distribution (and the corresponding size/age distribution) in terms of the cell birth-size distribution, in the particular case of one-dimensional growth in plant organs, where the relative growth rate is the same for all cells but may vary with time. This birth-size distribution is shown to be the principal eigenfunction of a Fredholm integral operator. Some special cases of the cell birth-size distribution are then solved using analytical techniques, and in more realistic examples, the eigen-function is found using a simple, generally applicable numerical iteration.     

Within-genus size distributions in angiosperms: Small is better

The composition of natural vegetation typically includes a wide range of species sizes, but usually, relatively small size classes are represented by the greatest number of resident species. This is the case even within habitat types where traditional theory predicts that the intensity of plant competition should be most severe. Here we show that distributions of species size metrics are generally right-skewed also at the within-genus level. Our analyses are based on published reports of maximum plant height, leaf size, and seed size for an unbiased sample of fourteen angiosperm genera, involving eleven families – including representation of both endemics and cosmopolitans, plus genera that differ widely in both size (number of species) and growth form diversity. Pair-wise relationships for these three traits were, in most cases, also generally positively correlated for con-generic species. These results indicate that the right-skewed species size distributions commonly reported for natural vegetation reflect a pervasive signal for adaptive size metrics, essentially unstructured by phylogenic relationships. From these data therefore, we infer that most episodes of species origination within virtually all angiosperm lineages must have generally involved favouring effects of natural selection associated with relatively small plant body size, leaf size, and seed size. This represents a striking disconnect with the conventional view that superior competitive ability in plants requires relatively large body size/biomass production. Our interpretation of why ‘small is better’ focuses on two recently developed hypotheses – the ‘physical-space-niche’ hypothesis, and the ‘fecundity allocation premium’ hypothesis. In future research, detailed phylogenies at the species level might be used to test the prediction that relatively small size metrics are especially well represented in the most recently evolved species within angiosperm lineages.