The consequences of size dependent foraging for food web topology

A general question in biology is how processes at one scale, for example that of individual organisms, influence patterns at larger scales, for example communities of interacting individuals. Here we ask how changing the size‐dependence of the foraging behaviour of individuals can influence the structure of food webs. We assembled communities using a model in which species interactions are determined by allometric foraging rules of (1) handling time and (2) attack rates, and also (3) the distribution of body sizes. We systematically varied these three factors and examined their effects on three community level, food web allometries: the generality ‐ mass correlation, the vulnerability ‐ mass correlation and the trophic height ‐ mass correlation. The results demonstrate how allometries of individual foraging behaviour (handling time and attack rates) are linked across scales of organisation: different community level allometries are influenced by different individual level allometries. For example, generality allometries in the community are most affected by the individual allometric relationships of the attack rate, whereas trophic level allometries in the community are more strongly influenced by variation in individual handling time allometries. Importantly, we also find that the shape of the body size distribution from which species are drawn has a substantial influence on how these links between scales operate. This study suggests that understanding the variation of size structure among ecological networks requires knowledge about the causes of variation in individual foraging behaviour and determinants of the regional body size distribution.     

A cure for the plague of parameters: constraining models of complex population dynamics with allometries

A major goal of ecology is to discover how dynamics and structure of multi-trophic ecological communities are related. This is difficult, because whole-community data are limited and typically comprise only a snapshot of a community instead of a time series of dynamics, and mathematical models of complex system dynamics have a large number of unmeasured parameters and therefore have been only tenuously related to real systems. These are related problems, because long time-series, if they were commonly available, would enable inference of parameters. The resulting ‘plague of parameters’ means most studies of multi-species population dynamics have been very theoretical. Dynamical models parametrized using physiological allometries may offer a partial cure for the plague of parameters, and these models are increasingly used in theoretical studies. However, physiological allometries cannot determine all parameters, and the models have also rarely been directly tested against data. We confronted a model of community dynamics with data from a lake community. Many important empirical patterns were reproducible as outcomes of dynamics, and were not reproducible when parameters did not follow physiological allometries. Results validate the usefulness, when parameters follow physiological allometries, of classic differential-equation models for understanding whole-community dynamics and the structure–dynamics relationship.     

A matter of measurements: challenges and approaches in the comparative analysis of static allometries

Comparisons of static allometries are frequently used to gain insights into patterns and processes underlying morphological and developmental evolution. A study by J. L. Tomkins and coworkers, recently published in the American Naturalist, examined complex nonlinear allometries in three insect species in which males are dimorphic in the expression of secondary sexual traits. Employing a novel approach to analyzing male allometries in these organisms, the authors were able to show that developmental reprogramming of trait primordia is not necessary to explain allometric scaling in two of the species examined, contrary to several previous studies on the same species. Instead, male dimorphisms could be explained by simple exponential growth, an important result that carries with it major evolutionary and developmental implications. Using this study as an example, I highlight some of the methodological challenges involved in analyzing and comparing static allometries and in inferring the developmental processes that underlie them. I end by discussing how correct application of hypothesis testing, on one side, and basic anatomy and developmental biology, on the other, should guide how morphology is measured.     

Perspectives and mechanisms for targeting mitotic catastrophe in cancer treatment

Mitotic catastrophe is distinct from other cell death modes due to unique nuclear alterations characterized as multi and/or micronucleation. Mitotic catastrophe is a common and virtually unavoidable consequence during cancer therapy. However, a comprehensive understanding of mitotic catastrophe remains lacking. Herein, we summarize the anticancer drugs that induce mitotic catastrophe, including microtubule-targeting agents, spindle assembly checkpoint kinase inhibitors, DNA damage agents and DNA damage response inhibitors. Based on the relationships between mitotic catastrophe and other cell death modes, we thoroughly evaluated the roles played by mitotic catastrophe in cancer treatment as well as its advantages and disadvantages. Some strategies for overcoming its shortcomings while fully utilizing its advantages are summarized and proposed in this review. We also review how mitotic catastrophe regulates cancer immunotherapy. These summarized findings suggest that the induction of mitotic catastrophe can serve as a promising new therapeutic approach for overcoming apoptosis resistance and strengthening cancer immunotherapy.     

There's something afoot in the evolution of ontogenies

Allometry, the association between size and shape, has long been considered an evolutionary constraint because of its ability to channel variation in particular directions in response to evolution of size. Several recent studies, however, have demonstrated that allometries themselves can evolve. Therefore, constraints based on these allometries are not constant over long evolutionary time scales. The changes in ontogeny appear to have a clear adaptive basis, which establishes a feedback loop from adaptive change of ontogeny through the altered developmental constraints to the potential for further evolutionary change. Altogether, therefore, this new evidence underscores the tight interactions between developmental and ecological factors in the evolution of morphological traits.     

Allometries and scaling laws interpreted as laws: a reply to Elgin

I analyze here biological regression equations known in the literature as allometries and scaling laws. My focus is on the alleged lawlike status of these equations. In particular I argue against recent views that regard allometries and scaling laws as representing universal, non-continent, and/or strict biological laws. Although allometries and scaling laws appear to be generalizations applying to many taxa, they are neither universal nor exceptionless. In fact there appear to be exceptions to all of them. Nor are the constants in allometries and scaling laws truly constant, stable, or universal in character, but vary in value across different taxa and background conditions. Moreover, these equations represent evolutionary, strongly contingent generalizations, which threatens their lawlike status. Lastly, allometries and scaling laws do not offer stable probabilities to which they hold in different backgrounds. I further suggest that many allometries and scaling laws function to elucidate explananda rather than explanantia or covering laws.     

Nonequilibrium self-assembly of linear fibers: microscopic treatment of growth, decay, catastrophe and rescue

Many of the large structures of cells are constructed from fibers. These fibers self-assemble from individual proteins in a far-from-equilibrium fashion. Nonequilibrium self-assembly results in a highly dynamic process at the subcellular level that can be regulated and tuned to carry out many of the biological functions of the cell: growth, division and locomotion. We construct and analyze a nonequilibrium model of the dynamic end of a biological fiber that possesses site-resolved resolution. We solve for the steady states of this nonequilibrium system using a variational method. The results are compared to exact numerical solutions for systems with modest size. Using an effective reaction coordinate, we construct an effective potential from the steady-state distribution. The stochastic transitions of the system can be analyzed in this representation. We then apply this method to model microtubule systems. Predictions for macroscopic catastrophe, rescue and dynamic instability in the steady states are analyzed. We find that the length of the cap of the microtubule is small. The relations between the catastrophe/rescue rate and the growth rate are also discussed.     

Developmental causes of allometry: new models and implications for phenotypic plasticity and evolution

Shapes change during development because tissues, organs, and various anatomical features differ in onset, rate, and duration of growth. Allometry is the study of the consequences of differences in the growth of body parts on morphology, although the field of allometry has been surprisingly little concerned with understanding the causes of differential growth. The power-law equation y?=?ax(b), commonly used to describe allometries, is fundamentally an empirical equation whose biological foundation has been little studied. Huxley showed that the power-law equation can be derived if one assumes that body parts grow with exponential kinetics, for exactly the same amount of time. In life, however, the growth of body parts is almost always sigmoidal, and few, if any, grow for exactly the same amount of time during ontogeny. Here, we explore the shapes of allometries that result from real growth patterns and analyze them with new allometric equations derived from sigmoidal growth kinetics. We use an extensive ontogenetic dataset of the growth of internal organs in the rat from birth to adulthood, and show that they grow with Gompertz sigmoid kinetics. Gompertz growth parameters of body and internal organs accurately predict the shapes of their allometries, and that nonlinear regression on allometric data can accurately estimate the underlying kinetics of growth. We also use these data to discuss the developmental relationship between static and ontogenetic allometries. We show that small changes in growth kinetics can produce large and apparently qualitatively different allometries. Large evolutionary changes in allometry can be produced by small and simple changes in growth kinetics, and we show how understanding the development of traits can greatly simplify the interpretation of how they evolved.     

An optimum body size for mammals? Comparative evidence from bats

1. The distribution of body sizes among mammalian species has been modelled by Brown, Marquet & Taper (1993), who suggest that reproductive power (the rate at which energy from the environment is channelled into offspring production) is maximized at a size of 100 g, and the observed size distribution among species reflects the way reproductive power depends on size. The model makes a testable prediction about life-history allometries: namely, that components of reproductive power should not scale linearly with body size but should change sign at the optimum size.
2. A large set of life-history data from a single clade of small mammals, the bats (Order: Chiroptera), was analysed to test this key prediction. The analyses in this study offer no support for the idea that allometries of reproductive power change sign in bats, either at 100 g or at any other size. Furthermore the life-history allometries of bats, which are mostly below the 100 g optimum, were broadly the same as in mammalian taxa larger than the optimum size.
3. These findings together contradict a key prediction of Brown et al. 's (1993) model to explain the skewed body size distribution across mammalian species.     

Relationships among ontogenetic,static, and evolutionary allometry

The relationship between ontogenetic, static, and evolutionary levels of allometry is investigated. Extrapolation from relative size relationships in adults to relative growth in ontogeny depends on the variability of slopes and intercepts of ontogenetic vectors relative to variability in length of the vector. If variability in slopes and intercepts is low relative to variability in length, ontogenetic and static allometries will be similar. The similarity of ontogenetic and static allometries was tested by comparing the first principal component, or size vector, for correlations among 48 cranial traits in a cross-sectional ontogenetic sample of rhesus macaques from Cayo Santiago with a static sample from which all age- and sex-related variation had been removed. The vector correlation between the components is high but significantly less than one while two of three allometric patterns apparent in the ontogenetic component are not discernable in the static component. This indicates that there are important differences in size and shape relationships among adults and within ontogenies. Extrapolation from intra- or interspecific phenotypic allometry to evolutionary allometry is shown to depend on the similarity of genetic and phenotypic allometry patterns. Similarity of patterns was tested by comparing the first principal components of the phenotypic, genetic, and environmental correlation matrices calculated using standard quantitative genetic methods. The patterns of phenotypic, genetic, and environmental allometry are dissimilar; only the environmental allometries show ontogenetic allometric patterns. This indicates that phenotypic allometry may not be an accurate guide to patterns of evolutionary change in size and shape.     

突变级数法在生态适宜度评价中的应用——以镇江新区为例

《开发区区域环境影响评价技术导则》（HJ／T2003）已将生态适宜度评价列为区域环境影响评价的主要内容,并明确提出了三级指标集成的框架要求,但并未推荐具体的技术方法。在当前的环评工作实际中,出现了多种生态适宜度的评价技术,如排列成比较技术、层次分析、模糊评价法等,然而这些方法却普遍存在着权重分配过程中的主观性问题。而对于生态适宜度评价这类多指标集成的问题,无论采用何种技术方法,只有减少权重赋值的主观性才能体现评价结论的科学性。鉴于此,推荐了一种新型的生态适宜度评价方法——突变级数法。通过镇江新区环评的具体案例分析,突变级数法表现出在生态适宜度评价方面较好的适用性。更为重要的是,通过对前述3种方法的数理分析对比,突变级数法表现出主营以下两方面的比较优势：首先该法不使用权重,只需按指标间的内在逻辑关系对指标的重要程度进行排序,很大限度地避免了人为制定权重的主观性;同时,作为定性与定量相结合的技术方法,突变级数法不仅可以对各地块是否适合其利用类型做出评价,还可以运用模型计算出各个地块生态适宜度的具体数值,对不同地块的生态适宜性程度进行定量的对比。诚然,应该客观地指出,在按指标的重要程度排序过程、以及评价指标的量化分级过程中,突变级数法仍然不能完全避免人为主观性,这也需要今后继续探索整合其他技术方法。加以进一步完善。     

Crown allometries are less responsive than stem allometry to tree size and habitat variations in an Indian monsoon forest

While theoretical allometric models postulate universal scaling exponents, empirical relationships between tree dimensions show marked variability that reflects changes in the biomass allocation pattern. As growth of the various tree compartments may be controlled by different functions, it is hypothesized that they may respond differently to factors of variation, resulting in variable tree morphologies and potentially in trade-offs between allometric relationships. We explore the variability of tree stem and crown allometries using a dataset of 1,729 trees located in an undisturbed wet evergreen forest of the Western Ghats, India. We specifically test whether species adult stature, terrain slope, tree size and crown light exposure affect the relationships between stem diameter and stem height (stem allometry), and between stem diameter and crown width, crown area and crown volume (crown allometries). Results show that both stem and crown allometries are subject to variations in relation to both endogenous (tree size, species adult stature) and exogenous (terrain slope, crown light exposure) factors. Stem allometry appears to be more affected by these factors than are crown allometries, including the stem diameter–crown volume relationship, which proved to be particularly stable. Our results support the idea that height is a prevailing adjustment factor for a tree facing variable growth (notably light) conditions, while stem diameter–crown volume allometry responds more to internal metabolic constraints. We ultimately discuss the various sources of variability in the stem and crown allometries of tropical trees that likely play an important role in forest community dynamics.     

Catastrophe Theory Enables Moves to be Detected Towards and Away from Self-Organization: The Example of Epileptic Seizure Onset

Macroscopic systems with many interacting subunits, when driven far from equilibrium, exhibit self-organization, for example when a pathological rhythm appears suddenly in an epileptic patient. Sudden changes occurring while conditions vary smoothly have, in cases of interest, underlying mathematics that are the subject of Thom’s catastrophe theory. The assumption made herein that the system’s state variables, akin to order parameters, reduce in practice to only one single real variable, ensures that the system derives from a potential function, and warrants recourse to the catastrophe theory. The order parameter is, furthermore, interpreted as a measure of the electropathophysiological activity in the brain, increasing monotonously with the degree of neuronal synchronism. With two neuronal influences, excitatory and inhibitory, as control parameters, the catastrophe is the archetypal cusp. Implementation of catastrophe theory leads to equations showing that fluctuations in a system’s dynamics may be utilised for signalling steps precursory to oncoming catastrophes. Pre-seizure dynamics in epileptic patients exhibit steps towards and away from catastrophe; the steps away are interpreted in terms of homeostatic feedback, consequent on changing patterns of neuronal activity. A number of characteristics of epileptic seizures of differing types merely follow from the geometry of the cusp equilibrium surface. In particular, types of seizures are distinguished by their angle of final approach to onset in parameter space. The measurable parameters by which approach to catastrophe is characterized, may be of use in investigations of the organism’s plasticity in epileptic patients, and in tests of therapeutic means for preventing seizures. There is no need to resort to a model, in the usual sense of the word, and therefore no differential equation needs to be set up.     

Evolution of multivariate wing allometry in schizophoran flies (Diptera: Schizophora)

The proximate and ultimate mechanisms underlying scaling relationships as well as their evolutionary consequences remain an enigmatic issue in evolutionary biology. Here, I investigate the evolution of wing allometries in the Schizophora, a group of higher Diptera that radiated about 65 million years ago, by studying static allometries in five species using multivariate approaches. Despite the vast ecological diversity observed in contemporary members of the Schizophora and independent evolutionary histories throughout most of the Cenozoic, size‐related changes represent a major contributor to overall variation in wing shape, both within and among species. Static allometries differ between species and sexes, yet multivariate allometries are correlated across species, suggesting a shared developmental programme underlying size‐dependent phenotypic plasticity. Static allometries within species also correlate with evolutionary divergence across 33 different families (belonging to 11 of 13 superfamilies) of the Schizophora. This again points towards a general developmental, genetic or evolutionary mechanism that canalizes or maintains the covariation between shape and size in spite of rapid ecological and morphological diversification during the Cenozoic. I discuss the putative roles of developmental constraints and natural selection in the evolution of wing allometry in the Schizophora.     

Circular dichroism of polynucleotides: A general method applied to dimers

A method is described which relates the circular dichroism of a polymer to its conformation. The method takes into account near and accidental degeneracies and eliminates the artificial distinction between degenerate and nondegenerate systems. Comparison of this method with perturbation theory indicates that the errors inherent in nondegenerate perturbation theory tend to cancel when a circular dichroism spectrum is calculated. The method is applied to dinucleoside phosphates.     

Extending the viability theory framework of resilience to uncertain dynamics,and application to lake eutrophication

Resilience, the capacity for a system to recover from a perturbation so as to keep its properties and functions, is of growing concern to a wide range of environmental systems. The challenge is often to render this concept operational without betraying it, nor diluting its content. The focus here is on building on the viability theory framework of resilience to extend it to discrete-time stochastic dynamical systems. The viability framework describes properties of the system as a subset of its state space. This property is resilient to a perturbation if it can be recovered and kept by the system after a perturbation: its trajectory can come back and stay in the subset. This is shown to reflect a general definition of resilience. With stochastic dynamics, the stochastic viability kernel describes the robust states, in which the system has a high probability of staying in the subset for a long time. Then, probability of resilience is defined as the maximal probability that the system reaches a robust state within a time horizon. Management strategies that maximize the probability of resilience can be found through dynamic programming. It is then possible to compute a range of statistics on the time for restoring the property. The approach is illustrated on the example of lake eutrophication and shown to foster the use of different indicators that are adapted to distinct situations. Its relevance for the management of ecological systems is also discussed.     

Artificial selection on allometry: change in elevation but not slope

To what extent within-species (static) allometries constitute a constraint on evolution is the subject of a long-standing debate in evolutionary biology. A prerequisite for the constraint hypothesis is that static allometries are hard to change. Several studies have attempted to test this hypothesis with artificial-selection experiments, but their results remain inconclusive due to various methodological issues. Here, we present results from an experiment in which we selected independently on the slope and the elevation of the allometric relationship between caudal-fin size and body size in male guppies (Poecilia reticulata). After three episodes of selection, the allometric elevation (i.e. intercept at constant slope) had diverged markedly between the lines selected to increase or decrease it, and showed a realized heritability of 50%. In contrast, the allometric slope remained unaffected by selection. These results suggest that the allometric elevation is more evolvable than the allometric slope, this latter representing a potential constraint on adaptive trait evolution. To our knowledge, this study is the first artificial-selection experiment that directly tests the evolvability of static allometric slopes.     

基于椭圆脐点突变模型的大熊猫生存状态研究

得益于有力的保护,大熊猫受威胁等级由"濒危"降为"易危"。根据全国大熊猫调查数据,近年来,大熊猫野生种群与栖息地面积总体上均处于持续增加态势;同时,大熊猫栖息地破碎化与局域种群隔离也呈加剧的趋势。两相对比,形成悖论现象,难以正确认知当前大熊猫的生存状态。大熊猫作为高度特化的K对策大型动物,其生存高度依赖于栖息地生态系统,极易受栖息地丧失与破碎化的影响。对大熊猫生存状态的研究,不应局限于栖息地或种群等单项指标的变化,而应基于系统科学的整体视角。结合全国第三、四次大熊猫调查数据,对大熊猫野生种群数量与栖息地及潜在栖息地的面积进行复相关分析,发现大熊猫野生种群数量与栖息地、潜在栖息地的面积之间存在着高度显著正相关,表明三者之间存在着稳定而密切的耦合关系,进而建立了大熊猫种群与栖息地、潜在栖息地之间的耦合函数。突变理论作为一种成熟的系统科学理论,提供了较完备的数学方法,利用系统中少量的关键指标便可实现对系统行为的刻画。基于突变理论,以大熊猫分布区生态系统为研究对象,选取了大熊猫种群数量、栖息地与潜在栖息地的面积为系统关键指标,利用种群与栖息地、潜在栖息地之间的耦合函数,构建了"大熊猫—栖息地"系统椭圆脐点突变模型,对生态系统的稳定性进行研究。发现虽然野生种群数量、栖息地与潜在栖息地的面积均持续增长,但严峻的局域种群生存危机与栖息地的高度破碎化,从总体上削弱了系统的稳定性,大熊猫分布区生态系统的稳定性处于持续下降态势,且濒临系统临界状态,生态系统具有较大的退化压力,大熊猫的生存危机依然严峻。     

Limit cycles in periodically perturbed population systems

A perturbation method is proposed to calculate approximately the limit cycle type nonequilibrium steady-state resulting from periodic perturbation of coefficients of stable population systems; the two species Lotka-Volterra competition system is explicity studied and the results are formulated for general multi-species population systems. Avoidance of competitive or other types of exclusion of species in a periodic environment is indicated.     

Morphological divergence patterns among populations of Poecilia vivipara (Teleostei Poeciliidae): test of an ecomorphological paradigm

The structure of body size and shape divergence among populations of Poecilia vivipara inhabiting quaternary lagoons in South-eastern Brazil was studied. This species is abundant throughout an environmental gradient formed by water salinity differences. The salinity gradient influences the habitat structure (presence of macrophytes) and the fish community (presence of large predators). Size and shape variation within and among populations was quantified by geometric morphometrics and analysed by indirect and direct gradient ordinations, using salinity and geography as a framework. Morphological divergence was associated with the salinity gradient. The evolutionary allometries observed were independent of within-group static allometries. Sexually dimorphic patterns were observed in size variation and within-population allometries. Specimens from freshwater (higher predation) sites presented smaller sizes, relatively longer caudal regions, lower anterior regions and a ventrally displaced eye. These features are consistent with an ecomorphological paradigm for aquatic organisms from populations subject to intense predation. A process of directional selection is postulated as the most likely force driving diversification among P. vivipara populations.  © 2008 The Linnean Society of London, Biological Journal of the Linnean Society , 2008, 93 , 799–812.