Measurement scale in maximum entropy models of species abundance

The consistency of the species abundance distribution across diverse communities has attracted widespread attention. In this paper, I argue that the consistency of pattern arises because diverse ecological mechanisms share a common symmetry with regard to measurement scale. By symmetry, I mean that different ecological processes preserve the same measure of information and lose all other information in the aggregation of various perturbations. I frame these explanations of symmetry, measurement, and aggregation in terms of a recently developed extension to the theory of maximum entropy. I show that the natural measurement scale for the species abundance distribution is log-linear: the information in observations at small population sizes scales logarithmically and, as population size increases, the scaling of information grades from logarithmic to linear. Such log-linear scaling leads naturally to a gamma distribution for species abundance, which matches well with the observed patterns. Much of the variation between samples can be explained by the magnitude at which the measurement scale grades from logarithmic to linear. This measurement approach can be applied to the similar problem of allelic diversity in population genetics and to a wide variety of other patterns in biology.     

Genetic and phenotypic models of natural selection

The following theorem is proposed: when two phenotypes differ in attributes affecting their relative fitness, selection will cease to cause further evolutionary change when the two phenotypes have the same fitness, provided that certain modes of inheritance apply; in particular, all genotypes specifying the same phenotype must have the same average fitness. If these conditions of “uniform fitness” patterns of inheritance are not met, particular genetic models of natural selection should replace an analysis of phenotypes. If the conditions are met, an analysis of the stationary conditions when the phenotypes have equal fitnesses permits quantitative statements about the outcome of selection without recourse to genetic models. Phenotypic analyses of natural selection are illustrated by models of sex ratios in plants, sexual versus asexual reproduction in plants, and parental investment by animals.     

The effect of natural selection on the performance of maximum parsimony

Background  

Maximum parsimony is one of the most commonly used and extensively studied phylogeny reconstruction methods. While current evaluation methodologies such as computer simulations provide insight into how well maximum parsimony reconstructs phylogenies, they tell us little about how well maximum parsimony performs on taxa drawn from populations of organisms that evolved subject to natural selection in addition to the random factors of drift and mutation. It is clear that natural selection has a significant impact on Among Site Rate Variation (ASRV) and the rate of accepted substitutions; that is, accepted mutations do not occur with uniform probability along the genome and some substitutions are more likely to occur than other substitutions. However, little is know about how ASRV and non-uniform character substitutions impact the performance of reconstruction methods such as maximum parsimony. To gain insight into these issues, we study how well maximum parsimony performs with data generated by Avida, a digital life platform where populations of digital organisms evolve subject to natural selective pressures.     

Speciation by natural and sexual selection: models and experiments

A large number of mathematical models have been developed that show how natural and sexual selection can cause prezygotic isolation to evolve. This article attempts to unify this literature by identifying five major elements that determine the outcome of speciation caused by selection: a form of disruptive selection, a form of isolating mechanism (assortment or a mating preference), a way to transmit the force of disruptive selection to the isolating mechanism (direct selection or indirect selection), a genetic basis for increased isolation (a one- or two-allele mechanism), and an initial condition (high or low initial divergence). We show that the geographical context of speciation (allopatry vs. sympatry) can be viewed as a form of assortative mating. These five elements appear to operate largely independently of each other and can be used to make generalizations about when speciation is most likely to happen. This provides a framework for interpreting results from laboratory experiments, which are found to agree generally with theoretical predictions about conditions that are favorable to the evolution of prezygotic isolation.     

Productivity,relevance and natural selection

Recent papers by a number of philosophers have been concerned with the question of whether natural selection is a causal process, and if it is, whether the causes of selection are properties of individuals or properties of populations. I shall argue that much confusion in this debate arises because of a failure to distinguish between causal productivity and causal relevance. Causal productivity is a relation that holds between events connected via continuous causal processes, while causal relevance is a relationship that can hold between a variety of different kinds of facts and the events that counterfactually depend upon them. I shall argue that the productive character of natural selection derives from the aggregation of individual processes in which organisms live, reproduce and die. At the same time, a causal explanation of the distribution of traits will necessarily appeal both to causally relevant properties of individuals and to causally relevant properties that exist only at the level of the population.

Enzyme kinetics and the maximum entropy production principle

A general proof is derived that entropy production can be maximized with respect to rate constants in any enzymatic transition. This result is used to test the assumption that biological evolution of enzyme is accompanied with an increase of entropy production in its internal transitions and that such increase can serve to quantify the progress of enzyme evolution. The state of maximum entropy production would correspond to fully evolved enzyme. As an example the internal transition ES?EP in a generalized reversible Michaelis-Menten three state scheme is analyzed. A good agreement is found among experimentally determined values of the forward rate constant in internal transitions ES→EP for three types of β-Lactamase enzymes and their optimal values predicted by the maximum entropy production principle, which agrees with earlier observations that β-Lactamase enzymes are nearly fully evolved. The optimization of rate constants as the consequence of basic physical principle, which is the subject of this paper, is a completely different concept from a) net metabolic flux maximization or b) entropy production minimization (in the static head state), both also proposed to be tightly connected to biological evolution.     

Natural selection, fitness entropy, and the dynamics of coevolution

The coevolutionary dynamics of interacting populations were studied by combining continuous time Lotka-Volterra models of population growth with single-locus genetic models of weak selection. The effects of natural selection on population growth were evaluated using Ginzburg's fitness entropy function as a measure of the deviation of a population's initial allele frequencies from their polymorphic equilibrium values. This entropy measure was used to relate the dynamics of a community composed of evolving populations to the dynamics of a "reference community" whose populations are initially in genetic equilibrium. Specifically, a quantity called the "selective difference area" was defined as the total difference between the population size trajectories of a reference and evolving population. The selective difference area represents the amount of extra life a species would realize if the entire community were at genetic equilibrium. It was shown that this selective difference area is a simple linear function of the initial fitness entropies of each species. This prediction is independent of the strength of selection and holds for any arbitrary set of initial population densities. Numerical examples were presented to illustrate the results. Under the assumption of weak selection, a generalization for arbitrary population growth models was outlined.     

Characterization of nucleotidic sequences using maximum entropy techniques

A statistical method for characterizing nucleotidic sequences based on maximum entropy techniques is presented. The method uses only codon usage tables and takes into account the length of sequences, and preserves the information contained in each codon by a punctual index. We present the methodological aspects of the analysis, showing an application relative to nucleotidic sequences of eukaryotes.     

Symbiogenesis,natural selection,and the dynamic Earth

One century ago, Constantin S. Mereschkowsky introduced the symbiogenesis theory for the origin of chloroplasts from ancient cyanobacteria which was later supplemented by Ivan E. Wallin’s proposal that mitochondria evolved from once free-living bacteria. Today, this Mereschkowsky–Wallin principle of symbiogenesis, which is also known as the serial primary endosymbiosis theory, explains the evolutionary origin of eukaryotic cells and hence the emergence of all eukaryotes (protists, fungi, animals and plants). In 1858, the concept of natural selection was described independently by Charles Darwin and Alfred R. Wallace. In the same year, Antonio Snider-Pellegrini proposed the idea of shifting continents, which was later expanded by Alfred Wegener, who published his theory of continental drift eight decades ago. Today, directional selection is accepted as the major cause of adaptive evolution within natural populations of micro- and macro-organisms and the theory of the dynamic Earth (plate tectonics) is well supported. In this article, I combine the processes and principles of symbiogenesis, natural selection and the dynamic Earth and propose an integrative ‘synade-model’ of macroevolution which takes into account organisms from all five Kingdoms of life.     

Ocean waves, nearshore ecology, and natural selection

Although they are subjected to one of the most stressful physical environments on earth, wave-swept rocky shores support a highly diverse community of plants and animals. The surprising presence of such diversity amidst severe environmental adversity provides a unique opportunity for exploration of the role of extreme water flows in community ecology and natural selection. Methods are described by which the maximal water velocity and acceleration can be predicted for a site on the shore, and from these values maximal hydrodynamic forces are calculated. These forces can limit the range and foraging activity of some species, and can determine the rate of disturbance in others, but in general, wave-swept organisms have surprisingly high factors of safety. This apparent over-design can help to explain the diversity of forms present on wave-swept shores, and provides examples of how mechanics can limit the ability of natural selection to guide specialization. Although flow itself may commonly be prohibited from selecting for optima in morphology, it nonetheless continues to play a potentially important role in evolution by providing a mechanism for breaking or dislodging individuals that have been selected by other means.     

Two-dimensional distributions of activation enthalpy and entropy from kinetics by the maximum entropy method.

The maximum entropy method (MEM) is used to numerically invert the kinetics of ligand rebinding at low temperatures to obtain the underlying two-dimensional distribution of activation enthalpies and entropies, g(H,S). A global analysis of the rebinding of carbon monoxide (CO) to myoglobin (Mb), monitored in the Soret band at temperatures from 60 to 150 K, is performed using a Newton-Raphson optimization algorithm. The MEM approach describes the data much better than traditional least-squares analyses, reducing chi 2 by an order of magnitude. The MEM resolves two barrier distributions suggestive of rebinding to different bound conformations of MbCO, the so-called A1 and A3 substates, whose activation barriers have been independently estimated from kinetics monitored in the infrared. The distribution corresponding to A3 possesses higher activation entropies, also consistent with infrared measurements. Within an A substate, correlations of S and H are recovered qualitatively from simulated data but can be difficult to obtain from experimental data. When the rebinding measured at 60 K is excluded from the inversion, two peaks are no longer clearly resolved. Thus, data of very high quality are required to unambiguously determine the kinetic resolvability of subpopulations and the shape of the barrier distribution for a single A substate.     

Maladaptation and natural selection

The transformations George Williams initiated in evolutionary biology seem so blindingly obvious in retrospect that they spur the question of why he saw what no one else did. While most humans are prone to see only what theory predicts, Williams sees in bold relief whatever does not fit. Not an adaptationist or an anti-adaptationist, Williams is better described as a maladaptionist. The challenge of finding evolutionary explanations for apparent maladaptations has been overlooked with casualness akin to that once typical for group selection. Suboptimal traits tend to be dismissed as illustrations of the weakness and stochastic nature of selection compared with mutation and drift. A closer look suggests that such constraints are only one of six possible kinds of explanations for apparently suboptimal designs: mismatch, coevolution, tradeoffs, constraints, reproductive advantage at the expense of the individual, and defenses that are aversive but useful Medicine has asked proximate questions at every possible level but has only begun to ask evolutionary questions about why bodies are vulnerable to disease. Considering all six possible evolutionary reasons for apparently suboptimal traits will spur progress not only in medicine but also more generally in biology. 'Williams Vision" may not yield a net benefit to the possessor, but it is invaluable for the species.     

Grandmothering and natural selection

Humans are unique among primates in that women regularly outlive their reproductive period by decades. The grandmother hypothesis proposes that natural selection increased the length of the human post-menopausal period—and, thus, extended longevity—as a result of the inclusive fitness benefits of grandmothering. However, it has yet to be demonstrated that the inclusive fitness benefits associated with grandmothering are large enough to warrant this explanation. Here, we show that the inclusive fitness benefits are too small to affect the evolution of longevity under a wide range of conditions in simulated populations. This is due in large part to the relatively weak selection that applies to women near or beyond the end of their reproductive period. However, we find that grandmothers can facilitate the evolution of a shorter reproductive period when their help decreases the weaning age of their matrilineal grandchildren. Because selection favours a shorter reproductive period in the presence of shorter interbirth intervals, this finding holds true for any form of allocare that helps mothers resume cycling more quickly. We conclude that while grandmothering is unlikely to explain human-like longevity, allocare could have played an important role in shaping other unique aspects of human life history, such as a later age at first birth and a shorter female reproductive period.     

Sexual selection, natural selection and copulatory patterns in male primates.

Complex copulatory patterns, involving multiple brief intromissions or prolonged single intromissions (PI) occur most frequently among primate species in which females mate with a number of partners (multimale and dispersed mating systems). However, the PI pattern is also confined almost exclusively to arboreal primates - to either smaller-bodied, cryptic, nocturnal species or much larger diurnal forms. Predation pressures may have limited the evolution of the PI pattern, particularly where small-bodied diurnal primates or terrestrial forms are concerned. The available evidence indicates that both sexual selection and natural selection may have influenced the evolution of copulatory patterns.     

最大熵原理及其在生态学研究中的应用

最大熵原理(the principle of maximum entropy)起源于信息论和统计力学,是基于有限的已知信息对未知分布进行无偏推断的一种数学方法.这一方法在很多领域都有成功应用,但只是近几年才被应用到生态学研究中,并且还存在很多争论.我们从基本概念和方法出发,用掷骰子的例子阐明了最大熵原理的概念,并提出运用最大熵原理解决问题需要遵从的步骤.最大熵原理在生态学中的应用主要包括以下方面:(1)用群落水平功能性状的平均值作为约束条件来预测群落物种相对多度的模型;(2)基于气候、海拔、植被等环境因子构建物种地理分布的生态位模型;(3)对物种多度分布、种一面积关系等宏生态学格局的推断;(4)对物种相互作用的推断;(5)对食物网度分布的研究等等.最后我们综合分析了最大熵原理在生态学应用中所存在的争议,包括相应模型的有效性、可靠性等方面,介绍了一些对最大熵原理预测能力及其局限性的检验结果,强调了生态学家应用最大熵原理需要注意的问题,比如先验分布的选择、约束条件的设置等等.在物种相互作用、宏生态学格局等方面对最大熵原理更广泛的讨论与应用可能会给生态学带来新的发展机会.     

A maximum likelihood approach to correlation dimension and entropy estimation

To obtain the correlation dimension and entropy from an experimental time series we derive estimators for these quantities together with expressions for their variances using a maximum likelihood approach. The validity of these expressions is supported by Monte Carlo simulations. We illustrate the use of the estimators with a local recording of atrial fibrillation obtained from a conscious dog.