Analyzing Taylor’s Scaling Law: qualitative differences of social and territorial behavior on colonization/extinction dynamics

The power law relation between the mean population count and its variance (Taylor’s Power Law, TPL) is among the few general patterns in population ecology. While the TPL has been described to be pervasive across taxa, the causes of variation of the exponent describing this relation is not well understood. We compare the TPL exponents for two species with different social systems and behavior: Piñon jays (Gymnorhinus cyanocephalus) and Western scrub-jays (Aphelocoma californica). We analyze the underlying processes that generate the expected values of population size and its variance. Using a probabilistic model, we identify and estimate important processes involved in the generation of the TPL exponents. While both species show a scaling relationship between their mean and abundance, share a common negative relation between mean abundance and colonization–extinction rates, they differ greatly in the statistical distributions of colonization, extinction, the mean number of colonists, the probability of zero abundance and population sizes. We show how different aspects of the processes that generate abundance affect the TPL exponent, thereby providing empirical guidelines to interpret differences in the scaling relation between mean and variance of population size.     

Consequences of Environmental Fluctuations on Taylor’s Power Law and Implications for the Dynamics and Persistence of Populations

Conservation Biologists have found that demographic stochasticity causes the mean time to extinction to increase exponentially with population size. This has proved helpful in analyses determining extinction times and characterizing the pathway to extinction. The aim of this investigation is to explore the possible interactions between environmental/demographic noises and the scaling effect of the mean population size with its variance, which is expected to follow Taylor’s power law relationship. We showed that the combined effects of environmental/demographic noises and the scaling of population size variability interact with the population dynamics and affect the mean time to extinction.     

International Law and Western Sahara’s Maritime Area

Abstract

Western Sahara’s coastal waters have become contentious because of seabed petroleum exploration and fisheries undertaken pursuant to treaties between Morocco and the European Union, Japan, and Russia. These activities have been protested by the territory’s government-in-exile, the Saharawi Arab Democratic Republic. In 2017 Morocco announced its intention to adopt legislation to create an exclusive economic zone (EEZ) on the territory’s coast. This article considers the status of Saharan coastal waters in the circumstances of decolonization and occupation. The obligations on states interested in exploring and extracting Saharan ocean resources are considered and are argued to be restrictive regardless of the status of the territory’s coastal waters and recognition of a Saharawi state.     

Benford’s Law: Textbook Exercises and Multiple-Choice Testbanks

Benford’s Law describes the finding that the distribution of leading (or leftmost) digits of innumerable datasets follows a well-defined logarithmic trend, rather than an intuitive uniformity. In practice this means that the most common leading digit is 1, with an expected frequency of 30.1%, and the least common is 9, with an expected frequency of 4.6%. Currently, the most common application of Benford’s Law is in detecting number invention and tampering such as found in accounting-, tax-, and voter-fraud. We demonstrate that answers to end-of-chapter exercises in physics and chemistry textbooks conform to Benford’s Law. Subsequently, we investigate whether this fact can be used to gain advantage over random guessing in multiple-choice tests, and find that while testbank answers in introductory physics closely conform to Benford’s Law, the testbank is nonetheless secure against such a Benford’s attack for banal reasons.     

Taylor’s power law of fluctuation scaling and the growth-rate theorem

Taylor’s law (TL), a widely verified empirical relationship in ecology, states that the variance of population density is approximately a power-law function of mean density. The growth-rate theorem (GR) states that, in a subdivided population, the rate of change of the overall growth rate is proportional to the variance of the subpopulations’ growth rates. We show that continuous-time exponential change implies GR at every time and, asymptotically for large time, TL with power-law exponent 2. We also show why diverse population-dynamic models predict TL in the limit of large time by identifying simple features these models share: If the mean population density and the variance of population density are (exactly or asymptotically) non-constant exponential functions of a parameter (e.g., time), then the variance of density is (exactly or asymptotically) a power-law function of mean density.     

Zipf’s Law: Balancing Signal Usage Cost and Communication Efficiency

We propose a model that explains the reliable emergence of power laws (e.g., Zipf’s law) during the development of different human languages. The model incorporates the principle of least effort in communications, minimizing a combination of the information-theoretic communication inefficiency and direct signal cost. We prove a general relationship, for all optimal languages, between the signal cost distribution and the resulting distribution of signals. Zipf’s law then emerges for logarithmic signal cost distributions, which is the cost distribution expected for words constructed from letters or phonemes.     

From Idea to Law: Theory,Concept and Terminological Formation in Ernst Haeckel’s Works

Russian Journal of Developmental Biology - Since Charles Darwin (1809–1882) and Ernst Haeckel (1834–1919) published their trailblazing ideas, the scientific community’s discussion...     

Assessing Conformance with Benford’s Law: Goodness-Of-Fit Tests and Simultaneous Confidence Intervals

Benford’s Law is a probability distribution for the first significant digits of numbers, for example, the first significant digits of the numbers 871 and 0.22 are 8 and 2 respectively. The law is particularly remarkable because many types of data are considered to be consistent with Benford’s Law and scientists and investigators have applied it in diverse areas, for example, diagnostic tests for mathematical models in Biology, Genomics, Neuroscience, image analysis and fraud detection. In this article we present and compare statistically sound methods for assessing conformance of data with Benford’s Law, including discrete versions of Cramér-von Mises (CvM) statistical tests and simultaneous confidence intervals. We demonstrate that the common use of many binomial confidence intervals leads to rejection of Benford too often for truly Benford data. Based on our investigation, we recommend that the CvM statistic Ud2, Pearson’s chi-square statistic and 100(1 − α)% Goodman’s simultaneous confidence intervals be computed when assessing conformance with Benford’s Law. Visual inspection of the data with simultaneous confidence intervals is useful for understanding departures from Benford and the influence of sample size.     

Neuroinflammation,Gut Microbiome,and Alzheimer’s Disease

Alzheimer’s disease (AD) is a progressive neurodegenerative disease that develops insidiously and causes dementia finally. There are also clinical complications in advanced dementia, such as eating problems, infections, which will lead to the decline of patients’ life quality, and the rising cost of care for AD to our society. AD will be important public health challenge. Early detection of AD may be a key issue to prevent, delay, and stop the disease. Gut microbiome and neuroinflammation are closely related with nervous system diseases, although the specific mechanism is not clear. This review introduces the relationship between neuroinflammation, gut microbiome, and AD.     

Magic,semantics, and Putnam’s vat brains

In this paper we offer an exegesis of Hilary Putnam’s classic argument against the brain-in-a-vat hypothesis offered in his Reason, truth and history (1981). In it, Putnam argues that we cannot be brains in a vat because the semantics of the situation make it incoherent for anyone to wonder whether they are a brain in a vat. Putnam’s argument is that in order for ‘I am a brain in a vat’ to be true, the person uttering it would have to be able to refer successfully to those things: the vat, and the envatted brain. Putnam thinks that reference can’t be secured without relevant kinds of causal relations, which, if envatted, the brain would lack, and so, it fails to be able to meaningfully utter ‘I am a brain in a vat’. We consider the implications of Putnam’s arguments for Cartesian scepticism and suggest that there may yet be some ways out of Putnam’s arguments for the traditional sceptic. In conclusion, we discuss the role of Putnam’s arguments against the brain in a vat hypothesis in his larger defense of his own internal realism against metaphysical realism.     

Large-Scale Analysis of Zipf’s Law in English Texts

Despite being a paradigm of quantitative linguistics, Zipf’s law for words suffers from three main problems: its formulation is ambiguous, its validity has not been tested rigorously from a statistical point of view, and it has not been confronted to a representatively large number of texts. So, we can summarize the current support of Zipf’s law in texts as anecdotic. We try to solve these issues by studying three different versions of Zipf’s law and fitting them to all available English texts in the Project Gutenberg database (consisting of more than 30 000 texts). To do so we use state-of-the art tools in fitting and goodness-of-fit tests, carefully tailored to the peculiarities of text statistics. Remarkably, one of the three versions of Zipf’s law, consisting of a pure power-law form in the complementary cumulative distribution function of word frequencies, is able to fit more than 40% of the texts in the database (at the 0.05 significance level), for the whole domain of frequencies (from 1 to the maximum value), and with only one free parameter (the exponent).     

Empathy’s purity,sympathy’s complexities; De Waal,Darwin and Adam Smith

Frans de Waal’s view that empathy is at the basis of morality directly seems to build on Darwin, who considered sympathy as the crucial instinct. Yet when we look closer, their understanding of the central social instinct differs considerably. De Waal sees our deeply ingrained tendency to sympathize (or rather: empathize) with others as the good side of our morally dualistic nature. For Darwin, sympathizing was not the whole story of the “workings of sympathy”; the (selfish) need to receive sympathy played just as central a role in the complex roads from sympathy to morality. Darwin’s understanding of sympathy stems from Adam Smith, who argued that the presence of morally impure motives should not be a reason for cynicism about morality. I suggest that De Waal’s approach could benefit from a more thorough alignment with the analysis of the workings of sympathy in the work of Darwin and Adam Smith.     

Asperger’s Syndrome,Subjectivity and the Senses

Situated at the intersection of anthropological work on illness narratives and research on the anthropology of autism, this paper is a close reading of an autobiographical narrative recounted by Peter, a young man diagnosed with Asperger’s Syndrome, a type of autism spectrum disorder (ASD). Responding to Solomon’s (2010a:252) call for phenomenologically grounded accounts of “the subjective, sensory, and perceptual experiences of autism … based on personal narratives and practices of being and self-awareness,” this paper calls into question key assumptions in the clinical and popular literature about ASD relating to theory of mind, empathy, capacity for metaphorical thinking, and ASD as a life-long condition.     

Darwin’s two theories, 1844 and 1859

Darwin’s first two, relatively complete, explicit articulations of his theorizing on evolution were his Essay of 1844 and On the Origin of Species published in 1859. A comparative analysis concludes that they espoused radically different theories despite exhibiting a continuity of strategy, much common structure and the same key idea. Both were theories of evolution by means of natural selection. In 1844, organic adaptation was confined to occasional intervals initiated and controlled by de-stabilization events. The modified descendants rebalanced the particular “plant and animal forms … unsettled by some alteration in their circumstances.” But by 1859, organic adaptation occurred continuously, potentially modifying the descendants of all organisms. Even natural selection, the persistent core of Darwin’s theorizing, does not prove to be a significant basis for theory similarity. Consequently, Darwin’s Origin theory cannot reasonably be considered as a mature version of the Essay. It is not a modification based on adjustments, further justifications and the integration of a Principle of Divergence. The Origin announced a new “scientific paradigm” while the Essay did little more than seemingly misconfigure the operation of a novel mechanism to extend varieties beyond their accepted bounds, and into the realm of possible new species. Two other collections of Darwin’s theorizing are briefly considered: his extensive notes of the late 1830s and his contributions to the famous meeting of 1 July 1858. For very different reasons, neither constitutes a challenge to the basis for this comparative study. It is concluded that, in addition to the much-debated social pressures, an unacknowledged further reason why Darwin did not publish his theorizing until 1859, could have been down to his perceptive technical judgement: wisely, he held back from rushing to publish demonstrably flawed theorizing.