Appearances of Local Prolific Ewes in Semarang Regency Central Java Indonesia

The present study examined the quantitative and qualitative physical parameters of prolific local ewes in Bawen and Jambu districts, Central Java. We used purposive sampling to select and categorized 132 local, three-lambing ewes into three groups based on their prolific capacity: 66 single, 49 twins and 17 triplets. The data were subjected to analysis of variance using Chi-Square. The result showed that many quantitative properties of prolific ewes resembled those of fat-tailed sheep: thin tail, highly significant (P<0.01) compared to fat tails; straight face, highly significant (P<0.01); and fewer convex face and short body, significant (P<0.05) with a tall body in the non-prolific ewes. Few prolific ewes had big ears and black-white wool and significantly different (P<0.05) from the non-prolific ewes. Conclusively, local prolific ewes had a qualitative appearance more closely related to that of thin-tailed ewes, but greater quantitative performances than the non-prolific ewes.

Understanding the Improbable: A Survey of Fat Tails in Environmental Economics

We survey the growing literature on fat-tailed distributions in environmental economics. We then examine the theoretical and statistical properties of such distributions, focusing especially on when these properties are likely to arise in environmental problems. We find that a number of variables are fat tailed in environmental economics, including the climate sensitivity, natural disaster impacts, spread of infectious diseases, and stated willingness to pay. We argue that different fat-tailed distributions arise from common pathways. Finally, we review the literature on the policy implications of fat-tailed distributions and controversies over their interpretation. We conclude that the literature has made great strides in demonstrating when fat tails matter for optimal environmental policy. Yet, much is less well understood, including how alternative policies affect fat-tailed distributions, the optimal policy in a computational economy with many fat-tailed problems, and how to account for imprecision in empirical tests for fat tails. Expected final online publication date for the Annual Review of Resource Economics, Volume 13 is October 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Fat Tail in the Phytoplankton Movement Patterns and Swimming Behavior: New Insights into the Prey-Predator Interactions

Phytoplankton movement patterns and swimming behavior are important and basic topics in aquatic biology. Heavy tail distribution exists in diverse taxa and shows theoretical advantages in environments. The fat tails in the movement patterns and swimming behavior of phytoplankton in response to the food supply were studied. The log-normal distribution was used for fitting the probability density values of the movement data of Oxyrrhis marina. Results showed that obvious fat tails exist in the movement patterns of O. marina without and with positive stimulations of food supply. The algal cells tended to show a more chaotic and disorderly movement, with shorter and neat steps after adding the food source. At the same time, the randomness of turning rate, path curvature and swimming speed increased in O. marina cells with food supply. Generally, the responses of phytoplankton movement were stronger when supplied with direct prey cells rather than the cell-free filtrate. The scale-free random movements are considered to benefit the adaption of the entire phytoplankton population to varied environmental conditions. Inferentially, the movement pattern of O. marina should also have the characteristics of long-range dependence, local self-similarity and a system of fractional order.

Uniqueness of fat-tailed self-similar profiles to Smoluchowski’s coagulation equation for a perturbation of the constant kernel

This article is concerned with the question of uniqueness of self-similar profiles for Smoluchowski’s coagulation equation which exhibit algebraic decay (fat tails) at infinity. More precisely, we consider a rate kernel K K which can be written as K = 2 + ε W K=2+\varepsilon W . The perturbation is assumed to have homogeneity zero and might also be singular both at zero and at infinity. Under further regularity assumptions on W W , we will show that for sufficiently small ε \varepsilon there exists, up to normalisation of the tail behaviour at infinity, at most one self-similar profile. Establishing uniqueness of self-similar profiles for Smoluchowski’s coagulation equation is generally considered to be a difficult problem which is still essentially open. Concerning fat-tailed self-similar profiles this article actually gives the first uniqueness statement for a non-solvable kernel.

Searching for fat tails in CRISPR-Cas systems: Data analysis and mathematical modeling

Understanding CRISPR-Cas systems—the adaptive defence mechanism that about half of bacterial species and most of archaea use to neutralise viral attacks—is important for explaining the biodiversity observed in the microbial world as well as for editing animal and plant genomes effectively. The CRISPR-Cas system learns from previous viral infections and integrates small pieces from phage genomes called spacers into the microbial genome. The resulting library of spacers collected in CRISPR arrays is then compared with the DNA of potential invaders. One of the most intriguing and least well understood questions about CRISPR-Cas systems is the distribution of spacers across the microbial population. Here, using empirical data, we show that the global distribution of spacer numbers in CRISPR arrays across multiple biomes worldwide typically exhibits scale-invariant power law behaviour, and the standard deviation is greater than the sample mean. We develop a mathematical model of spacer loss and acquisition dynamics which fits observed data from almost four thousand metagenomes well. In analogy to the classical ‘rich-get-richer’ mechanism of power law emergence, the rate of spacer acquisition is proportional to the CRISPR array size, which allows a small proportion of CRISPRs within the population to possess a significant number of spacers. Our study provides an alternative explanation for the rarity of all-resistant super microbes in nature and why proliferation of phages can be highly successful despite the effectiveness of CRISPR-Cas systems.