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-Polish Arabian horses are one of the oldest and the most important Arab populations in the world. The Polish Arabian Stud Book and the Genealogical Charts by Skorkowski are the main sources of information on the ancestors of Polish Arabs. Both publications were viewed as credible sources of information until the 1990s when the data regarding one of the dam lines was questioned. The aim of the current study was to check the accuracy of the pedigree data of Polish dam lines using mtDNA analysis. The analyses of a 458 bp mtDNA D-loop fragment from representatives of 15 Polish Arabian dam lines revealed 14 distinct haplotypes. The results were inconsistent with pedigree data in the case of two lines. A detailed analysis of the historical sources was performed to explain these discrepancies. Our study revealed that representatives of different lines shared the same haplotypes. We also noted a genetic identity between some lines founded by Polish mares of unknown origin and lines established by desert-bred mares. mitochondrial DNA / horse / pedigree / phylogeny

-Polish Arabian horses are one of the oldest and the most important Arab populations in the world. The Polish Arabian Stud Book and the Genealogical Charts by Skorkowski are the main sources of information on the ancestors of Polish Arabs. Both publications were viewed as credible sources of information until the 1990s when the data regarding one of the dam lines was questioned. The aim of the current study was to check the accuracy of the pedigree data of Polish dam lines using mtDNA analysis. The analyses of a 458 bp mtDNA D-loop fragment from representatives of 15 Polish Arabian dam lines revealed 14 distinct haplotypes. The results were inconsistent with pedigree data in the case of two lines. A detailed analysis of the historical sources was performed to explain these discrepancies. Our study revealed that representatives of different lines shared the same haplotypes. We also noted a genetic identity between some lines founded by Polish mares of unknown origin and lines established by desert-bred mares. mitochondrial DNA / horse / pedigree / phylogeny

Polish Arabian horses are one of the most important populations of this breed in the world. Their post-war history can be divided into two periods, with the dominant role of state studs until 1989, and the increasing significance of private breeding in the next years. The goal of the study was to evaluate genetic diversity and structure of the population under a new breeding policy. The analyses of breeding and microsatellite data from 1996 to 2012 provide a coherent picture of the population with constant flow of horses only in one direction from state to private studs. An increase in the number of broodmares was observed, from 396 mares in 1996 to 1021 mares in 2012. The proportion of foreign sires used in Polish studs also increased, from 7.1% to 37.0%. An increasing number of alleles and progressive differentiation in mares were observed. STRUCTURE analysis indicated that the Polish horses were clearly separated from foreign horses used in Polish breeding, although only one of the 75 alleles found can be considered as typically Polish. The high heterozygosity is an important feature of the Polish population; however, the decrease of heterozygosity in state broodmares was noted. This issue needs to be studied further.

In the present paper, we investigate the Gompertz function, which is commonly used, mostly as diffusion model, in economics and management. Our approach is based on indicating in a given time series, presumably with a Gompertz trend, some characteristic points corresponding to zeroes of successive derivatives of this function. This allows us to predict the saturation level of a phenomenon under investigation, by using only the early values of the time series. We also give an example of applications of this method.

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