scholarly journals Inbreeding in a Family Tree and in a Population

2020 ◽  
Vol 1 (1) ◽  
pp. 21-34
Author(s):  
A.N. Volobuev
Keyword(s):  
Differential Equation ◽  
Natural Selection ◽  
Numerical Solution ◽  
Allele Frequency ◽  
Recessive Allele ◽  
Discrete Equation ◽  
Family Tree ◽  
Inbred Population ◽  
Standard Parameter

On the basis of Hardy – Weinberg’s law the problem of inbreeding in a family tree and a population was investigated. With use of an inbreeding factor are received the discrete equation for a family tree and differential equation for a population. The numerical solution of the differential equation for a population was found and analyzed at various values of the inbreeding factor. Migration of inbred population is investigated in view of natural selection. It was shown that velocity of migration falls with increase of the inbreeding factor. Interrelation of the recessive allele frequency at woman for a migrating population with inbreeding factor and standard parameter of selection was found.

scholarly journals New Applications of a Kind of Infinitesimal-Operator Lie Algebra

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Honwah Tam ◽  
Yufeng Zhang ◽  
Xiangzhi Zhang
Keyword(s):  
Differential Equation ◽  
Lie Algebras ◽  
Transformation Group ◽  
Order Differential Equation ◽  
Lie Symmetry ◽  
Discrete Equation ◽  
Infinitesimal Operator ◽  
Lie Transformation ◽  
Symmetry Operators ◽  
New Applications

Applying some reduced Lie algebras of Lie symmetry operators of a Lie transformation group, we obtain an invariant of a second-order differential equation which can be generated by a Euler-Lagrange formulism. A corresponding discrete equation approximating it is given as well. Finally, we make use of the Lie algebras to generate some new integrable systems including (1+1) and (2+1) dimensions.

scholarly journals Using seasonal genomic changes to understand historical adaptation: parallel selection on stickleback in highly-variable estuaries

2020 ◽  
Author(s):  
Alan Garcia-Elfring ◽  
Antoine Paccard ◽  
Timothy J. Thurman ◽  
Ben A. Wasserman ◽  
Eric P. Palkovacs ◽  
...  
Keyword(s):  
Natural Selection ◽  
Allele Frequency ◽  
Calcium Binding ◽  
Gasterosteus Aculeatus ◽  
Environmental Changes ◽  
Threespine Stickleback ◽  
Functional Enrichment ◽  
Genomic Changes ◽  
Parallel Selection ◽  
Frequency Changes

AbstractParallel evolution is considered strong evidence for natural selection. However, few studies have investigated the process of parallel selection as it plays out in real time. The common approach is to study historical signatures of selection in populations already well adapted to different environments. Here, to document selection in action under natural conditions, we study six populations of threespine stickleback (Gasterosteus aculeatus) inhabiting bar-built estuaries that undergo seasonal cycles of environmental changes. Estuaries are periodically isolated from the ocean due to sandbar formation during dry summer months, with concurrent environmental shifts that resemble the long-term changes associated with postglacial colonization of freshwater habitats by marine populations. We used pooled whole-genome sequencing (Pool-WGS) to track seasonal allele frequency changes in these populations and search for signatures of natural selection. We found consistent changes in allele frequency across estuaries, suggesting a potential role for parallel selection. Functional enrichment among candidate genes included transmembrane ion transport and calcium binding, which are important for osmoregulation and ion balance. The genomic changes that occur in threespine stickleback from bar-built estuaries could provide a glimpse into the early stages of adaptation that have occurred in many historical marine to freshwater transitions.

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