Considerations on the genetic equilibrium law

@article{Camosso2017ConsiderationsOT,
  title={Considerations on the genetic equilibrium law},
  author={Simone Camosso},
  journal={IOSR Journal of Mathematics},
  year={2017},
  volume={13},
  pages={01-03}
}
  • Simone Camosso
  • Published 11 May 2016
  • Mathematics
  • IOSR Journal of Mathematics
In the first part of the paper I will present a brief review on the Hardy-Weinberg equilibrium and its formulation in projective algebraic geometry. In the second and last part I will discuss examples and generalizations on the topic. 

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References

SHOWING 1-10 OF 12 REFERENCES

Foundations Of Mathematical Genetics

TLDR
The genetic model is compared to a number of single-locus models used in medicine, including diallelic loci, where two alleles at a single locus and Fisher's fundamental theorem are compared to three.

Solving the Likelihood Equations

TLDR
Algebraic algorithms are presented for computing all critical points of this function, with the aim of identifying the local maxima in the probability simplex, and the maximum likelihood degree of a generic complete intersection is determined.

The maximum likelihood degree

Maximum likelihood estimation in statistics leads to the problem of maximizing a product of powers of polynomials. We study the algebraic degree of the critical equations of this optimization

Likelihood Geometry

We study the critical points of monomial functions over an algebraic subset of the probability simplex. The number of critical points on the Zariski closure is a topological invariant of that

Principles of population genetics

Genetic and Phenotypic Variation Organisation of Genetic Variation Random Genetic Drift Mutation and the Neutral Theory Darwinian Selection Inbreeding, Population Subdivision, and Migration Molecular

Maximum likelihood for matrices with rank constraints

TLDR
This work discusses methods for finding the global maximum of the likelihood function, presents a duality theorem due to Draisma and Rodriguez, and shares recent work with Kubkas and Robeva concerning nonnegative rank and the EM algorithm.

The maximum likelihood degree of Fermat hypersurfaces

We study the critical points of the likelihood function over the Fermat hypersurface. This problem is related to one of the main problems in statistical optimization: maximum likelihood estimation.

An Introduction to Conservation Genetics

TLDR
In Introduction to Conservation Genetics, Frankham, Ballou, and Briscoe have endeavored to provide a textbook to introduce students to genetic analysis in conservation biology that maintains an impressive fluidity and is both thorough and instructive, but it has a few weaknesses worth mentioning.

Tutorial on maximum likelihood estimation

Maximum likelihood on four taxa phylogenetic trees: analytic solutions

TLDR
It is proved that under the MC assumption, both the fork and the comb topologies have a unique (local and global) ML point, and it is shown that in contrast to the fork, the comb has no closed form solutions (expressed by radicals in the input data).