The Hardy-Weinberg law with overlapping generations

1974 ◽  
Vol 6 (1) ◽  
pp. 4-6 ◽  
Author(s):  
Brian Charlesworth
Keyword(s):  
Population Genetics ◽  
Genetic Drift ◽  
Age Structure ◽  
Continuous Time ◽  
Arbitrary Number ◽  
Overlapping Generations ◽  
Birth Rate ◽  
Allele Frequencies ◽  
Autosomal Locus ◽  
Weak Ergodicity

The Hardy-Weinberg law is generally regarded as one of the most important results of population genetics. It was originally proved for the case of populations with distinct generations (Hardy (1908), Weinberg (1908)); a general proof for populations with overlapping generations has apparently not been given before. The case of a single autosomal locus with an arbitrary number of alleles is considered here. Births and deaths are assumed to occur in continuous time. The weak ergodicity property of the birth rate and age structure of such a population, first derived by Norton (1928), is used to establish the fact that allele frequencies tend to constant limits in the absence of mutation, migration, selection and genetic drift.

The Hardy-Weinberg law with overlapping generations

1974 ◽  
Vol 6 (01) ◽  
pp. 4-6
Author(s):  
Brian Charlesworth
Keyword(s):  
Population Genetics ◽  
Genetic Drift ◽  
Age Structure ◽  
Continuous Time ◽  
Arbitrary Number ◽  
Overlapping Generations ◽  
Birth Rate ◽  
Allele Frequencies ◽  
Autosomal Locus ◽  
Weak Ergodicity

The Hardy-Weinberg law is generally regarded as one of the most important results of population genetics. It was originally proved for the case of populations with distinct generations (Hardy (1908), Weinberg (1908)); a general proof for populations with overlapping generations has apparently not been given before. The case of a single autosomal locus with an arbitrary number of alleles is considered here. Births and deaths are assumed to occur in continuous time. The weak ergodicity property of the birth rate and age structure of such a population, first derived by Norton (1928), is used to establish the fact that allele frequencies tend to constant limits in the absence of mutation, migration, selection and genetic drift.

scholarly journals A conditional likelihood is required to estimate the selection coefficient in ancient DNA

2016 ◽  
Author(s):  
Angelo Valleriani
Keyword(s):  
Time Series ◽  
Population Genetics ◽  
Natural Selection ◽  
Genetic Drift ◽  
Ancient Dna ◽  
Fitness Landscape ◽  
Likelihood Function ◽  
Allele Frequencies ◽  
Conditional Likelihood ◽  
Selection Coefficient

AbstractTime-series of allele frequencies are a useful and unique set of data to determine the strength of natural selection on the background of genetic drift. Technically, the selection coefficient is estimated by means of a likelihood function built under the hypothesis that the available trajectory spans a sufficiently large portion of the fitness landscape. Especially for ancient DNA, however, often only one single such trajectories is available and the coverage of the fitness landscape is very limited. In fact, one single trajectory is more representative of a process conditioned both in the initial and in the final condition than of a process free to visit the available fitness landscape. Based on two models of population genetics, here we show how to build a likelihood function for the selection coefficient that takes the statistical peculiarity of single trajectories into account. We show that this conditional likelihood delivers a precise estimate of the selection coefficient also when allele frequencies are close to fixation whereas the unconditioned likelihood fails. Finally, we discuss the fact that the traditional, unconditioned likelihood always delivers an answer, which is often unfalsifiable and appears reasonable also when it is not correct.

scholarly journals Interplay of population genetics and dynamics in the genetic control of mosquitoes

2014 ◽  
Vol 11 (93) ◽  
pp. 20131071 ◽  
Author(s):  
Nina Alphey ◽  
Michael B. Bonsall
Keyword(s):  
Population Genetics ◽  
Overlapping Generations ◽  
Large Scale ◽  
Genetic Model ◽  
Homing Endonuclease ◽  
Wild Type ◽  
Larval Competition ◽  
Selfish Genetic Elements ◽  
Fitness Effects ◽  
Ecological Aspects

Some proposed genetics-based vector control methods aim to suppress or eliminate a mosquito population in a similar manner to the sterile insect technique. One approach under development in Anopheles mosquitoes uses homing endonuclease genes (HEGs)—selfish genetic elements (inherited at greater than Mendelian rate) that can spread rapidly through a population even if they reduce fitness. HEGs have potential to drive introduced traits through a population without large-scale sustained releases. The population genetics of HEG-based systems has been established using discrete-time mathematical models. However, several ecologically important aspects remain unexplored. We formulate a new continuous-time (overlapping generations) combined population dynamic and genetic model and apply it to a HEG that targets and knocks out a gene that is important for survival. We explore the effects of density dependence ranging from undercompensating to overcompensating larval competition, occurring before or after HEG fitness effects, and consider differences in competitive effect between genotypes (wild-type, heterozygotes and HEG homozygotes). We show that population outcomes—elimination, suppression or loss of the HEG—depend crucially on the interaction between these ecological aspects and genetics, and explain how the HEG fitness properties, the homing rate (drive) and the insect's life-history parameters influence those outcomes.

Population Genetics: Consanguinity, Genetic Drift

1997 ◽  
pp. 549-582 ◽  
Author(s):  
Friedrich Vogel ◽  
Arno G. Motulsky
Keyword(s):  
Population Genetics ◽  
Genetic Drift

Applications of Supercomputers in Population Genetics

2015 ◽  
pp. 176-200
Author(s):  
Gerard G. Dumancas
Keyword(s):  
Population Genetics ◽  
Natural Selection ◽  
Genetic Drift ◽  
Critical Role ◽  
Allele Frequency Distribution ◽  
Modern Approach ◽  
Mathematical Discipline ◽  
Modern Evolutionary Synthesis ◽  
Changes Over Time ◽  
Over Time

Population genetics is the study of the frequency and interaction of alleles and genes in population and how this allele frequency distribution changes over time as a result of evolutionary processes such as natural selection, genetic drift, and mutation. This field has become essential in the foundation of modern evolutionary synthesis. Traditionally regarded as a highly mathematical discipline, its modern approach comprises more than the theoretical, lab, and fieldwork. Supercomputers play a critical role in the success of this field and are discussed in this chapter.

MULTILOCUS POPULATION GENETICS WITH WEAK EPISTASIS. I. EQUILIBRIUM PROPERTIES OF TWO-LOCUS TWO-ALLELE MODELS

Genetics ◽  
1985 ◽  
Vol 109 (4) ◽  
pp. 799-812
Author(s):  
Alan Hastings
Keyword(s):  
Population Genetics ◽  
Experimental Design ◽  
Recombination Rate ◽  
Allele Frequencies ◽  
Perturbation Techniques ◽  
Biological Importance ◽  
Mean Fitness ◽  
The Mean ◽  
Neutral Models

ABSTRACT Using perturbation techniques, I determine the equilibrium of two-locus two-allele models with overdominance and weak epistasis. To lowest order, the allele frequencies, the mean fitness and the covariance between heterokaryotic and homokaryotic flies arising in the Sturtevant experimental design are independent of the recombination rate, r. The disequilibrium varies as one divided by the recombination rate, in contrast to neutral models. Although the disequilibrium generated by weak epistasis is small, too small to be experimentally detected, it can be large enough to have biological importance.

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