Isolation by distance in a hierarchically clustered population

1983 ◽  
Vol 20 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Stanley Sawyer ◽  
Joseph Felsenstein
Keyword(s):  
Total Population ◽  
Genetic Relatedness ◽  
Isolation By Distance ◽  
Random Mating ◽  
Physical Distance ◽  
Population Densities ◽  
Total Population Size ◽  
Biological Population ◽  
Equilibrium Probability ◽  
Different Levels

A biological population with local random mating, migration, and mutation is studied which exhibits clustering at several different levels. The migration is determined by the clustering rather than actual geographic or physical distance. Darwinian selection is assumed to be absent, and population densities are such that nearby individuals have a probability of being related. An expression is found for the equilibrium probability of genetic relatedness between any two individuals as a function of their clustering distance. Asymptotics for a small mutation rate u are discussed for both a finite number of clustering levels (and of total population size), and for an infinite number of levels. A natural example is discussed in which the probability of heterozygosity varies as u to a power times a periodic function of log(l/u).

Isolation by distance in a hierarchically clustered population

1983 ◽  
Vol 20 (01) ◽  
pp. 1-10 ◽  
Author(s):  
Stanley Sawyer ◽  
Joseph Felsenstein
Keyword(s):  
Total Population ◽  
Genetic Relatedness ◽  
Isolation By Distance ◽  
Random Mating ◽  
Physical Distance ◽  
Population Densities ◽  
Total Population Size ◽  
Biological Population ◽  
Equilibrium Probability ◽  
Different Levels

A biological population with local random mating, migration, and mutation is studied which exhibits clustering at several different levels. The migration is determined by the clustering rather than actual geographic or physical distance. Darwinian selection is assumed to be absent, and population densities are such that nearby individuals have a probability of being related. An expression is found for the equilibrium probability of genetic relatedness between any two individuals as a function of their clustering distance. Asymptotics for a small mutation rateuare discussed for both a finite number of clustering levels (and of total population size), and for an infinite number of levels. A natural example is discussed in which the probability of heterozygosity varies asuto a power times a periodic function of log(l/u).

scholarly journals Genetic relatedness reveals total population size of white sharks in eastern Australia and New Zealand

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
R. M. Hillary ◽  
M. V. Bravington ◽  
T. A. Patterson ◽  
P. Grewe ◽  
R. Bradford ◽  
...  
Keyword(s):  
New Zealand ◽  
Population Size ◽  
Total Population ◽  
Genetic Relatedness ◽  
Total Population Size ◽  
Eastern Australia

Genetic Relationships of Cory's Shearwater: Parentage, Mating Assortment, and Geographic Differentiation Revealed by DNA Fingerprinting

The Auk ◽  
2000 ◽  
Vol 117 (3) ◽  
pp. 651-662 ◽  
Author(s):  
Corinne Rabouam ◽  
Vincent Bretagnolle ◽  
Yves Bigot ◽  
Georges Periquet
Keyword(s):  
Genetic Variation ◽  
Genetic Structure ◽  
Dna Fingerprinting ◽  
Genetic Relatedness ◽  
Isolation By Distance ◽  
Genetic Relationships ◽  
Cory’S Shearwater ◽  
Genetic Structure Of Populations ◽  
The Social ◽  
Calonectris Diomedea

Abstract We used DNA fingerprinting to assess genetic structure of populations in Cory's Shearwater (Calonectris diomedea). We analyzed mates and parent-offspring relationships, as well as the amount and distribution of genetic variation within and among populations, from the level of subcolony to subspecies. We found no evidence of extrapair fertilization, confirming that the genetic breeding system matches the social system that has been observed in the species. Mates were closely related, and the level of genetic relatedness within populations was within the range usually found in inbred populations. In contrast to previous studies based on allozymes and mtDNA polymorphism, DNA fingerprinting using microsatellites revealed consistent levels of genetic differentiation among populations. However, analyzing the two subspecies separately revealed that the pattern of genetic variation among populations did not support the model of isolation by distance. Natal dispersal, as well as historic and/or demographic events, probably contributed to shape the genetic structure of populations in the species.

The Kota of the Nilgiri hills: a demographic study

1976 ◽  
Vol 8 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Aloke Kumar Ghosh
Keyword(s):  
Total Population ◽  
Random Mating ◽  
High Rate ◽  
Moderate Intensity ◽  
Biological Study ◽  
Isolated Population ◽  
Demographic Structure ◽  
Effective Population ◽  
Mating Population ◽  
The Village

A population–biological study of the Kota of the Nilgiri Hills was undertaken between May 1966 and January 1968. This paper discusses the demographic structure of the tribe and its genetic implications.The Kota is a small tribe of 1203 individuals distributed in only seven villages; it is an isolated population with a low rate of fertility and a high rate of infant mortality. The Kota is not a random mating population. The rate of consanguineous marriages is high and the coefficient of inbreeding is almost equal to the highest recorded value. Besides cousin marriages, marriage within the village is very much preferred. The admixture rate (0·29%) among the Kota is very low. The effective population size is only 28·87% of the total population. The coefficient of breeding isolation is 1·01, which indicates that genetic drift may produce important differentiation in this population. The data show that selection is acting with moderate intensity in this population.

scholarly journals Simulating the impact of vaccination rates on the initial stages of a COVID-19 outbreak in New Zealand (Aotearoa) with a stochastic model

2021 ◽  
Author(s):  
Leighton M Watson
Keyword(s):  
New Zealand ◽  
Stochastic Model ◽  
Process Model ◽  
Branching Process ◽  
Total Population ◽  
Median Number ◽  
Vaccination Rate ◽  
Vaccination Rates ◽  
The Impact ◽  
Different Levels

Aim: The August 2021 COVID-19 outbreak in Auckland has caused the New Zealand government to transition from an elimination strategy to suppression, which relies heavily on high vaccination rates in the population. As restrictions are eased and as COVID-19 leaks through the Auckland boundary, there is a need to understand how different levels of vaccination will impact the initial stages of COVID-19 outbreaks that are seeded around the country. Method: A stochastic branching process model is used to simulate the initial spread of a COVID-19 outbreak for different vaccination rates. Results: High vaccination rates are effective at minimizing the number of infections and hospitalizations. Increasing vaccination rates from 20% (approximate value at the start of the August 2021 outbreak) to 80% (approximate proposed target) of the total population can reduce the median number of infections that occur within the first four weeks of an outbreak from 1011 to 14 (25th and 75th quantiles of 545-1602 and 2-32 for V=20% and V=80%, respectively). As the vaccination rate increases, the number of breakthrough infections (infections in fully vaccinated individuals) and hospitalizations of vaccinated individuals increases. Unvaccinated individuals, however, are 3.3x more likely to be infected with COVID-19 and 25x more likely to be hospitalized. Conclusion: This work demonstrates the importance of vaccination in protecting individuals from COVID-19, preventing high caseloads, and minimizing the number of hospitalizations and hence limiting the pressure on the healthcare system.

scholarly journals Quantifying the prevalence of assortative mating in a human population

2019 ◽  
Author(s):  
Klaus Jaffe
Keyword(s):  
Assortative Mating ◽  
Genetic Relatedness ◽  
Random Mating ◽  
Human Populations ◽  
Genetic Composition ◽  
Genetic Studies ◽  
Maintenance Of Sex ◽  
Animal Populations ◽  
The Uk ◽  
First Time

AbstractFor the first time, empirical evidence allowed to construct the frequency distribution of a genetic relatedness index between the parents of about half a million individuals living in the UK. The results suggest that over 30% of the population is the product of parents mating assortatively. The rest is probably the offspring of parents matching the genetic composition of their partners randomly. High degrees of genetic relatedness between parents, i.e. extreme inbreeding, was rare. This result shows that assortative mating is likely to be highly prevalent in human populations. Thus, assuming only random mating among humans, as widely done in ecology and population genetic studies, is not an appropriate approximation to reality. The existence of assortative mating has to be accounted for. The results suggest the conclusion that both, assortative and random mating, are evolutionary stable strategies. This improved insight allows to better understand complex evolutionary phenomena, such as the emergence and maintenance of sex, the speed of adaptation, runaway adaptation, maintenance of cooperation, and many others in human and animal populations.

Two theorems on solutions of differential-difference equations and applications to epidemic theory

1967 ◽  
Vol 4 (02) ◽  
pp. 271-280 ◽  
Author(s):  
Norman C. Severo
Keyword(s):  
Differential Equation ◽  
Difference Equations ◽  
Total Population ◽  
Original System ◽  
Initial Distribution ◽  
Fixed Number ◽  
Total Population Size ◽  
Stochastic Epidemic ◽  
Iterative Solutions ◽  
General Stochastic

We present two theorems that provide simple iterative solutions of special systems of differential-difference equations. We show as examples of the theorems the simple stochastic epidemic (cf. Bailey, 1957, p. 39, and Bailey, 1963) and the general stochastic epidemic (cf. Bailey, 1957; Gani, 1965; and Siskind, 1965), in each of which we let the initial distribution of the number of uninfected susceptibles and the number of infectives be arbitrary but assume the total population size bounded. In all of the references cited above the methods of solution involve solving a corresponding partial differential equation, whereas we deal directly with the original system of ordinary differential-difference equations. Furthermore in the cited references the authors begin at time t = 0 with a population having a fixed number of uninfected susceptibles and a fixed number of infectives. For the simple stochastic epidemic with arbitrary initial distribution we provide solutions not obtainable by the results given by Bailey (1957 or 1963). For the general stochastic epidemic, if we use the results of Gani or Siskind, then the solution of the problem having an arbitrary initial distribution would involve additional steps that would sum proportionally-weighted conditional results.

scholarly journals When science mirrors life: on the origins of the Price equation

2020 ◽  
Vol 375 (1797) ◽  
pp. 20190352 ◽  
Author(s):  
Oren Harman
Keyword(s):  
Population Genetics ◽  
Genetic Relatedness ◽  
Personal Life ◽  
Price Equation ◽  
Narrow Sense ◽  
Theme Issue ◽  
Young Girls ◽  
Link Type ◽  
Mother And Daughter ◽  
Different Levels

The Price equation was a piece of abstract mathematics. What kind of a connection could it possibly have had to George Price's personal life and biography? Here, I will argue that the initial impetus for Price's foray into mathematical population genetics stemmed from a preoccupation with the origins of family, one that was born following a divorce from his wife and the abandonment of their two young girls. What is special about the Price equation is the way in which it associates statistically between two groups, a ‘mother’ and ‘daughter’ population. The association need not mean genetic relatedness in the narrow sense of direct descent, and it allows us to see selection working at different levels simultaneously, a fact that was not lost on William Hamilton. Hamilton was one of the few friends who desperately tried to save Price from falling into the abyss of depression and homelessness in the period following the publication of ‘Selection and covariance’ (Price 1928 Nature 227 , 520–521 ( doi:10.1038/227520a0 )). Viewed in this light, the Price equation assumes new meaning. This article is part of the theme issue ‘Fifty years of the Price equation’.

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