Gene genealogy in a population of variable size

ABSTRACT The genealogical properties of a small population with continuous overlapping generations that fluctuates randomly in size are studied using a model based on a stochastic

birth–death process. The distribution of the coalescence times is presented, as well as a method for computing the expected overall length of the genealogy as a function of the individual

birth rate λ, the individual death rate µ, and the present population size. The relationship between the birth and death rates and the shape of the resulting genealogy is studied. The total

length of the genealogy is shown to be maximized when λ = µ. The joint distribution of the coalescence times is shown to be invariant in λ and µ, conditional on the current population size,

so that exponential growth of a population cannot be distinguished from exponential decline based on the shape of the resulting genealogy. The model is used to predict the probability that

all genetic variation is lost from a recent founder population. SIMILAR CONTENT BEING VIEWED BY OTHERS INFERENCE WITH SELECTION, VARYING POPULATION SIZE, AND EVOLVING POPULATION STRUCTURE:

APPLICATION OF ABC TO A FORWARD–BACKWARD COALESCENT PROCESS WITH INTERACTIONS Article 30 October 2020 GRAPH-STRUCTURED POPULATIONS ELUCIDATE THE ROLE OF DELETERIOUS MUTATIONS IN LONG-TERM

EVOLUTION Article Open access 10 March 2025 THE POPULATION GENOMICS OF ADAPTIVE LOSS OF FUNCTION Article Open access 11 February 2021 ARTICLE PDF REFERENCES * Feller, W. 1939. Die grundlagen

der volterraschen theorie des kampfes ums dasein in wahrsheinlichkeits theoretischen behandlung. _Acta Biotheoret_, 5, 1–40. Article  Google Scholar  * Griffiths, R C, and Tavaré, S. 1994.

Sampling theory for neutral alleles in a varying environment. _Phil Trans R Soc_, _B_, 344, 403–410. Article  CAS  Google Scholar  * Hudson, R R. 1990. Gene genealogies and the coalescent,

process. _Oxford Surveys Evol Biol_, 7, 1–44. Google Scholar  * Karlin, S, and McGregor, J. 1967. The number of mutant forms maintained in a population. 5th Berkeley Symposium on

Mathematical Statistics and Probability, pp. 415–438. University of California Press, Berkeley, CA. * Kendall, D G. 1948. On some modes of population growth leading to R. A. Fisher's

logarithmic series distribution. _Biometrika_, 35, 6–15. Article  CAS  PubMed  Google Scholar  * Kendall, D G. 1949. Stochastic processes and population growth. _J R Statist Soc_, _B_, 11,

230–264. Google Scholar  * Kendall, D G. 1975. Some problems in mathematical genealogy. In: Gani, J. (ed.) _Perspectives in Probability and Statistics: Papers in Honour of M S Bartlett on

the Occasion of his Sixty-Fifth Birthday_, pp. 325–348. Applied Probability Trust, New York. Google Scholar  * Kimura, M. 1969. The number of heterozygous nucleotide sites maintained in a

finite population due to steady flux of mutations. _Genetics_, 61, 893–903. CAS  PubMed  PubMed Central  Google Scholar  * Kingman, J C. 1982. On the genealogy of large populations. _J Appl

Prob_, 19A, 27–43. Article  Google Scholar  * Kuhner, M K, Yamato, J, and Felsenstein, J. 1995. Estimating effective population size and mutation rate from sequence data using

Metropolis-Hastings sampling. _Genetics_, 140, 1421–1430. CAS  PubMed  PubMed Central  Google Scholar  * Moran, P A P. 1958. The general theory of the distribution of gene frequencies. I.

Overlapping generations. II. Non-overlapping generations. _Proc R Soc_, _B_, 149, 102–116. CAS  Google Scholar  * Nee, S, Holmes, E C, Rambaut, A, and Harvey, P H. 1995. Inferring population

history from molecular phylogenies. _Phil Trans R Soc_, _B_, 349, 25–31. Article  CAS  Google Scholar  * Nee, S, May, R M, and Harvey, P H. 1994. The reconstructed evolutionary process.

_Phil Trans R Soc_ _B_, 344, 305–311. Article  CAS  Google Scholar  * Rannala, B. 1996. The sampling theory of neutral alleles in an island population of fluctuating size. _Theoret Pop

Biol_, 50, 91–104. Article  CAS  Google Scholar  * Rogers, A R, and Harpending, H. 1992. Population growth makes waves in the distribution of pairwise genetic differences. _Mol Biol Evol_,

9, 552–569. CAS  PubMed  Google Scholar  * Slatkin, M, and Hudson, R R. 1991. Pairwise comparison of mitochondrial DNA sequences in stable and exponentially growing populations. _Genetics_,

129, 555–562. CAS  PubMed  PubMed Central  Google Scholar  * Taïb, Z. 1992. _Branching Processes and Neutral Evolution_. Springer, New York. Book  Google Scholar  * Tavaré, S. 1984.

Line-of-descent and genealogical processes, and their applications in population genetics models. _Theor Pop Biol_, 26, 119–164. Article  Google Scholar  * Tavare, S. 1989. The genealogy of

the birth, death, and immigration process. In: Feldman, M. (ed.) _Mathematical Evolutionary Theory_, pp. 41–56. Princeton University Press, Princeton, NJ. Google Scholar  * Thompson, E A.

1975. _Human Evolutionary Trees_. Cambridge University Press, Cambridge. Google Scholar  * Wolfram Research. 1992. _Mathematica_, version 2.2. Wolfram Researcy, Inc., Champaign, IL. Download

references AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Department of Integrative Biology, University of California, Berkeley, CA 94720-3140, USA Bruce Rannala Authors * Bruce Rannala View

author publications You can also search for this author inPubMed Google Scholar CORRESPONDING AUTHOR Correspondence to Bruce Rannala. RIGHTS AND PERMISSIONS Reprints and permissions ABOUT

THIS ARTICLE CITE THIS ARTICLE Rannala, B. Gene genealogy in a population of variable size. _Heredity_ 78, 417–423 (1997). https://doi.org/10.1038/hdy.1997.65 Download citation * Received:

07 May 1996 * Issue Date: 01 April 1997 * DOI: https://doi.org/10.1038/hdy.1997.65 SHARE THIS ARTICLE Anyone you share the following link with will be able to read this content: Get

shareable link Sorry, a shareable link is not currently available for this article. Copy to clipboard Provided by the Springer Nature SharedIt content-sharing initiative KEYWORDS *

birth–death process * conservation genetics * founder population * gene coalescent * genetic diversity * stochastic demography