Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

When Can One Detect Overdominant Selection in the Infinite-Alleles Model?

Paul Joyce, Stephen M. Krone and Thomas G. Kurtz
The Annals of Applied Probability
Vol. 13, No. 1 (Feb., 2003), pp. 181-212
Stable URL: http://www.jstor.org/stable/1193141
Page Count: 32
  • Read Online (Free)
  • Download ($19.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
When Can One Detect Overdominant Selection in the Infinite-Alleles Model?
Preview not available

Abstract

One of the goals of this paper is to show that the infinite-alleles model with overdominant selection "looks like" the neutral infinite-alleles model when the selection intensity and mutation rate get large together. This rather surprising behavior was noticed by Gillespie (1999) in simulations. To make rigorous and refine Gillespie's observations, we analyze the limiting behavior of the likelihood ratio of the stationary distributions for the model under selection and neutrality, as the mutation rate and selection intensity go to ∞ together in a specified manner. In particular, we show that the likelihood ratio tends to 1 as the mutation rate goes to ∞, provided the selection intensity is a multiple of the mutation rate raised to a power less than 3/2. (Gillespie's simulations correspond to the power 1.) This implies that we cannot distinguish between the two models in this setting. Conversely, if the selection intensity grows like a multiple of the mutation rate raised to a power greater than 3/2, selection can be detected; that is, the likelihood ratio tends to 0 under neutrality and ∞ under selection. We also determine the nontrivial limit distributions in the case of the critical exponent 3/2. We further analyze the limiting behavior when the exponent is less than 3/2 by determining the rate at which the likelihood ratio converges to 1 and by developing results for the distributions of finite samples.

Page Thumbnails

  • Thumbnail: Page 
181
    181
  • Thumbnail: Page 
182
    182
  • Thumbnail: Page 
183
    183
  • Thumbnail: Page 
184
    184
  • Thumbnail: Page 
185
    185
  • Thumbnail: Page 
186
    186
  • Thumbnail: Page 
187
    187
  • Thumbnail: Page 
188
    188
  • Thumbnail: Page 
189
    189
  • Thumbnail: Page 
190
    190
  • Thumbnail: Page 
191
    191
  • Thumbnail: Page 
192
    192
  • Thumbnail: Page 
193
    193
  • Thumbnail: Page 
194
    194
  • Thumbnail: Page 
195
    195
  • Thumbnail: Page 
196
    196
  • Thumbnail: Page 
197
    197
  • Thumbnail: Page 
198
    198
  • Thumbnail: Page 
199
    199
  • Thumbnail: Page 
200
    200
  • Thumbnail: Page 
201
    201
  • Thumbnail: Page 
202
    202
  • Thumbnail: Page 
203
    203
  • Thumbnail: Page 
204
    204
  • Thumbnail: Page 
205
    205
  • Thumbnail: Page 
206
    206
  • Thumbnail: Page 
207
    207
  • Thumbnail: Page 
208
    208
  • Thumbnail: Page 
209
    209
  • Thumbnail: Page 
210
    210
  • Thumbnail: Page 
211
    211
  • Thumbnail: Page 
212
    212