O problema do tempo de espera em um modelo de população hominini

quinta-feira, setembro 17, 2015

The waiting time problem in a model hominin population

John Sanford1*, Wesley Brewer2, Franzine Smith3 and John Baumgardner4

* Corresponding author: John Sanford jcs21@cornell.edu

Author Affiliations

1 Horticulture Dept., NYSAES, Cornell University, Geneva 14456, NY, USA

2 Fluid Physics International, Houston 77266, TX, USA

3 FMS Foundation, Inc., Waterloo 13165, NY, USA

4 Los Alamos National Lab (retired), Los Alamos 87545, NM, USA

Theoretical Biology and Medical Modelling 2015, 12:18 doi:10.1186/s12976-015-0016-z

Received: 8 July 2015

Accepted: 7 September 2015

Published: 17 September 2015

© 2015 Sanford et al. 

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

Source/Fonte: R. M. E. Sabbatini



Functional information is normally communicated using specific, context-dependent strings of symbolic characters. This is true within the human realm (texts and computer programs), and also within the biological realm (nucleic acids and proteins). In biology, strings of nucleotides encode much of the information within living cells. How do such information-bearing nucleotide strings arise and become established?


This paper uses comprehensive numerical simulation to understand what types of nucleotide strings can realistically be established via the mutation/selection process, given a reasonable timeframe. The program Mendel’s Accountant realistically simulates the mutation/selection process, and was modified so that a starting string of nucleotides could be specified, and a corresponding target string of nucleotides could be specified. We simulated a classic pre-human hominin population of at least 10,000 individuals, with a generation time of 20 years, and with very strong selection (50 % selective elimination). Random point mutations were generated within the starting string. Whenever an instance of the target string arose, all individuals carrying the target string were assigned a specified reproductive advantage. When natural selection had successfully amplified an instance of the target string to the point of fixation, the experiment was halted, and the waiting time statistics were tabulated. Using this methodology we tested the effect of mutation rate, string length, fitness benefit, and population size on waiting time to fixation.


Biologically realistic numerical simulations revealed that a population of this type required inordinately long waiting times to establish even the shortest nucleotide strings. To establish a string of two nucleotides required on average 84 million years. To establish a string of five nucleotides required on average 2 billion years. We found that waiting times were reduced by higher mutation rates, stronger fitness benefits, and larger population sizes. However, even using the most generous feasible parameters settings, the waiting time required to establish any specific nucleotide string within this type of population was consistently prohibitive.


We show that the waiting time problem is a significant constraint on the macroevolution of the classic hominin population. Routine establishment of specific beneficial strings of two or more nucleotides becomes very problematic.

Keywords: Biological information; Text strings; Nucleotide strings; Waiting time; Functional threshold; Evolution; Mutation density; Numerical simulation; Mendel’s Accountant