---
_id: '626'
abstract:
- lang: eng
text: 'Our focus here is on the infinitesimal model. In this model, one or several
quantitative traits are described as the sum of a genetic and a non-genetic component,
the first being distributed within families as a normal random variable centred
at the average of the parental genetic components, and with a variance independent
of the parental traits. Thus, the variance that segregates within families is
not perturbed by selection, and can be predicted from the variance components.
This does not necessarily imply that the trait distribution across the whole population
should be Gaussian, and indeed selection or population structure may have a substantial
effect on the overall trait distribution. One of our main aims is to identify
some general conditions on the allelic effects for the infinitesimal model to
be accurate. We first review the long history of the infinitesimal model in quantitative
genetics. Then we formulate the model at the phenotypic level in terms of individual
trait values and relationships between individuals, but including different evolutionary
processes: genetic drift, recombination, selection, mutation, population structure,
…. We give a range of examples of its application to evolutionary questions related
to stabilising selection, assortative mating, effective population size and response
to selection, habitat preference and speciation. We provide a mathematical justification
of the model as the limit as the number M of underlying loci tends to infinity
of a model with Mendelian inheritance, mutation and environmental noise, when
the genetic component of the trait is purely additive. We also show how the model
generalises to include epistatic effects. We prove in particular that, within
each family, the genetic components of the individual trait values in the current
generation are indeed normally distributed with a variance independent of ancestral
traits, up to an error of order 1∕M. Simulations suggest that in some cases the
convergence may be as fast as 1∕M.'
author:
- first_name: Nicholas H
full_name: Barton, Nicholas H
id: 4880FE40-F248-11E8-B48F-1D18A9856A87
last_name: Barton
orcid: 0000-0002-8548-5240
- first_name: Alison
full_name: Etheridge, Alison
last_name: Etheridge
- first_name: Amandine
full_name: Véber, Amandine
last_name: Véber
citation:
ama: 'Barton NH, Etheridge A, Véber A. The infinitesimal model: Definition derivation
and implications. Theoretical Population Biology. 2017;118:50-73. doi:10.1016/j.tpb.2017.06.001'
apa: 'Barton, N. H., Etheridge, A., & Véber, A. (2017). The infinitesimal model:
Definition derivation and implications. Theoretical Population Biology.
Academic Press. https://doi.org/10.1016/j.tpb.2017.06.001'
chicago: 'Barton, Nicholas H, Alison Etheridge, and Amandine Véber. “The Infinitesimal
Model: Definition Derivation and Implications.” Theoretical Population Biology.
Academic Press, 2017. https://doi.org/10.1016/j.tpb.2017.06.001.'
ieee: 'N. H. Barton, A. Etheridge, and A. Véber, “The infinitesimal model: Definition
derivation and implications,” Theoretical Population Biology, vol. 118.
Academic Press, pp. 50–73, 2017.'
ista: 'Barton NH, Etheridge A, Véber A. 2017. The infinitesimal model: Definition
derivation and implications. Theoretical Population Biology. 118, 50–73.'
mla: 'Barton, Nicholas H., et al. “The Infinitesimal Model: Definition Derivation
and Implications.” Theoretical Population Biology, vol. 118, Academic Press,
2017, pp. 50–73, doi:10.1016/j.tpb.2017.06.001.'
short: N.H. Barton, A. Etheridge, A. Véber, Theoretical Population Biology 118 (2017)
50–73.
date_created: 2018-12-11T11:47:34Z
date_published: 2017-12-01T00:00:00Z
date_updated: 2021-01-12T08:06:50Z
day: '01'
ddc:
- '576'
department:
- _id: NiBa
doi: 10.1016/j.tpb.2017.06.001
ec_funded: 1
file:
- access_level: open_access
checksum: 7dd02bfcfe8f244f4a6c19091aedf2c8
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:12:45Z
date_updated: 2020-07-14T12:47:25Z
file_id: '4964'
file_name: IST-2017-908-v1+1_1-s2.0-S0040580917300886-main_1_.pdf
file_size: 1133924
relation: main_file
file_date_updated: 2020-07-14T12:47:25Z
has_accepted_license: '1'
intvolume: ' 118'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 50 - 73
project:
- _id: 25B07788-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '250152'
name: Limits to selection in biology and in evolutionary computation
publication: Theoretical Population Biology
publication_identifier:
issn:
- '00405809'
publication_status: published
publisher: Academic Press
publist_id: '7169'
pubrep_id: '908'
quality_controlled: '1'
scopus_import: 1
status: public
title: 'The infinitesimal model: Definition derivation and implications'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 118
year: '2017'
...
---
_id: '952'
abstract:
- lang: eng
text: A novel strategy for controlling the spread of arboviral diseases such as
dengue, Zika and chikungunya is to transform mosquito populations with virus-suppressing
Wolbachia. In general, Wolbachia transinfected into mosquitoes induce fitness
costs through lower viability or fecundity. These maternally inherited bacteria
also produce a frequency-dependent advantage for infected females by inducing
cytoplasmic incompatibility (CI), which kills the embryos produced by uninfected
females mated to infected males. These competing effects, a frequency-dependent
advantage and frequency-independent costs, produce bistable Wolbachia frequency
dynamics. Above a threshold frequency, denoted pˆ, CI drives fitness-decreasing
Wolbachia transinfections through local populations; but below pˆ, infection frequencies
tend to decline to zero. If pˆ is not too high, CI also drives spatial spread
once infections become established over sufficiently large areas. We illustrate
how simple models provide testable predictions concerning the spatial and temporal
dynamics of Wolbachia introductions, focusing on rate of spatial spread, the shape
of spreading waves, and the conditions for initiating spread from local introductions.
First, we consider the robustness of diffusion-based predictions to incorporating
two important features of wMel-Aedes aegypti biology that may be inconsistent
with the diffusion approximations, namely fast local dynamics induced by complete
CI (i.e., all embryos produced from incompatible crosses die) and long-tailed,
non-Gaussian dispersal. With complete CI, our numerical analyses show that long-tailed
dispersal changes wave-width predictions only slightly; but it can significantly
reduce wave speed relative to the diffusion prediction; it also allows smaller
local introductions to initiate spatial spread. Second, we use approximations
for pˆ and dispersal distances to predict the outcome of 2013 releases of wMel-infected
Aedes aegypti in Cairns, Australia, Third, we describe new data from Ae. aegypti
populations near Cairns, Australia that demonstrate long-distance dispersal and
provide an approximate lower bound on pˆ for wMel in northeastern Australia. Finally,
we apply our analyses to produce operational guidelines for efficient transformation
of vector populations over large areas. We demonstrate that even very slow spatial
spread, on the order of 10-20 m/month (as predicted), can produce area-wide population
transformation within a few years following initial releases covering about 20-30%
of the target area.
article_processing_charge: No
author:
- first_name: Michael
full_name: Turelli, Michael
last_name: Turelli
- first_name: Nicholas H
full_name: Barton, Nicholas H
id: 4880FE40-F248-11E8-B48F-1D18A9856A87
last_name: Barton
orcid: 0000-0002-8548-5240
citation:
ama: 'Turelli M, Barton NH. Deploying dengue-suppressing Wolbachia: Robust models
predict slow but effective spatial spread in Aedes aegypti. Theoretical Population
Biology. 2017;115:45-60. doi:10.1016/j.tpb.2017.03.003'
apa: 'Turelli, M., & Barton, N. H. (2017). Deploying dengue-suppressing Wolbachia:
Robust models predict slow but effective spatial spread in Aedes aegypti. Theoretical
Population Biology. Elsevier. https://doi.org/10.1016/j.tpb.2017.03.003'
chicago: 'Turelli, Michael, and Nicholas H Barton. “Deploying Dengue-Suppressing
Wolbachia: Robust Models Predict Slow but Effective Spatial Spread in Aedes Aegypti.”
Theoretical Population Biology. Elsevier, 2017. https://doi.org/10.1016/j.tpb.2017.03.003.'
ieee: 'M. Turelli and N. H. Barton, “Deploying dengue-suppressing Wolbachia: Robust
models predict slow but effective spatial spread in Aedes aegypti,” Theoretical
Population Biology, vol. 115. Elsevier, pp. 45–60, 2017.'
ista: 'Turelli M, Barton NH. 2017. Deploying dengue-suppressing Wolbachia: Robust
models predict slow but effective spatial spread in Aedes aegypti. Theoretical
Population Biology. 115, 45–60.'
mla: 'Turelli, Michael, and Nicholas H. Barton. “Deploying Dengue-Suppressing Wolbachia:
Robust Models Predict Slow but Effective Spatial Spread in Aedes Aegypti.” Theoretical
Population Biology, vol. 115, Elsevier, 2017, pp. 45–60, doi:10.1016/j.tpb.2017.03.003.'
short: M. Turelli, N.H. Barton, Theoretical Population Biology 115 (2017) 45–60.
date_created: 2018-12-11T11:49:22Z
date_published: 2017-06-01T00:00:00Z
date_updated: 2023-09-22T10:02:21Z
day: '01'
ddc:
- '576'
department:
- _id: NiBa
doi: 10.1016/j.tpb.2017.03.003
external_id:
pmid:
- '28411063'
file:
- access_level: open_access
checksum: 9aeff86fa7de69f7a15cf4fc60d57d01
content_type: application/pdf
creator: dernst
date_created: 2019-04-17T06:39:45Z
date_updated: 2020-07-14T12:48:16Z
file_id: '6327'
file_name: 2017_TheoreticalPopulationBio_Turelli.pdf
file_size: 2073856
relation: main_file
file_date_updated: 2020-07-14T12:48:16Z
has_accepted_license: '1'
intvolume: ' 115'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Submitted Version
page: 45 - 60
pmid: 1
publication: Theoretical Population Biology
publication_identifier:
issn:
- '00405809'
publication_status: published
publisher: Elsevier
publist_id: '6463'
pubrep_id: '972'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Deploying dengue-suppressing Wolbachia: Robust models predict slow but effective
spatial spread in Aedes aegypti'
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 115
year: '2017'
...