scholarly journals Modelling the spread of Wolbachia in spatially heterogeneous environments

2012 ◽  
Vol 9 (76) ◽  
pp. 3045-3054 ◽  
Author(s):  
Penelope A. Hancock ◽  
H. Charles J. Godfray
Keyword(s):  
Habitat Quality ◽  
Spatial Dynamics ◽  
Reaction Diffusion ◽  
Analytical Description ◽  
Host Population ◽  
Heterogeneous Environments ◽  
Spatial Spread ◽  
Density Dependent ◽  
Spatially Correlated ◽  
Reaction Diffusion Model

The endosymbiont Wolbachia infects a large number of insect species and is capable of rapid spread when introduced into a novel host population. The bacteria spread by manipulating their hosts' reproduction, and their dynamics are influenced by the demographic structure of the host population and patterns of contact between individuals. Reaction–diffusion models of the spatial spread of Wolbachia provide a simple analytical description of their spatial dynamics but do not account for significant details of host population dynamics. We develop a metapopulation model describing the spatial dynamics of Wolbachia in an age-structured host insect population regulated by juvenile density-dependent competition. The model produces similar dynamics to the reaction–diffusion model in the limiting case where the host's habitat quality is spatially homogeneous and Wolbachia has a small effect on host fitness. When habitat quality varies spatially, Wolbachia spread is usually much slower, and the conditions necessary for local invasion are strongly affected by immigration of insects from surrounding regions. Spread is most difficult when variation in habitat quality is spatially correlated. The results show that spatial variation in the density-dependent competition experienced by juvenile host insects can strongly affect the spread of Wolbachia infections, which is important to the use of Wolbachia to control insect vectors of human disease and other pests.

scholarly journals Spatial gene drives and pushed genetic waves

2017 ◽  
Author(s):  
Hidenori Tanaka ◽  
Howard A. Stone ◽  
David R. Nelson
Keyword(s):  
Reaction Diffusion ◽  
Two Dimensions ◽  
Wild Type Allele ◽  
Gene Drive ◽  
Wild Type ◽  
Wave Regime ◽  
Spatial Spread ◽  
Type Allele ◽  
Reaction Diffusion Model ◽  
Gene Drives

Gene drives have the potential to rapidly replace a harmful wild-type allele with a gene drive allele engineered to have desired functionalities. However, an accidental or premature release of a gene drive construct to the natural environment could damage an ecosystem irreversibly. Thus, it is important to understand the spatiotemporal consequences of the super-Mendelian population genetics prior to potential applications. Here, we employ a reaction-diffusion model for sexually reproducing diploid organisms to study how a locally introduced gene drive allele spreads to replace the wild-type allele, even though it posses a selective disadvantages> 0. Using methods developed by N. Barton and collaborators, we show that socially responsible gene drives require 0.5 <s< 0.697, a rather narrow range. In this “pushed wave” regime, the spatial spreading of gene drives will be initiated only when the initial frequency distribution is above a threshold profile called “critical propagule”, which acts as a safeguard against accidental release. We also study how the spatial spread of the pushed wave can be stopped by making gene drives uniquely vulnerable (“sensitizing drive”) in a way that is harmless for a wild-type allele. Finally, we show that appropriately sensitized drives in two dimensions can be stopped even by imperfect barriers perforated by a series of gaps.

scholarly journals Density-dependent quiescence in glioma invasion: instability in a simple reaction–diffusion model for the migration/proliferation dichotomy

2012 ◽  
Vol 6 (sup1) ◽  
pp. 54-71 ◽  
Author(s):  
Kara Pham ◽  
Arnaud Chauviere ◽  
Haralambos Hatzikirou ◽  
Xiangrong Li ◽  
Helen M. Byrne ◽  
...  
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Glioma Invasion ◽  
Density Dependent ◽  
Simple Reaction ◽  
Reaction Diffusion Model

scholarly journals Spatial gene drives and pushed genetic waves

2017 ◽  
Vol 114 (32) ◽  
pp. 8452-8457 ◽  
Author(s):  
Hidenori Tanaka ◽  
Howard A. Stone ◽  
David R. Nelson
Keyword(s):  
Reaction Diffusion ◽  
Two Dimensions ◽  
Wild Type Allele ◽  
Gene Drive ◽  
Wild Type ◽  
Wave Regime ◽  
Spatial Spread ◽  
Type Allele ◽  
Reaction Diffusion Model ◽  
Gene Drives

Gene drives have the potential to rapidly replace a harmful wild-type allele with a gene drive allele engineered to have desired functionalities. However, an accidental or premature release of a gene drive construct to the natural environment could damage an ecosystem irreversibly. Thus, it is important to understand the spatiotemporal consequences of the super-Mendelian population genetics before potential applications. Here, we use a reaction–diffusion model for sexually reproducing diploid organisms to study how a locally introduced gene drive allele spreads to replace the wild-type allele, although it possesses a selective disadvantages> 0. Using methods developed by Barton and collaborators, we show that socially responsible gene drives require 0.5 <s< 0.697, a rather narrow range. In this “pushed wave” regime, the spatial spreading of gene drives will be initiated only when the initial frequency distribution is above a threshold profile called “critical propagule,” which acts as a safeguard against accidental release. We also study how the spatial spread of the pushed wave can be stopped by making gene drives uniquely vulnerable (“sensitizing drive”) in a way that is harmless for a wild-type allele. Finally, we show that appropriately sensitized drives in two dimensions can be stopped, even by imperfect barriers perforated by a series of gaps.

A study of nitric oxide dynamics in a growing biofilm using a density dependent reaction-diffusion model

2020 ◽  
Vol 485 ◽  
pp. 110053 ◽  
Author(s):  
Maryam Ghasemi ◽  
Benjamin Jenkins ◽  
Andrew C. Doxey ◽  
Sivabal Sivaloganathan
Keyword(s):  
Nitric Oxide ◽  
Diffusion Model ◽  
Reaction Diffusion ◽  
Density Dependent ◽  
Reaction Diffusion Model

scholarly journals Nonlinear density-dependent diffusion for competing species interactions: Large-time asymptotic behaviour

1984 ◽  
Vol 27 (2) ◽  
pp. 131-144 ◽  
Author(s):  
Anthony W. Leung
Keyword(s):  
Species Interactions ◽  
General Setting ◽  
Reaction Diffusion ◽  
Diffusion Reaction ◽  
General Situation ◽  
Competing Species ◽  
Density Dependent ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Reaction Diffusion Model

In many biological diffusion-reaction studies, it was found that one should include the effect of density dependent rates, drift terms and spatially varying growth rates, in order to obtain more accurate results. (See e.g. [7],[10], [8] , [3]). On the other hand, many recent mathematical results on reaction-diffusion systems do not include such general setting. This article investigates the behaviour of competing-species reaction-diffusion model under this more general situation. Efforts are made to obtain results concerning coexistence, survival and extinction, by methods similar to that in [5], [6].

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