Speciation and the “shifting balance” in a continuous population

Rouhani, S.; Barton, Nick

doi:10.1016/0040-5809(87)90016-5

Cited by 76 publications

(87 citation statements)

References 42 publications

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“…a pattern of long-term hybrid zone stasis followed by an abrupt transition where the selected type suddenly gains a foothold, mushrooms in number, and supplants the two previously existing species as it spreads to fixation. The phenomenon is reminiscent of the appearance and spread of a 'critical bubble' in a previously uniform, continuous population (Rouhani & Barton, 1987). A key factor underlying this change in dynamics seems to be the number of individuals of the optimal type present in the population.…”

Section: Discussionmentioning

confidence: 99%

A theoretical assessment of recombinational speciation

1995

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Using a computer simulation, we have examined the dynamics of recombinational speciation, a potentially rapid mode of evolution dependent on chromosomal reassortment in populations of partially sterile interspecific hybrids. We describe how various parameters affect the time required for a new recombinant species to become established within the setting of a spatially structured hybrid zone. Our results indicate that recombinational speciation is most likely to occur where (1) the hybrid zone interface is long, (2) the organisms involved are predominantly selfing, (3) the hybrids are relatively fertile, and (4) the number of differences in chromosomal structure between the parental species is small. The speciation dynamics are characterized by long-term stasis followed by an abrupt transition to a new reproductively isolated type. The results are largely the same whether the nascent recombinant species is favoured by a fertility or a viability advantage. Recombinational speciation, like polyploidy, appears to be a feasible mechanism for sympatric speciation in plants.

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Section: Discussionmentioning

confidence: 99%

A theoretical assessment of recombinational speciation

1995

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“…Although the critical bubble has not been analytically determined for two dimensions, it can be approximated as ( ), corresponding to the limit at whicĥ p r 1/2 a r 0 invasion is slowest. As shown by Rouhani and Barton (1987), for small a, the bubble is large, with scaled radius, denoted , proportional to and cross section pro- * R 1/a portional to . This is roughly a radially sym- * (Lewis and Kareiva [1993] Ϫ log (a) also show that the critical radius for successful introduction approaches infinity at the rate .)…”

Section: Critical Bubble Versus Critical Propagule Size In Two Dimensmentioning

confidence: 99%

“…Integrating their formula for the critical bubble, Rouhani and Barton (1987) obtained a function that is pro-M(a) portional to the total number that must be introduced to start a wave of fixation, assuming the critical bubble as the initial configuration,…”

Section: One Dimension: "Critical Bubbles" Versus Initial Conditions mentioning

confidence: 99%

“…In one dimension, Rouhani and Barton (1987) explicitly found the critical bubble by using a method analogous to one used by Haldane (1948) in his pioneering cline article (see app. C).…”

Section: One Dimension: "Critical Bubbles" Versus Initial Conditions mentioning

confidence: 99%

“…In other words, at what rate will a critical propagule be established by chance? For disruptive selection on a quantitative trait with fixed genetic variance, Rouhani and Barton (1987) analytically approximated the rate of shifts in a two-dimensional population as , where Nb is the neighbor-∼ exp [ϪNb/(6a)] hood size. Thus, stochastic shifts are likely only when Nb is small and the selective asymmetry high (i.e., so a ∼ 1 that ).…”

Section: Stochastic Effects From Finite Population Sizes and Density mentioning

confidence: 99%

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Spatial Waves of Advance with Bistable Dynamics: Cytoplasmic and Genetic Analogues of Allee Effects

Barton

Turelli

2011

The American Naturalist

202

400

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. abstract: Unlike unconditionally advantageous "Fisherian" variants that tend to spread throughout a species range once introduced anywhere, "bistable" variants, such as chromosome translocations, have two alternative stable frequencies, absence and (near) fixation. Analogous to populations with Allee effects, bistable variants tend to increase locally only once they become sufficiently common, and their spread depends on their rate of increase averaged over all frequencies. Several proposed manipulations of insect populations, such as using Wolbachia or "engineered underdominance" to suppress vector-borne diseases, produce bistable rather than Fisherian dynamics. We synthesize and extend theoretical analyses concerning three features of their spatial behavior: rate of spread, conditions to initiate spread from a localized introduction, and wave stopping caused by variation in population densities or dispersal rates. Unlike Fisherian variants, bistable variants tend to spread spatially only for particular parameter combinations and initial conditions. Wave initiation requires introduction over an extended region, while subsequent spatial spread is slower than for Fisherian waves and can easily be halted by local spatial inhomogeneities. We present several new results, including robust sufficient conditions to initiate (and stop) spread, using a one-parameter cubic approximation applicable to several models. The results have both basic and applied implications. The University of Chicago Press and

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