A stochastic model for speciation by mating preferences. (English) Zbl 1390.60282
Summary: Mechanisms leading to speciation are a major focus in evolutionary biology. In this paper, we present and study a stochastic model of population where individuals, with type \(a\) or \(A\), are equivalent from ecological, demographical and spatial points of view, and differ only by their mating preference: two individuals with the same genotype have a higher probability to mate and produce a viable offspring. The population is subdivided in several patches and individuals may migrate between them. We show that mating preferences by themselves, even if they are very small, are enough to entail reproductive isolation between patches, and we provide the time needed for this isolation to occur as a function of the carrying capacity. Our results rely on a fine study of the stochastic process and of its deterministic limit in large population, which is given by a system of coupled nonlinear differential equations. Besides, we propose several generalisations of our model, and prove that our findings are
robust for those generalisations.
MSC:
| 60J27 | Continuous-time Markov processes on discrete state spaces |
| 37N25 | Dynamical systems in biology |
| 92D40 | Ecology |
Keywords:
birth and death process with competition; mating preference; reproductive isolation; dynamical systemsReferences:
| [1] | Abu Awad D, Billiard S (2017) The double edged sword: the demographic consequences of the evolution of self-fertilization. Evolution 71(5):1178-1190 · doi:10.1111/evo.13222 |
| [2] | Akerman A, Bürger R (2014) The consequences of gene flow for local adaptation and differentiation: a two-locus two-deme model. J Math Biol 68(5):1135-1198 · Zbl 1302.92085 · doi:10.1007/s00285-013-0660-z |
| [3] | Athreya KB, Ney PE (1972) Branching processes. Springer, Berlin · Zbl 0259.60002 |
| [4] | Avise JC, Mank JE (2009) Evolutionary perspectives on hermaphroditism in fishes. Sex Dev 3(2-3):152-163 · doi:10.1159/000223079 |
| [5] | Bank C, Bürger R, Hermisson J (2012) The limits to parapatric speciation: Dobzhansky-Muller incompatibilities in a continent-island model. Genetics 191(3):845-863 · doi:10.1534/genetics.111.137513 |
| [6] | Bolker B, Pacala SW (1997) Using moment equations to understand stochastically driven spatial pattern formation in ecological systems. Theor Popul Biol 52(3):179-197. John Wiley & Sons, New York · Zbl 0890.92020 |
| [7] | Boughman JW (2001) Divergent sexual selection enhances reproductive isolation in sticklebacks. Nature 411(6840):944-948 · doi:10.1038/35082064 |
| [8] | Boul KE, Funk WC, Darst CR, Cannatella DC, Ryan MJ (2007) Sexual selection drives speciation in an amazonian frog. Proc R Soc Lond B Biol Sci 274(1608):399-406 · doi:10.1098/rspb.2006.3736 |
| [9] | Bürger R, Schneider KA (2006) Intraspecific competitive divergence and convergence under assortative mating. Am Nat 167(2):190-205 · doi:10.1086/499375 |
| [10] | Champagnat N (2006) A microscopic interpretation for adaptive dynamics trait substitution sequence models. Stoch Process Appl 116(8):1127-1160 · Zbl 1100.60055 · doi:10.1016/j.spa.2006.01.004 |
| [11] | Champagnat N, Ferrière R, Méléard S (2006) Unifying evolutionary dynamics: from individual stochastic processes to macroscopic models. Theor Popul Biol 69(3):297-321 · Zbl 1118.92039 · doi:10.1016/j.tpb.2005.10.004 |
| [12] | Chaput-Bardy A, Grégoire A, Baguette M, Pagano A, Secondi J (2010) Condition and phenotype-dependent dispersal in a damselfly, Calopteryx splendens. PLoS ONE 5(5):e10.694 · doi:10.1371/journal.pone.0010694 |
| [13] | Chicone C (2006) Ordinary differential equations with applications, 2nd edn. Springer, New York. doi:10.1007/0-387-35794-7 · Zbl 1120.34001 |
| [14] | Clobert J, Danchin E, Dhondt AA, Nichols JD (2001) Dispersal. Oxford University Press, Oxford |
| [15] | Collet P, Méléard S, Metz JAJ (2013) A rigorous model study of the adaptive dynamics of mendelian diploids. J Math Biol 67(3):569-607 · Zbl 1300.92075 |
| [16] | Coron C (2015) Slow-fast stochastic diffusion dynamics and quasi-stationarity for diploid populations with varying size. J Math Biol 72(1-2):1-32 |
| [17] | Coron C, Méléard S, Porcher E, Robert A (2013) Quantifying the mutational meltdown in diploid populations. Am Nat 181(5):623-636 · doi:10.1086/670022 |
| [18] | Costa M, Hauzy C, Loeuille N, Méléard S (2015) Stochastic eco-evolutionary model of a prey-predator community. J Math Biol 72(3):573-622 · Zbl 1335.60159 · doi:10.1007/s00285-015-0895-y |
| [19] | Darwin C (1871) The descent of man, and selection in relation to sex. Murray, London · doi:10.5962/bhl.title.110063 |
| [20] | Dieckmann, U.; Law, R.; Dieckmann, U. (ed.); Law, R. (ed.); Metz, JAJ (ed.), Relaxation projections and the method of moments, 412-455 (2000), Cambridge · doi:10.1017/CBO9780511525537.025 |
| [21] | Ethier SN, Kurtz TG (1986) Markov processes: characterization and convergence. Wiley, New York · Zbl 0592.60049 |
| [22] | Fournier N, Méléard S (2004) A microscopic probabilistic description of a locally regulated population and macroscopic approximations. Ann Appl Probab 14(4):1880-1919 · Zbl 1060.92055 · doi:10.1214/105051604000000882 |
| [23] | Freidlin M, Wentzell AD (1984) Random perturbations of dynamical systems, vol 260. Springer, New York · Zbl 0522.60055 |
| [24] | Gavrilets S (2003) Perspective: models of speciation: what have we learned in 40 years? Evolution 57(10):2197-2215 · doi:10.1111/j.0014-3820.2003.tb00233.x |
| [25] | Gavrilets S (2004) Fitness landscapes and the origin of species. Princeton University Press, Princeton |
| [26] | Gavrilets S (2014) Models of speciation: where are we now? J Hered 105(S1):743-755 · doi:10.1093/jhered/esu045 |
| [27] | Gavrilets S, Boake CRB (1998) On the evolution of premating isolation after a founder event. Am Nat 152(5):706-716 · doi:10.1086/286201 |
| [28] | Griffiths AJF, Miller JH, Suzuki DT, Lewontin RC, Gelbart WM (2000) An introduction to genetic analysis, 7th edn. W.H. Freeman, New-York |
| [29] | Haesler MP, Seehausen O (2005) Inheritance of female mating preference in a sympatric sibling species pair of Lake Victoria cichlids: implications for speciation. Proc R Soc Lond B Biol Sci 272(1560):237-245 · doi:10.1098/rspb.2004.2946 |
| [30] | Herrero M (2003) Male and female synchrony and the regulation of mating in flowering plants. Philos Trans R Soc B Biol Sci 358:1019-1024 · doi:10.1098/rstb.2003.1285 |
| [31] | Higashi M, Takimoto G, Yamamura N (1999) Sympatric speciation by sexual selection. Nature 402(6761):523-526 · doi:10.1038/990087 |
| [32] | Hollocher H, Ting CT, Pollack F, Wu CI (1997) Incipient speciation by sexual isolation in drosophila melanogaster: variation in mating preference and correlation between sexes. Evolution 51(4):1175-1181 |
| [33] | Höner OP, Wachter B, East ML, Streich WJ, Wilhelm K, Burke T, Hofer H (2007) Female mate-choice drives the evolution of male-biased dispersal in a social mammal. Nature 448:797-802 · doi:10.1038/nature06040 |
| [34] | Jiang Y, Bolnick DI, Kirkpatrick M (2013) Assortative mating in animals. Am Nat 181(6):E125-E138 · doi:10.1086/670160 |
| [35] | Jones AG, Ratterman NL (2009) Mate choice and sexual selection: what have we learned since darwin? PNAS 106(1):10,001-10,008 · doi:10.1073/pnas.0901129106 |
| [36] | Kirkpatrick M (1982) Sexual selection and the evolution of female choice. Evolution 41:1-12 · doi:10.1111/j.1558-5646.1982.tb05003.x |
| [37] | Kondrashov AS, Shpak M (1998) On the origin of species by means of assortative mating. Proc R Soc Lond B Biol Sci 265(1412):2273-2278 · doi:10.1098/rspb.1998.0570 |
| [38] | Kopp M, Hermisson J (2008) Competitive speciation and costs of choosiness. J Evolut Biol 21:1005-1023 · doi:10.1111/j.1420-9101.2008.01547.x |
| [39] | Lande R (1981) Models of speciation by sexual selection on polygenic traits. Proc Natl Acad Sci 78(6):3721-3725 · doi:10.1073/pnas.78.6.3721 |
| [40] | Lande R, Kirkpatrick M (1988) Ecological speciation by sexual selection. J Theor Biol 133(1):85-98 · doi:10.1016/S0022-5193(88)80026-2 |
| [41] | LaSalle JP (1960) Some extensions of Liapunov’s second method. IRE Trans Circuit Theory 7(4):520-527 · doi:10.1109/TCT.1960.1086720 |
| [42] | Leman H (2016) Convergence of an infinite dimensional stochastic process to a spatially structured trait substitution sequence. Stoch Partial Differ Equ Anal Comput 4(4):791-826 · Zbl 1387.60117 |
| [43] | Matessi C, Gimelfarb A, Gavrilets S (2002) Long-term buildup of reproductive isolation promoted by disruptive selection: how far does it go? Selection 2(1-2):41-64 · doi:10.1556/Select.2.2001.1-2.4 |
| [44] | McLain DK, Boromisa RD (1987) Male choice, fighting ability, assortative mating and the intensity of sexual selection in the milkweed longhorn beetle, Tetraopes tetraophthalmus (coleoptera, cerambycidae). Behav Ecol Sociobiol 20(4):239-246 · doi:10.1007/BF00292176 |
| [45] | Mendelson TC, Shaw KL (2005) Sexual behaviour: rapid speciation in an arthropod. Nature 433(7024):375-376 · doi:10.1038/433375a |
| [46] | Merrill RM, Wallbank RWR, Bull V, Salazar PCA, Mallet J, Stevens M, Jiggins CD (2012) Disruptive ecological selection on a mating cue. Proc R Soc Lond B Biol Sci 279(1749):4907-4913 · doi:10.1098/rspb.2012.1968 |
| [47] | M’Gonigle LK, Mazzucco R, Otto SP, Dieckmann U (2012) Sexual selection enables long-term coexistence despite ecological equivalence. Nature 484(7395):506-509 · doi:10.1038/nature10971 |
| [48] | Nei M (1975) Molecular population genetics and evolution. North-Holland Publishing Company, Amsterdam |
| [49] | Neukirch R, Bovier A (2016) Survival of a recessive allele in a mendelian diploid model. J Math Biol 75(1):1-54 · Zbl 1370.92093 |
| [50] | Otte D (1989) Speciation in hawaiian crickets. In: Otte D, Endler JA (eds) Speciation and its consequences. Sinauer, Sunderland, pp 482-526 · Zbl 1100.60055 |
| [51] | Payne RJH, Krakauer DC (1997) Sexual selection, space, and speciation. Evolution 51(1):1-9 · doi:10.1111/j.1558-5646.1997.tb02382.x |
| [52] | Pennings PS, Kopp M, Meszéna G, Dieckmann U, Hermisson J (2008) An analytically tractable model for competitive speciation. Am Nat 171(1):E44-E71 · doi:10.1086/523952 |
| [53] | Ravigné V, Barberousse A, Bierne N, Britton-Davidian J, Capy P, Desdevises Y, Giraud T, Jousselin E, Moulia C, Smadja C et al (2010) La speciation. In: Thomas F, Lefèvre T, Raymond M (eds) Biologie Evolutive. De Boeck, pp 165-210 |
| [54] | Ritchie MG (2007) Sexual selection and speciation. Annu Rev Ecol Evol Syst 38(1):79-102 · doi:10.1146/annurev.ecolsys.38.091206.095733 |
| [55] | Rudnicki R, Zwoleński P (2015) Model of phenotypic evolution in hermaphroditic populations. J Math Biol 70(6):1295-1321 · Zbl 1316.92056 · doi:10.1007/s00285-014-0798-3 |
| [56] | Savolainen V, Anstett MC, Lexer C, Hutton I, Clarkson JJ, Norup MV, Powell MP, Springate D, Salamin N, Baker WJ (2006) Sympatric speciation in palms on an oceanic island. Nature 441:210-213 · doi:10.1038/nature04566 |
| [57] | Schwagmeyer PL (1988) Scramble-competition polygyny in an asocial mammal: male mobility and mating success. Am Nat 131:885-892 · doi:10.1086/284828 |
| [58] | Seehausen O, Van Alphen JJM, Witte F (1997) Cichlid fish diversity threatened by eutrophication that curbs sexual selection. Science 277(5333):1808-1811 · doi:10.1126/science.277.5333.1808 |
| [59] | Seehausen O, Terai Y, Magalhaes I, Carleton K, Mrosso H, Miyagi R, van der Sluijs I, Schneider M, Maan M, Tachida H, Imai H, Okada N (2008) Speciation through sensory drive in cichlid fish. Nature 455(7213):620-626 · doi:10.1038/nature07285 |
| [60] | Servedio MR (2010) Limits to the evolution of assortative mating by female choice under restricted gene flow. Proc R Soc Lond B Biol Sci 278(1703):179-187 · doi:10.1098/rspb.2010.1174 |
| [61] | Servedio MR, Bürger R (2014) The counterintuitive role of sexual selection in species maintenance and speciation. Proc Natl Acad Sci 111(22):8113-8118 · doi:10.1073/pnas.1316484111 |
| [62] | Servedio MR, Bürger R (2015) The effects of sexual selection on trait divergence in a peripheral population with gene flow. Evolution 69(10):2648-2661 · doi:10.1111/evo.12762 |
| [63] | Shaw KL, Parsons YM (2002) Divergence of mate recognition behavior and its consequences for genetic architectures of speciation. Am Nat 159(S3):S61-S75 · doi:10.1086/338373 |
| [64] | Smadi C (2015) An eco-evolutionary approach of adaptation and recombination in a large population of varying size. Stoch Process Appl 125(5):2054-2095 · Zbl 1322.60180 · doi:10.1016/j.spa.2014.12.007 |
| [65] | Turner GF, Burrows MT (1995) A model of sympatric speciation by sexual selection. Proc R Soc Lond B Biol Sci 260(1359):287-292 · doi:10.1098/rspb.1995.0093 |
| [66] | Van Doorn GS, Noest AJ, Hogeweg P (1998) Sympatric speciation and extinction driven by environment dependent sexual selection. Proc R Soc Lond B Biol Sci 265(1408):1915-1919 · doi:10.1098/rspb.1998.0520 |
| [67] | Van Doorn GS, Dieckmann U, Weissing FJ (2004) Sympatric speciation by sexual selection: a critical reevaluation. Am Nat 163(5):709-725 · doi:10.1086/383619 |
| [68] | Weissing FJ, Edelaar P, Van Doorn GS (2011) Adaptive speciation theory: a conceptual review. Behav Ecol Sociobiol 65(3):461-480 · doi:10.1007/s00265-010-1125-7 |
| [69] | Wu CI (1985) A stochastic simulation study on speciation by sexual selection. Evolution 39(1):66-82 · doi:10.1111/j.1558-5646.1985.tb04080.x |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
