arXiv:0708.3103v1 [q-bio.PE] 22 Aug 2007 an h oorplmrhs.Totpso pharyngeal of main- types field Two selection the polymorphism. in sexual colour both that the [8], tains suggesting well captivity, as according in observed mating and been normal assortative has with Strong colour [7], to morphs. described gold been and has polychromatism a ihvr iepeddsrbto.For distribution. widespread 3.- very and with Apoyo, Lake distribution citrinellus lakes, its crater phus the in of restricted one is to that species Nicaragua elongated Lake 2.- an lakes Managua, big the Lake to and restricted be 1.- to thought complex: cichlid Midas Labiatus the within [6] large to a ability niches. successfully great trophic exploit their of to diversity for and habitats pharyngeal responsible innovation new key the be this colonize and to in jaws, presumed jaws oral the is of to are pair addition fishes in a area Cichlid by characterized Morph. or Gold also orange, fish, which red, coloured form, brightly yellowish conspicuous in a resulting have spots, or melanophores, them or lacks Morph, bars of Normal dark as with some brown known or example, grey for colouring, cryptic them, differ- morphological between Nicaragua substantial ences in are species fish There any of freshwaters. biomass represent in largest they the as Combined, far well are by area. as the [6] Nicaragua in complex lakes of crater species Lakes several Great cichlid the Midas in The distributed in 5]. speciation sympatric [4, by nature evolution of example possible ∗ rpi ergto skona ypti speciation fishes, sympatric Cichlid geo- as through 3]. known flow 2, [1, is gene segregation of prevention graphic without species lcrncades [email protected]ff.br address: Electronic he ieetseishv led enrecognized been already have species different Three h vlto fasnl ouainit w rmore or two into population single a of evolution The optrsmltoso h ypti pcainmdsfor modes speciation sympatric the on simulations Computer h e ei ihi,aflsylpe species fleshy-lipped a cichlid, devil red the , hl ntescn h aigadgntccniin utbe must conditions genetic drift. and conditions genetic mating genetic of the velocity and second ecological the the in while scenario, first the In oyopimo he pce fteMdsCcldseisc species Cichlid s Midas single the the of for a species need in of three conditions of genetic together splitting and polymorphism living mating the ecological, populations the simulated study both We we with paper mutations, this random in them, by ihi se r n ftebs oe ytmfrtesuyof study the for system model best the of one are fishes Cichlid h ia ihi,agnrls species generalist a cichlid, Midas the , .INTRODUCTION I. .Citrinellus A. apsd ri emla o igm Niter´oi, 24210-340, Viagem, Boa Vermelha, Praia da Campus .Zaliosus A. mhlpu Zaliosus Amphilophus .Luz-Burgoa, K. pcainpoes n ihadteohrwtotdisrupti without other the and with one process, speciation 1 nttt eFıia nvriaeFdrlFluminense, Federal F´ısica, Universidade de Instituto h ro cichlid, arrow the , .citrinellus A. 1 Amphilophus .Ms eOliveira, de Moss S. Dtd coe 6 2018) 26, October (Dated: Amphilo- r one are , pce complex species , n r oyopi ihppliomadmollariform and 1. papilliform Fig. with pharyngeal, polymorphic are and documented. been All have and jaws morphs, pharyngeal gold and papilliform normal only with [7], described been has n addessc ssal,weeste r eseffi- morphs less papilliform For are the than versa. they diets vice whereas and soft on snails, feeding as in the eat- such cient at diets performance: efficient hard more in and ing trade-off specialized a are is fish stud- mollariform there previous that These showed teeth. ies rounded mollariform thicker a and with teeth morph pointed slender with morph form of jaws rmtelkso iaau described. compl species Nicaragua cichlid of Midas lakes the the of from species three the of phism 1: FIG. 1,1] ihisaernwe o hi atdvriyof ecologi- diversity of vast degree extreme their often for and renowned morphologies argued trophic are speciation have Cichlids sympatric authors cause 14]. some also [13, hand, can selection other sexual the that On resources diverse 12]. for competition [11, natu- by frequency-dependent caused selection, disruptive ral by driven is ation codn otertclmdl 1] ypti speci- sympatric [10], models theoretical to According A. Citrinellus A. Zaliosus A. Labiatus .zaliosus A. Specimens 1 r ucett raetonwspecies, new two create to sufficient are dt erdc h oyhoaimand polychromatism the reproduce to ed n .S S´a Martins S. J. and mlx u eut hwtoscenarios two show results Our omplex. .citrinellus A. h ceesosteplcoaimadpolymor- and polycromatism the shows scheme The ypty hrn h aehabitat. same the sharing sympatry, ycrnzdi re ocnrlthe control to order in synchronized eisit w eaaeoe via ones separate two into pecies vlto fteseis Inspired species. the of evolution aecytccluig omlmorph, normal colouring, cryptic have oyhoaim Polymorphism Polychromatism .labiatus A. Gold Gold aebe ecie 9,apapilli- a [9], described been have J Brazil. RJ, Normal Normal Normal entrlselection. natural ve h ia cichlid Midas the 1 h aepolychromatism same the , ∗ Mollariform Mollariform Papilliform Papilliform Papilliform ex 2 cal specialization [9]. However, the sympatric occurrence A. Natural selection caused by competition of many sibling species that seem to differ only in colour- ing makes it unlikely for ecological specialization to be In the present model, competition for food is related the sole mechanism of speciation in this group. At the to a phenotype, j, represented by the second, non age- same time, genetic data [4] show that sympatric specia- structured, pair of bit-strings, which is constructed in tion by sexual selection alone is rather unlikely for the the same way as the first pair of the individual’ genome. speciation case of the crater lake Apoyo. We studied the This phenotypic characteristic is computed by counting ecological, mating and genetic conditions needed to re- the number of bit positions where both bits are set to produce the polychromatism and polymorphism of the 1, plus the number of dominant positions (chosen as 16) three species of the Midas Cichlid species complex, Fig. with at least one of the two bits set. It will therefore 1. Our study was based on simulations of an individual- be a number j between 0 and 32, which we will refer to based model where natural selection caused by compe- as the individual’s phenotype. We call Mj the mutation tition for diverse resources and sexual selection, tuned probability per locus of this ecological trait. A mutation by strength parameters on two quantitative and inde- can change the locus either from 0 to 1 or from 1 to 0. pendent traits, were considered. Our results show two In order to control the population’s size and introduce a scenarios for the sympatric speciation of A. Citrinellus competition we used the Verhulst factor, V (j, t). We con- species, one with and the other without disruptive natu- sidered three intra-specific competitions, [16], depending ral selection. In the first scenario, A. Zaliosus develops on the individual’s phenotype j, each one related to a jaw polymorphism while retaining a single colour morph, given phenotypic group: while in the second A. Labiatus develops polychromatism with a single jaw morph. V (j, t), 0 ≤ jn2) at time t, Pm(t) accounts for the the available resources, representing an ecological trait population with phenotype j ∈ [n1,n2], and F (j, t) is a such as the types of pharyngeal jaws in the case of cich- resource distribution. Individuals with intermediate phe- lid fishes. The third pair represents a trait only related notypes (Pm) compete among themselves and also with to sexual selection, a mating trait, such as the colour a fraction X of each specialist population. The Verhulst of cichlid fishes. At the beginning of the simulation, all factor for them is: individuals are born with random genomes. When a fe- Pm(t)+ X × [P1(t)+ P2(t)] male succeeds in staying alive until reaching a minimum Vm(j, t)= , (2.3) reproduction age, A, it looks for a male to mate with and F (j, t) generates b offspring every time step before dying, with a P P new choice for a mate being done at each time step. The Eq.(2.2) means that specialist individuals ( 1, 2) com- first pair of the offspring’s genome is constructed in the pete with those belonging to the same phenotypic group following way: each one of the first pair of strings of the and also with the whole intermediate population, but male, for instance, is broken at the same random position there is no competition between specialists of different and the complementary pieces, originated from different groups because we are assuming they are specialized to ,n n , strings, are joined to form two male gametes. One of the some extent ([0 1),( 2 32]) on particular resources, as is gametes is then randomly chosen to be passed on to the the case for papilliform and mollariform pharyngeal jaws offspring. After that, one random bad mutation is intro- in the Midas cichlid species complex. In equations 2.2 duced into this gamete, and the final result corresponds and 2.3, the resource distribution used varies according to one string of the new individual. The other string to: is constructed from the first pair of the female’s strings F (j, t) = C × (1 − G(j)) , with (2.4) by the same process, that simulates random crossover, − − 2 recombination and addition of one bad mutation. G(j) = Z × e (16 j) /64, 3 where C is a carrying capacity, and for all simulations it with zeroes and ones. The initial populations typically was set to C =2×105. The first case, Z = 0 in Eq. (2.4), consist of 60000 individuals, half males and half females. is used to simulate a scenario without disruptive selection The equilibrium population sizes depend on the carrying on the ecological trait. For this case, all individuals have capacity, but are never smaller than 38000 individuals. the same carrying capacity, Eq. (2.2) and Eq. (2.3). The second case, Z > 0 in Eq. (2.4), is used to simu- late disruptive natural selection with a strength Z. For A. Simulations for A. Labiatus species this case, all individuals with intermediate phenotypes are disadvantaged, with respect to specialist individuals, We took Z = 0 in the resource distribution, F (j, t) of according to a reversed gaussian, G(k). Eq. (2.4), and chose for the mutation probability per lo- cus of the ecological and for the mating trait the values Mj = 1.0 and Mk = 1.0, respectively. For all values of B. Sexual selection the sexual selection strength, Y , the phenotype frequency of the ecological trait is a stationary gaussian distribu- In the simulations, sexual selection is related to an- tion, Fig. 2 (a). The phenotype frequency of the mating other phenotype, k, and was represented by a new pair of trait is a bimodal distribution for Y > 0.7 and a gaussian non age-structured bit-strings, the mating trait, that also distribution, with a mean value k = 16, for the other Y obeys the general rules of crossing and recombination. values, Fig. 2 (b). This phenotype was computed in the same way as that for the ecological trait. It will therefore be a number k (b) Ecological character at X = 0.8, Z = 0 and Mk = 1.0 between 0 and 32, and we call Mk the mutation probabil- ity per locus of this mating trait, which can also mutate back and forth between 0 and 1. In order to consider as- sortative mating in a sympatric environment, we defined two phenotypic groups, one composed by the individu- 0.2 als that have k ∈ [0, 16) while individuals of the other 0.1 0.0 30 have k ∈ (16, 32]. With some probability, Y ∈ [0.0, 1.0], Phenotype Frequency 25 a female with phenotype k will mate with a male of the 0.2 20 0.4 15 same phenotypic group and with probability 1.0 − Y will Selectiveness,0.6 Y 10 Phenotype j mate with a male of the other phenotypic group, at each 0.8 5 1.0 0 time step of its life. For instance, if a female has pheno- type k ∈ [0, 16) and a random real number, r, uniformly distributed between 0 and 1, is tossed that is smaller (a) Mating character at X = 0.8, Z = 0 and Mk = 1.0 than Y , it selects its mate among Nm males of the same phenotypic group k ∈ [0, 16) by picking the one with the smallest phenotype value k. If a female has pheno- type k ∈ [0, 16) and the random real number, r, is larger than Y , it chooses a partner from the other phenotypic 0.2 group, k ∈ (16, 32]. A similar rule applies to females 0.1 0.0 30 with k ∈ (16, 32], with the proviso that now the female Phenotype Frequency 25 picks as mate, among N males of the same phenotypic 0.2 20 m 0.4 15 group, the one with the largest phenotype value k. The Selectiveness,0.6 Y 10 0.8 5 Phenotype k females with k = 16 mate only with males of phenotype 1.0 0 k = 16. If Y =0.5, the female population is not selective in mating; that is, panmictic mating is the behaviour of the population. For Y = 1.0, the female population has a completely assortative mating behaviour. FIG. 2: Results for the model without disruptive selection and with a competition strength X = 0.8. The phenotypes frequen- cies, for different sexual selection strengths, were measured during the last 106 simulation steps. (a) distribution of the III. RESULTS phenotype, j, related to the ecological trait and (b) distribution of the phenotype, k, related to the mating trait. We present now simulation results for which the val- ues of the parameters related to the first pairs of bitstring All these results, as well as the next one shown, are of the individuals’ genomes were chosen to be: A = 10, valid for all values of the competition strength smaller b = 5 and M = 1. The specialist populations have phe- than one, X < 1. If we change Nm = 5 to smaller values, notypes k ∈ [0,n1 = 13] and k ∈ [n2 = 19, 32], Eq. the phenotype frequency related to the mating trait is no (2.1) and each female chooses among Nm = 5 males. We longer a stationary distribution. If the mutation proba- start the simulations with all bitstrings randomly filled bility per locus of the ecological trait, Mj , is smaller than 4

1.0, for example Mj = 0.1, the distributions in Fig. 2 B. Simulations for A. Zaliosus species (a) and (b) do not change. When the mutation proba- bility of the mating trait, Mk, changes from 1.0 to 0.1, The characteristics of the A. Zaliosus species is to have for example, the phenotype frequency of the ecological a unimodal distribution for the mating trait and a bi- trait, Fig. 2 (a), does not change either. However, for modal distribution for the ecological one. We have al- Mk = 0.1 and Y > 0.5 the phenotype frequency of the ready seen, in the previous section, that for Z = 0 there mating trait, Fig. 2 (b), changes to a unimodal distribu- is no splitting of the ecological trait, unless if Y = 1.0 tion peaked at k = 0 or k = 32, with a 0.5 probability and X =1.0. On the other side, for Y =1.0 and X =1.0 for each. For example, the phenotype frequency of the the mating trait is also splitted, which is not the case of mating trait, for Y > 0.5, is a distribution with a peak at A. Zaliosus species. So in order to simulate the A. Za- k = 32, while for other values of Y and still Mk =0.1 the liosus process of speciation, we will take Z > 0 and will distribution is bimodal peaking at k = 16 and k = 32, first study each trait separately. Fig. 3. That means, if the mutation probability of the mating trait, Mk, has small values, the population suffers a genetic drift which becomes faster as the value of Y be- (b) Ecological character at X = 0.5, Y = 0.5 and Mk = 1.0 comes larger, meaning that the behaviour of the female population is predominantly one of assortative mating. In other words, for strong assortative mating the disrup- tion of the mating trait is not favoured for small values of the mutation probability of this trait when disruptive 0.1 natural selection, caused by resources distributions, is 0.0 30 25 not present in the population. 0.2 20 Phenotype Frequency 0.4 15 Disruptive,0.6 Z 10 0.8 5 Phenotype j 1.0 0 Mating character at X = 0.8, Z = 0.0 and Mk = 0.1

(a) Mating character at X = 0.5, Y = 0.5 and Mk = 1.0 0.6 0.4 0.2 0.0

Phenotype Frequency 30 0.2 0.1 0.2 20 0.4 0.0 30 0.6 10 0.8 Phenotype k 25 1.0 0 0.2 20 Selectiveness, Y 0.4 15 Phenotype Frequency Disruptive,0.6 Z 10 0.8 5 Phenotype k 1.0 0

FIG. 3: The phenotypes frequencies of the mating trait for dif- ferent sexual selection strength, Y , without disruptive natural selection and at a small mutation probability of the mating FIG. 4: The phenotypes frequencies for different resources dis- Z Y . X . trait, Mk. tributions, , for = 0 5 and = 0 5, (a) of the ecological trait and (b) of the mating trait.

In what follows, the character determining sexual se- Fig. 4 (a) shows the distribution of the ecological trait lection in the population is the colour of the individuals for Y = 0.5 and X = 0.5. From this figure we see that and the character that determines natural selection is the this distribution changes from a unimodal one to a bi- individuals’ jaws morphology, which is the case in the Mi- modal distribution depending on the value of the dis- das cichlid species complex. In common with A. Labiatus ruptive natural selection strength, Z. For Z ≈ 1, the species, Fig.1, it is possible to find polychromatism and existing intermediate phenotypes belong to individuals monomorphism in the ecological character for all values that die before reaching the minimum reproductive age. of the asymmetrical competition strength between the Fig. 4 (b) shows the distribution of the mating trait, intermediate and specialist phenotypes smaller than one, also for Y = 0.5 and X = 0.5. It can be seen that the X < 1 in Eq. (2.3) and (2.2), provided the following con- distribution is unimodal only for Z < 1; for Z ≈ 1 it ditions are met: (i) no disruptive natural selection Z = 0, is almost bimodal but not completely, since the interme- (ii) a sexual selection strength Y > 0.7 in the population, diate population, k = 16, is appreciable. The existence and (iii) a large value for the mutation probability of the of the intermediate phenotypes is due to the panmictic mating character Mk = 1, Fig. 2 (b). behaviour of the population, Y =0.5 5

The phenotype frequency of the ecological trait, Fig. 4 Ecological character at Y = 1.0, Z = 0.0 and M = 1.0 (a), does not change if we vary the mutation probabilities k 0.1 ≤ Mj ≤ 1.0 and 0.1 ≤ Mk ≤ 1.0. The phenotype frequency of the mating trait also does not change for 0.1 ≤ Mj ≤ 1.0. The same is not true when Mk < 1.0, since then the distribution is trimodal, Fig. 5, with peaks 0.2 at k = 0, k = 16 and k = 32 when Mk =0.1. 0.1 0.0 30 Phenotype Frequency 25 0.2 20 Mating character at X = 0.5, Y = 0.5 and Mk = 0.1 0.4 15 Competition,0.6 X 10 0.8 5 Phenotype j 1.0 0

0.2 0.1 FIG. 6: The phenotypes frequencies of the ecological trait in a 0.0 30 25 case without disruptive natural selection and for strong sexual 0.2 20 selection, Y = 1.0. 0.4 15 Phenotype Frequency Disruptive,0.6 Z 10 0.8 5 Phenotype k 1.0 0 IV. DISCUSSION

Although competition for resources and natural dis- FIG. 5: The phenotype frequencies of the mating trait for ruptive selection appear together in Eq. (2.2) and (2.3), different resources distributions, Z, and at a small mutation they lead to rather different situations. While competi- probability of the mating trait, Mk. tion depends on the population sizes and affects equally individuals of the same phenotypic group, disruptive nat- From these results we may conclude that when Z =6 0, ural selection caused by resources distributions acts on the splitting of the mating trait is favoured by small mu- each particular individual, according to its phenotype. tation probabilities, Mk, of this trait, which is not what As a result, disruptive selection becomes more effective we want for the A. Zaliosus species. From Figs. 4 (a) than competition. For instance, even for a panmictic be- and (b) we can see that the proper regions of parame- haviour, disruptive natural selection may lead to a split- ters to simulate the speciation process of this species are ting of both traits, depending only on the values of X and Z > 0.4, bimodal distribution for the ecological trait, Z, as already pointed in [12]. A small mutation probabil- and Z < 0.8, unimodal one for the mating trait. ity of the mating trait also favours this double splitting, as obtained in [11]. On the other hand, in order to split both phenotypic C. Simulations for species A. Citrinellus distributions without disruptive natural selection, Z = 0, it is imperative to have sexual selection, and now the One way to obtain the polycromatism and polymor- splitting process depends on the values of Y and X, and phism characteristic of the A. Citrinellus species, bi- in this case the mutation of the mating trait must be modal distributions of the both traits, is to consider uni- large in order to prevent genetic drift effects. form distribution of resources without disruptive natural Anyway, the A. Citrinellus case is the evolution of the selection. We have already shown that simulations with splitting in both traits distributions must be driven by Z =0.0 and Y =1.0, only assortative mating, give a bi- disruptive natural selection or by sexual selection, and modal distribution for the mating trait, Fig. 2 (b), inde- the only statistical difference we found between these pendently of the competition strength, X, provided the two scenarios is that the correlation between the traits is mutation probability is Mk = 1.0. However, to obtain smaller when the splitting is driven by sexual selection. also bimodal distribution of the ecological trait, with- It so happens because the large mutation rate of the mat- out disruptive natural selection, it is necessary to have ing trait, mentioned above, introduces large fluctuations X =1.0, that is, a symmetric competition between spe- in this correlation. cialist and intermediate phenotypes, as shown in Fig. 6. For Z > 0, it is also possible to split both phenotype distributions, but then it is necessary to consider small Acknowledgments mutation probabilities of the mating trait, Mk, a weak assortative mating, Y & 0.5, and proper values of the resource distribution, Z, depending on the competition We thank the agencies CNPq, FAPERJ (E- strength, X. For instance, Z > 0.7 for X = 0.5, Fig 4 26/170.699/2004), and CAPES for financial support and (a). J. Nogales for fruitful discussions. 6

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