Ecology Letters, (2004) 7: 165–169
doi: 10.1111/j.1461-0248.2004.00569.x
IDEA
Coexistence of cryptic species
Da-Yong Zhang1, Kui Lin1 and Ilkka Hanski2* 1
MOE Key Laboratory for
Biodiversity Science and Ecological Engineering and Institute of Ecology, Beijing Normal University, Beijing 100875, China 2
Department of Ecology and
Systematics, PO Box 65, Viikinkaari 1, University of
Abstract Recent discovery of cryptic species in fig-pollinating wasps creates a puzzle for the ecological competition theory: how do two or more apparently identical species coexist? Conventional theory predicts that they should not. Chesson (Trends Ecol. Evol., 1991, 6, 26–28) identified one exception which he considered unlikely to occur in reality: coexistence might be possible if appropriate social behaviour was discriminately directed towards conspecifics and heterospecifics. Here we present an example of the exception by showing that two identical species with local mate competition and population sizedependent sex ratio adjustment may coexist. The new findings about fig-pollinating wasps provide a putative example of unexpected coexistence of identical competitors via this mechanism.
Helsinki, FIN-00014 Helsinki, Finland *Correspondence: E-mail:
[email protected]
Keywords Coexistence, fig wasp, identical competitors, inbreeding, local mate competition, sex ratio adjustment. Ecology Letters (2004) 7: 165–169
INTRODUCTION
Taxonomic studies employing molecular markers often lead to splitting of recognized species into two or more cryptic species. As an example, a recent study of Cotesia (Braconidae) wasps parasitizing melitaeine (checkerspot) butterflies increased the number of species in Europe and Asia from four to nine (Kankare & Shaw 2004). Often the newly discovered species are more specialized than the previously recognized species. In the melitaeine-associated Cotesia, the newly discovered cryptic species all appear to be specific to single host species (five species) or small groups of related host species (four species), and thus the previously recognized species, considered as host generalists, in fact consist of closely related specialists. This pattern is consistent with a general expectation based on competition theory: coexistence of seemingly similar species is facilitated by some distinct difference in their biology, such as host specificity in parasites. In the extreme case of identical species the conventional wisdom and most theory predict no stable coexistence, which implies recovery from low abundance because of increased growth rate. The relative abundances of identical competitors are expected to obey a random walk and, hence, all but one species are expected to go extinct during the course of time (Chesson 1991; Hubbell 2001). Chesson (1991) gives one possible exception: social behaviour, if it is discriminately directed towards conspecifics and heterospecifics,
might allow coexistence, although Chesson (1991) was rather sceptical about the importance of this mechanism in the real world. Molbo et al. (2003) have recently reported another instance of cryptic species revealed by molecular evidence, in their case in fig-pollinating wasps (Agaonidae). They found cryptic wasp species in four of the eight host fig species that were surveyed. Therefore, there are often two instead of one fig-wasp species pollinating a single fig species. Given these new findings, Molbo et al. (2003) showed that the evolutionary local mate-competition theory predicts observations about sex ratio adjustments by ovipositing females even better than would be apparent if the cryptic species were not recognized. While the discovery of cryptic species in fig wasps strengthens the support for the local mate-competition theory, the new results create a puzzle for the ecological competition theory: coexistence of seemingly identical competitors. We cannot, of course, be certain that the cryptic fig-wasp species are identical with respect to all relevant traits, but this seems a plausible hypothesis and definitely the pattern of host association in the fig wasps is very different from the more usual pattern exemplified by for example, the melitaeine-associated Cotesia. Although stable coexistence of identical competitors is widely regarded impossible, there are mechanisms that might make it possible (Zhang & Hanski 1998) and exemplify Chesson’s (1991) general argument about an exception to the 2004 Blackwell Publishing Ltd/CNRS
166 D.-Y. Zhang, K. Lin and I. Hanski
conventional theory. Intriguingly, one mechanism is based on population size-dependent variation in sex ratio (Zhang & Jiang 1995) – which is exactly the phenomenon predicted by the local mate-competition theory that is so firmly established for fig wasps. Theory predicts and observations show increasingly female-biased sex ratio with decreasing number of foundresses in a local resource patch (here an individual fruit). The average number of foundresses is necessarily lower in rare than in common species, which should provide the former the small population advantage (increased population growth rate) necessary for stable coexistence of competitors. In this study, we examine this idea with a model that is motivated by the biology of fig wasps (for a recent review see Cook & Rasplus 2003).
where
MODEL
Hamilton (1967) was the first to show that when one or a few females oviposit in a resource patch and mating is restricted to the offspring developing in that patch, a female-biased sex ratio is favoured. The reason is that in these circumstances mating is likely to occur among close relatives, leading to competition among brothers for mating opportunities, which reduces the fitness of the mother. Furthermore, in haplodiploid organisms, such as the figpollinating wasps, inbreeding (sib-mating) leads to a further female bias in the expected optimal sex ratio as mothers are more related to their daughters than to their sons (Hamilton 1979; Frank 1985; Herre 1985). Theory thus predicts that if n female foundresses ovipositing in a resource patch contribute equally to a brood, then the optimal sex ratio (the proportion of male progeny) is given by r¼
n 1 4S 2 ; 2n 4S 1
ð1Þ
where S is the inverse of the proportion of sib-mated females (an estimate of inbreeding) in the population (Herre 1985; see below). In this formula, the first term is the result of local mate competition, the second term inbreeding. Thus a species with a lower average foundress number should produce a more female-biased sex ratio, either as a result of local mate competition or sib-mating. The following model gives a simple description of the population dynamics of a single fig-wasp species. We assume a large number of resource patches (individual fruits), each of which produces F offspring. It is reasonable to assume that F is an increasing function of foundress number (n): F¼
Fmax n ; nþC
ð2Þ
where Fmax is the maximum number of offspring produced in a fruit when eggs (or the number of foundresses) are not 2004 Blackwell Publishing Ltd/CNRS
limiting, and C is a parameter determining the strength of response to increasing number of foundresses. If C ¼ 0 the brood size (F) is a constant, independent of foundress number. Moore et al. (2002) have shown that the brood size in Liporrhopalum tentacularis, a fig-pollinating wasp, does not increase with foundress number. Let a be the searching efficiency, such that aF(1)r) is the number of mated females emerging from one patch and successfully colonizing another patch in the next generation. Assuming that the number of foundresses colonizing a patch at time t follows a Poisson distribution with a mean of k, we can write the population dynamic equation as 1 X n 1 4S 2 aF 1 pðnÞ ð3Þ kðt þ 1Þ ¼ 2n 4S 1 n¼1 kðtÞn kðtÞ e : n! Herre (1985) used the inverse of the harmonic mean number of foundresses per brood to estimate the degree of sib-mating, S, which, under the present notation, can be written as 1 ekðtÞ S ¼ P1 pðnÞ : ð4Þ pðnÞ ¼
n¼1 n
It is important to note that Herre’s (1985) formula is exact only if several simplifying assumptions are made, among which is constant number of females produced from each resource patch regardless of the number of foundresses (i.e. C ¼ 0 in eqn 2). This condition is generally not met (Herre 1989), and eqn 4 is used here as a simple approximation of the general tendency that females of more inbred species are selected to produce more femalebiased sex ratios. Frank (1985) gave a more accurate but also a much more complex formula that can accommodate for differences in both sex ratio and relative brood size between patches with different foundress numbers. Results for two competing species
Let us now consider the case of two competing species. We distinguish between two cases. In case A, each female responds to the number of conspecific foundresses and adjusts the sex ratio of her offspring accordingly. In case B, each female responds to the number of foundresses of both species ovipositing in the resource patch. One might expect that case B is more likely, but the results of Molbo et al. (2003) suggest that females may in fact respond to the number of conspecific foundresses. In other cases, however, females appear to respond to the pooled number of foundresses (D. Molbo, personal communication).
Coexistence of cryptic species 167
15
10
ð5Þ
of which the fraction n1/(n1+bn2) belongs to species 1. Here b measures the relative competitive ability of species 2. In case A, when each female adjusts the sex ratio of her offspring based on the number of conspecific females, the sex ratio is given by eqn 1. In case B, when each female responds to the pooled number of females, the sex ratio for species i (i ¼ 1, 2) is
ðn1 þ n2 Þ 1 4Si 2 ri ¼ ; ð6Þ 2ðn1 þ n2 Þ 4Si 1 where Si is again the degree of sib-mating of species i, given by eqn 4. We do not focus on this formula because it is necessarily the best estimate of inbreeding in cases of two fig-wasp species, but because it is a simple and practical incarnation of the general expectation that more common species tend to be less inbred. Note that the sex ratio adjustment caused by inbreeding cannot occur instantly through behavioural plasticity, but only as an evolutionary response through long-term natural selection. Now the model for the population growth of the two species can be written as follows: 1 X 1 X n1 k1 ðt þ 1Þ ¼ aF ð1 r1 Þpðn2 Þpðn1 Þ n1 þ bn2 n1 ¼1 n2 ¼0 ð7Þ 1 X 1 X bn2 aF k2 ðt þ 1Þ ¼ ð1 r2 Þpðn1 Þpðn2 Þ: n1 þ bn2 n2 ¼1 n1 ¼0 We have solved these equations numerically, with results shown in Figs 1 and 2. In the simulations, a two-species equilibrium was considered to occur if the condition |ki(t+1))ki(t)| £ 10)7 (i ¼ 1, 2) was satisfied for at least 100 consecutive generations. We found that the initial values for species abundances had no influence on the steady-state, and thus coexistence, if any exists, is stable (we checked systematically all possible (49) combinations of the initial values {0.01ki*, 0.1ki*, 0.3ki*, 0.5ki*, 0.7ki*, 0.9ki*, and 0. 99ki*} for the two species, where ki* is the single-species equilibrium value for species i, with values of C being chosen as 0, 0.5 and 1.0, respectively). Figure 2 gives an example. If the species have the same competitive ability, b ¼ 1, then the two species can always coexist via the sex ratio adjustment, although they would respond to the pooled
5
0 0.5
0.6
0.7
0.6
0.7
b
0.8
0.9
1
0.8
0.9
1
(b) 20
15
a F max
Fmax ðn1 þ n2 Þ F¼ ; ðn1 þ n2 Þ þ C
(a) 20
a F max
Next consider what happens when the two competing fig-wasp species co-occur on the same host. We assume that the two species have the same searching efficiency and the same response to the number of foundresses such that in a patch with n1 foundresses of species 1 and n2 of species 2, the total number of offspring (F) is given by
10
5
0 0.5
b
Figure 1 Conditions of coexistence for two competing fig-wasp species in the space of the species competitive ability, b, and the potential productivity of female progeny per fruit, aFmax. Stable coexistence is possible to the right of the lines. The solid line represents the case where each female responds to the number of conspecific foundresses in the fruit, while the dashed line represents the case where each female responds to the number of foundresses of both species in the fruit. The horizontal dashed line is the minimum of aFmax that allows the persistence of a single species. The two panels give the results for C ¼ 0 (a) and C ¼ 1 (b).
number of foundresses (case B; Figs 1 and 2). In this case coexistence occurs because the inbreeding component causes female-biased sex ratio independently of local mate competition. If the females respond to the number of conspecific foundresses (case A), coexistence is greatly facilitated (Fig. 1). When the species have dissimilar competitive abilities, the more similar the two species are the more likely they are to coexist via facultative sex ratio adjustment. CONCLUSION
The contrast in the host associations of cryptic species of parasitic Cotesia and mutualistic fig-wasps is instructive. Cryptic species of Cotesia exhibit ecological specialization as 2004 Blackwell Publishing Ltd/CNRS
168 D.-Y. Zhang, K. Lin and I. Hanski
(a)
3
l 1(t) and l 2(t)
2.5 2 1.5 1 0.5 0 100
101
102
103
102
103
Time (t)
(b)
3
l 1(t) and l 2(t)
2.5 2 1.5 1 0.5 0 100
101
Time (t)
Figure 2 Simulation of the competitive dynamics of two fig-wasp species with identical competitive ability (b ¼ 1) under the condition of each female responding to the pooled number of foundresses of both species in a fruit. The two species differ in their initial abundances. Parameter values for case (a) aFmax ¼ 3.0, k1(0) ¼ 0.1, k2(0) ¼ 2.15 (the single-species equilibrium) and C ¼ 0; and for case (b) aFmax ¼ 3.0, k1(0) ¼ 0.1, k2(0) ¼ 0.96 (the single-species equilibrium) and C ¼ 1.
predicted by the ecological competition theory. In contrast, cryptic and seemingly identical species of fig wasps coexist on the same resource, which can be explained by the special mechanism of density-dependent sex ratio adjustment that is so well established for fig wasps. It is pleasing to note that the new findings about cryptic species in fig wasps demonstrate the power of both the evolutionary local mate competition and the ecological competition theory. Our model implicitly assumes that fig wasps can adjust their sex ratios at the same or even shorter time scale than population dynamics. This can be achieved either through behavioural plasticity or evolutionary change. Local matecompetition theory (the first term in eqn 1) is based on behavioural plasticity and hence leads to an immediate response to local density. On the contrary, the adjustment as a result of inbreeding (the second term in eqn 1) is based on an evolutionary response as a result of natural selection and hence will not occur instantly. However, it is important to note that in the case of identical competitors the ecological 2004 Blackwell Publishing Ltd/CNRS
dynamics of competitive exclusion or coexistence are slow, as they are based on random drift in the relative abundances of the competitors (Hubbell 2001). In the case of identical species, differences in population growth rates are expected to be smaller between species (relevant for competitive exclusion) than between genotypes within species (relevant for natural selection). Hence it is plausible that sex ratio adjustment because of natural selection may rescue a species that is drifting to extinction by giving it a density-dependent boost in growth rate. In our model, we assume a random distribution of foundresses, which is not usually the case (Herre 1989). In some species only one foundress enters the vast majority (>99%) of fruits, whereas in other species the average number of foundresses per fruit may be greater than four. A single foundress in each fig could arise either as a result of non-random distribution of foundresses or extremely low productivity because of say low-searching efficiency. In such cases, opportunities for local mate competition and sib mating must be restricted, and hence coexistence of cryptic species on the same host is unlikely via sex ratio adjustment. Therefore, coexisting cryptic species are expected to occur only in systems in which multiple foundresses occur regularly. Of the five host fig species in which cryptic wasp species have been detected (Molbo et al. 2003), there is one case (Ficus perforata; pollinating wasp Pegoscapus insularis) in which the proportion of one foundress fruits is more than 99% (Herre et al. 2001). In this case one may suspect that the co-occurrence of the two wasp species is based on something else than the mechanism discussed in this paper. The Panama canal zone where Molbo et al. (2003) conducted their research may be a contact zone of two species that are mostly geographically separated. Clearly, more empirical work along the lines of Molbo et al. (2003) is warranted. Our purpose has been to point out the possibility of an interesting ecological phenomenon, coexistence of identical species, that may exist in fig wasps and to clarify the conditions under which such coexistence is expected to occur. ACKNOWLEDGEMENTS
Financial support was provided to DYZ by MOST (G2000046802) and NNSF (39893360, 30125008) of China, and to IH by the Academy of Finland (Finnish Centre of Excellence Programme, grant number 44887). We thank D. Molbo and two anonymous referees for helpful comments. REFERENCES Chesson, P. (1991). A need for niches. Trends Ecol. Evol., 6, 26–28. Cook, J.M. & Rasplus, J.-Y. (2003). Mutualists with attitude: coevolving fig wasps and figs. Trends Ecol. Evol., 18, 241–248.
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Editor, J. Greeff Manuscript received 13 November 2003 First decision made 2 December 2003 Manuscript accepted 5 January 2004
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