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Biological Conservation 89 (1999) 143±152

Rapid displacement of native by : e€ects of hybridization

Gary R. Huxel* Department of Environmental Science and Policy and Institute of Theoretical Dynamics, University of California, Davis, CA 95616, USA

Received 23 March 1998; received in revised 24 October 1998; accepted 4 November 1998

Abstract The introduction of non-native can lead to the competitive exclusion (displacement) of native populations. This has been hypothesized to be further exacerbated by the potential of hybridization, which can dilute or genetically assimilate the native leaving no ``pure'' natives. With relatively moderate to high rates of immigration, the loss of the native species can be rapid with or without hybridization. Using single-, two- models, I ®nd that species replacement can occur very rapidly and the time to displacement decreases rapidly with increasing immigration and selection di€erential. Immigration and selection act in two di€erent ways: increasing immigration results in displacement by overwhelming the native; whereas increasing the selection di€erential in favor of the invader leads to displacement via . The implications of these results are the need for more empirical studies on the immigration patterns of invasive species and their potential for interbreeding with natives. # 1999 Elsevier Science Ltd. All rights reserved. Keywords: ; Species displacement; Hybridization; Genetic assimilation; Invading species

1. Introduction taxa or of the native taxa. Although theore- tical studies have addressed the introduction of new Hybridization is a common phenomenon in , into populations (i.e. the third phase of Wright's , ®sh, and many other taxa (Mayr, 1942; Grant, shifting balance theory), few have focused on the dis- 1981; Harrison, 1990; Grant and Grant, 1992, 1996; placement of native taxa (alleles). Here, I use single Dowling and DeMarais, 1993; Levin et al., 1996; Rhy- locus, two-allele (one native and one non-native) to mer and Simberlo€, 1996; Williamson, 1996; Arnold, examine the in¯uence of interbreeding with invading 1997). Yet in studying the displacement of native species taxa on native taxa. by invading species the potential for interbreeding Historically, geographical isolation has been a major between an invading species and a native species is often factor in limiting the impacts of hybridization and ignored or understated. It has been suggested that introgression. Today, however, taxa are being brought interbreeding increases the threat of extinction for a into contact with related taxa from which they have number of species due to hybridization introgression been isolated through many anthropogenic pathways (Levin et al., 1996; Rhymer and Simberlo€, 1996). For (Carlton, 1979, 1989; Carlton and Geller, 1993; Wil- example, ``pure'' native Pecos pup®sh may no longer liamson, 1996). For example, the movement of ballast exist due to introgression with an introduced bait ®sh, water throughout the world is increasing the opportu- the sheepshead minnow (Echelle and Connor, 1989). nities for closely related taxa to interbreed leading to Conditions under which hybridization is expected to homogenization of near-shore marine communities increase or decrease the rate of species displacement has worldwide and the widespread loss of species (Carlton, not been explicitly examined. In cases where related 1979, 1989, 1996; Carlton and Geller, 1993). Similar taxa are able to interbreed, introductions may lead to large distance (inter-regional), short time scale immi- the introduced taxa dying out, coexistence, new gration occurs with the introduction of nurse stocks of plants and the incidental movement of and * Tel.: +1-530-752-5162; fax: +1-530-752-3350; e-mail: grhuxel@ (Heywood, 1989). Furthermore, introduc- ucdavis.edu. tion of species has been extremely widespread

0006-3207/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S0006-3207(98)00153-0 144 G.R. Huxel / Biological Conservation 89 (1999) 143±152 throughout the world (Moulton and Pimm, 1986; produced compared with the number produced by other Moulton, 1993; Case, 1996). -mediated intro- . Thus, the interesting question in terms of the ductions can be frequent and re-occurring, greatly conservation of species, and the main question of this increasing immigration rates (Carlton and Geller, 1993). paper, is whether hybridization enhances or impedes the In the absence of hybridization the interaction rate of species displacement and whether this phenom- between the native and is essentially enon is a€ected by introgression. I address this question a competitive one between species that are similar in using single locus, two-allele models with varying many aspects of their and histories. Assum- degrees of interbreeding. Additionally, I examined the ing a homogeneous environment, without interbreeding, in¯uence of varying the ®tness of the heterozygote from the species with the greater ®tness (e.g. better compe- to overdominance in a system that titor or higher reproductive rate) will dominate at equi- exhibits introgression. librium. Switching from discussing individuals, I now focus on interactions between native and non-native genotypes. If immigration rates are very low and given 2. Model descriptions and analyses no (or a weak) selection advantage to the invader, then one would expect that Allee or stochastic e€ects may Let us consider two populations with non-over- lead quickly to elimination of the invader as its popula- lapping generations. One is native and has a tion density remains low. At very high rates of immi- ®xed allele at a given locus (BB) and the other is non- gration, Kondrashov (1992) has shown that native with a di€erent ®xed allele at the same locus immigration e€ects alone in the absence of interbreed- (AA). Non-native individuals can migrate into the ing can cause the loss of the native species. Alter- native but the opposite in not allowed. This may natively, large ®tness di€erentials, alone, lead to the represent stocking programs or other human-mediated ®xation of a favored genotype, therefore the relatively dispersal so that immigration rates can be much greater slow process of selection acting without immigration than otherwise found in natural systems. The popula- can be quickened by increasing the ®tness di€erential. tion is assumed to follow Hardy±Weinberg proportions For example, intermediate genotypes can be made lethal with selection immediately following immigration. This for a population with a large, but ®nite, population size assumes no , large populations and random so that the inferior parental genotype is rapidly lost . Furthermore, any competitive di€erences are (Kondrashov, 1992). accounted for in ®tness di€erentials. In the model, the In the presence of hybridization, one would expect population size is in®nite and ®xation of AA is said to costs associated with genetic assimilation and/or bene- occur when its frequency is greater than 0.99. Four ®ts of infusion of new into one or both parental cases of post mating isolation are modeled: (1) lethal taxa. However, hybrids can be fertile yet reproductively heterozygotes; (2) sterile hybrids; (3) hybrids with isolated from adults for various reasons including ferti- backcross sterility and (4) introgression. A ®fth case was lity selection (allopolyploidy, translocation hetero- examined which also involves introgression, but the ®t- , recombination , species-speci®c ness of the heterozygote is varied from underdominance di€erences in mitochrondial DNA) and pre-mating fac- to overdominance. The frequency of AA, pAA, (the tors (behavioural changes, reproductive phenology, introduced genotype) at time (t ‡ 1): niche separation). Interbreeding may also allow rare 0 genotypes to become established and then increase as pAA ˆ pAA 1 m†‡m; 1† backcrosses with the non-native parental taxa or inter- breeding between hybrids occurs. This of course, is where m is the migration rate. This assumes that simple in the single locus models used here, but is more migrating individuals each replace one resident indivi- complicated in real situations involving multiloci (see dual proportionally (no preference for displacement of below). Large selection advantages for non-native any genotype by immigrants). of the native spe- alleles should result in more rapid displacement of cies was assumed to be 1 in all models for mathematical native alleles with hybridization than without. and interpretive ease. While studies have shown that lowering the ®tness of Most theoretical studies have focussed on equilibrium hybrids can result in displacement (Kondrashov, 1992), analyses of introduced alleles, but I was most interested the question remains as to whether the rate of species in the time to displacement. The time frame of dis- displacement increases or decreases with increased placement has important conservation consequences interbreeding between an invading genotype and a due to human-mediated immigration rates and the lack native genotype. Genotypic displacement occurs when a of taxonomic work in many systems (Carleton and native species becomes extinct and is replaced by an Geller, 1993; Geller et al., 1997). Thus I allowed the invading species. By ®tness, I mean the relative compe- systems to run assuming a large population of constant titive ability expressed as the number of viable o€spring size from one generation to the next until displacement G.R. Huxel / Biological Conservation 89 (1999) 143±152 145 occurred or 500 generations had elapsed. I used the range of values for ®tness (!AAЮtness of AA in the ®rst four cases or !ABЮtness of AB in the last case) from 0 to 4.0 with step increases of 0.1 and m from 0 to 1.0 with step increases of 0.1. The initial is comprised only of natives (pBB ˆ 1).

2.1. Lethal heterozygotes

I simpli®ed the analyses by only following the intro- duced species in this case. If pAA is the frequency of the introduced genotype in the generation after selection and if no interbreeding can occur then

0 2 2 2 pAA ˆ !AApAA=b!AA pAA ‡ m†‡!AB 1 pAA† m†c 2†

where !AA is the ®tness of the ``pure'' invader genotype, pAA is the frequency of the ``pure'' invader genotype, m is the migration rate and !BB is the ®tness of the native genotype. This is the baseline case for the discussion, which is essentially a competitive situation where the species have remained reproductively isolated. Fixation of the invader genotype (pAA ˆ 1) always occurred when both immigration and !AA were at moderate levels [Fig. 1(a)]. Fixation also occurred when the invader had a disadvantage in ®tness (!AA < 1). For example, when !AA > 0:20, ®xation occurred whenever immigration was greater than 0.30. Under the condition of no immigration (m ˆ 0:0) the invader genotype is always lost. An interesting dynamic happens at m ˆ 0:1 which is below the critical immigration rate for which a Fig. 1. The no interbreeding case; (a) time to extinction and (b) fre- quency of AA. These patterns hold for the sterile hybrid and back- species cannot successfully replace another without cross sterility cases as well. selection when !AA ˆ 1 (Crow et al., 1990; Kondra- shov, 1992). As predicted with m at this level, at and greater population sizes than the native species and in below !AA of 2.0 the pAA slowly approaches 0.07 so that the absence of introgression may displace the native. ®xation does not occur in 500 generations, but increas- This seems to be occurring in the introduction of brook ing !AA to 2.1 leads to ®xation in just 33 generations. (Salvelinus fontinalis) into the habitat of native This is typical of the dynamics with no hybridization bull trout (S. con¯uentus) in the Columbia and Klamath where there exists a sharp boundary between rapid and River drainages (Leary et al., 1993). no ®xation with 500 generations (eventually however ®xation will always occur with one way migration and 2.2. Hybrid sterility !AA > 1). The frequency of AA after 500 generations was always less than 0.25 when ®xation did not occur Next I examine the extreme case of hybridization and was usually less than 0.10 [Fig. 1(b)]. When ®xation without introgression in which the hybrids are sterile occurred it always did so in less than 33 generations and (!AB ˆ 0), but are part of the t ‡ 1 generation. The as both !AA and m increased, this time to ®xation was equation for the frequency of AA (pAA) is the similar to reduced to less than 10 generations. Eq. (2), however to maintain a constant population size,

The case of no interbreeding demonstrates that dis- pAA at time t ‡ 1 one must account for the loss of placement is greatly in¯uenced by immigration and dif- hybrid individuals each generation. Therefore I assumed ferences in relative ®tness. Time to displacement, when that the two parental lineages produce sucient num- it occurred, was extremely rapid and decreased as m and bers of o€spring so that the population size is constant !AA increased. Immigration rates may be increased by from one generation to the next and do so at their human activities; examples of this are found in stocking respective proportions after selection. For example, if programs, in which the introduced species may have pAA ˆ 0:40 and pBB ˆ 0:60 (®tness of all genotypes is set 146 G.R. Huxel / Biological Conservation 89 (1999) 143±152 to 1 and m is set to zero for this example), random quency of the ``pure'' native. Compared to the ®rst two mating results in pAA ˆ 0:16, pAB ˆ 0:48, and cases, the time to displacement is faster at low immi- pBB ˆ 0:36. As the heterozygotes are sterile, the fre- gration and at low !AA values, slower otherwise. quency of A for contribution to the following genera- From the perspective of invading species with a low tion is 0.32/(0.32+0.72) or 0.307. Thus, the only immigration rate, this is favorable compared to a case di€erence between this model and the no interbreeding where no interbreeding occurs or the hybrids are sterile. case is that some reproductive e€ort is spent on the At low invasion numbers, the invader may su€er from hybrids which do not reproduce. the Allee e€ect, which can be molli®ed by interbreeding The pattern of the rate of species displacement found with the native species. In the one locusÐtwo-allele in this case was similar to the no interbreeding case (see model, even if introgression does not occur, breeding Fig. 1). The di€erence was that the transitions were among hybrids produces a signi®cant number of ``pure'' steeper, that is, when ®xation did not occur, pAA was invaders. In the sterile hybrid model, all reproductive lower. In many instances the invader genotype did not e€ort with natives is lost, e€ectively reducing the popu- become established even at high rates of immigration lation size of the invaders. At high immigration rates, (but low AA ®tness values). The number of generations sheer numbers alone can overcome the Allee e€ect. to species displacement, when it did occur, was the same as the no interbreeding case. The frequency of the native 2.4. Introgression

(pBB) only slowly decreased with m and !AA until the steep transition to displacement. The frequency of This is the standard Hardy±Weinberg scenario with hybrid (pAB) remained low while AA was low and were selection giving Eq. (3), but now lost with the native. 2 2 The results show that hybridization with sterile a ˆ pAA ‡ pAA=4 ‡ pAApAB=2† 1 m†‡m hybrids has little e€ect on species displacement as com- 2 pared to the no interbreeding case. This result is depen- b ˆ 2pAApBB ‡ p =2 ‡ pAApAB=2 ‡ pBBpAB=2† 1 m† dent upon the surviving ``pure'' individuals having great 2 2 c ˆ p ‡ p =4 ‡ pBBpAB=2† 1 m† enough fecundity to maintain a consistent population BB AB size. If fecundity of these individuals cannot maintain a consistent population size then they are likely to become Using this model, I performed two analyses. In the ®rst, extinct, which is a real possibility for populations that in this , I varied !AA as in the earlier two cases start with small numbers of individuals. Once the and in the second, Section 2.5, I varied !AB to examine extinction of natives and hybrids has occurred, the the e€ects of hybrid ®tness. In the former, !AB and !BB invader may then become established. Furthermore, this were set to 1 and in the latter, !AA and !BB were set to case demonstrates that even when the invader is at low 1. Hybrid vigor can occur whenever hybrids are pro- density, small increases in immigration or ®tness of the duced, sterile hybrids may thrive by vegetative growth invader can lead to rapid displacement. and reproductively isolated hybrids may also have increased ®tness. For demonstrative purposes, I chose 2.3. Hybridization with backcross sterility only to model sexual in Section 2.5. As with all other cases, ®xation occurs over a wide In this case the hybrids are fertile yet have become range of m and !AA values [Fig. 2(a)]. However, in this reproductively isolated from the two parental lineages case ®xation does not occur when !AA < 0:50, but does (which can interbreed). This can be modeled by the fol- occur when m50:05 and !AA > 0:90. Thus, ®xation can lowing: arise at lower levels of immigration, but displacement is restricted to conditions when the relative ®tness of the 0 pAA ˆ !AAfag=‰!AAfag‡!ABfbg‡!BBfcgŠ native is low. Comparing time to ®xation, the introgres- 0 sion model takes longer than the previous three models, pAB ˆ !ABfbg=‰!AAfag‡!ABfbg‡!BBfcgŠ p0 ˆ ! fcg=‰! fag‡! fbg‡! fcgŠ but the di€erences are relatively small. The frequency of BB BB AA AB BB AA is also much greater when ®xation does not occur in 2 2 a ˆ pAA ‡ pAB=4† 1 m† this case compared to the others [Fig. 2(b)]. Because of 2 high frequencies of hybrids, p was much lower in this b ˆ 2pAApBB ‡ pAB=2† 1 m† BB 2 2 case than the previous models [Fig. 2(c)]. As m and !AA c ˆ pBB ‡ pAB=4† 1 m†; 3† values (as well as pAA) increased, pAB became greater than pBB [Fig. 2(d)]. The hybrid increased as m and !AA where a, b and c are the total contributions to the next increased until the native was driven to low frequencies generation from each genotype for AA, AB and BB, and then both pAB and pBB went extinct. respectively; pAA is the frequency of the ``pure'' invader; In the case of introgression, the rate of species dis- pAB is the frequency of the hybrid; and pBB is the fre- placement is faster at low levels of immigration, but G.R. Huxel / Biological Conservation 89 (1999) 143±152 147

Fig. 2. The introgression case; (a) time to extinction; (b) frequency of AA; (c) frequency of AB; and (d) frequency of BB. slower at lower values of relative ®tness of the invader pared to the ®rst two cases, but they have lower fre- when compared to the no interbreeding case [Figs. 1(a) quencies compared to the introgression case. and 2(a)]. Owning to a lower frequency of the native genotype and increased frequency of the hybrid, the 2.5. Heterozygote ®tness native is more susceptible to demographic or environ- mental stochasticity as well as genetic assimilation by At values of !AB < 1 (underdominance), the species the invader. The presence of large numbers of hybrids displacement of the native is enhanced [Fig. 3(a) and may also arise at points of contact between species at (b)]. However, when !AB > 1 (overdominance), this was the limits of their ranges creating hybrid zones. As an greatly reduced and complete displacement did not example, introgression seems to be playing a role in the occur at any level of m when !AB > 2:1. As pAB loss of the ``pure'' native red deer in Scotland (Aber- increased with !AB, pBB was driven to <0.13 at low m, nethy, 1994). In this system a was created decreasing to pBB < 0:02 at m > 0:40 [Fig. 3(c) and (d)]. and it is in disequilibrium so that the zone is shifting, The hybrid also became dominant over the ``pure'' resulting in a decrease of the native red deer range. invader as pAA decreased and !AB increased at all levels Displacement occurs at lower values of !AA for of m [Fig. 3(b)]. These results may be an artifact of the immigration rates greater than 0.05 in comparison of single locus models in which hybrids interbreeding the introgression case with the hybridization with back- among themselves or with either parental genotype cross sterility case. Similarly, the hybridization with can produce ``pure'' parental genotypes (see below). backcross sterility case is intermediate in terms of the This may not occur given a large number of interacting frequency of the three genotypes. The native has a lower loci. frequency when it persists compared to all other cases. The loss of the ``pure'' native due to genetic assimila- The other two genotypes have greater frequencies com- tion can be hastened by hybrid vigor (overdominance) 148 G.R. Huxel / Biological Conservation 89 (1999) 143±152

Fig. 3. The introgression with underdominance and overdominance: (a) time to extinction; (b) frequency of AA; (c) frequency of AB; and (d) fre- quency of BB. whether introgression occurs or the hybrids are repro- new species has since displaced both ``pure'' species and ductively isolated from the parental lineages. Though the sterile hybrid and become a dominant extend- complete displacement may be reduced as the relative ing much further down into the tidal zone while the ®tness of the hybrid increases, the frequency of the original hybrid has not spread (Thompson, 1991). native decreases (above a threshold) and approaches zero when the rate of immigration is high [Fig. 3(a)]. As an illustration, the introduction of Spartina alter- 3. Discussion ni¯ora into the British Isles shows aspects of hybrid sterility, hybridization without and hybrid The results suggest that displacement of native taxa vigor. In plants (and other ), hybrids may be by non-native taxa can occur very rapidly [e.g. less than reproductively isolated from the parental lineages due to ®ve generations; see Fig. 2(a)]. Given the number of . When this occurs and the new species shows cryptic species and the high rates of human-mediated hybrid vigor, both ``pure'' species may be displaced. species introductions, may be on the increase This can be seen in the case of S. anglica (Thompson, from the e€ects of hybridization alone. 1991). The introduction of S. alterni¯ora, a native of the The results of the models are dependent on a number North American Atlantic coast, into the British Isles of factors implicitly assumed in the model. These lead to its hybridizing with S. maritima, a European include: (i) that the ®tness of AA and AB can have a native, producing S.  townsendii which was sterile. large range of values; (ii) migration rates can be extre- Subsequently a doubling occurred in S.  mely high; (iii) a single locus can infer large relative ®t- townsendii producing S. anglica, which was fertile but ness di€erences; and (iv) mating is random. Below I reproductively isolated from the parental lineages. This brie¯y discuss each of these. G.R. Huxel / Biological Conservation 89 (1999) 143±152 149

3.1. Fitness of AA and AB 3.2. Migration

The range of values of ®tness for AA used in this The movement of coastal marine species via ship study may seem fairly extreme, however in the context fouling, incidental passengers and ballast water has of an invading species these values may not be extreme. been occurring for many of years, with most the move- Invading species that are transported across large barriers ment in terms of ballast water occurring recently (Carl- may have the advantage of escaping from predators, ton, 1979, 1989; Carlton and Geller, 1993). With many parasites and competitors (Elton, 1958). Essentially species in the marine environment yet undescribed, the species can land in ``enemy free space''. This may explain impact of species displacement may be highly sig- some of the diculty in developing general theories con- ni®cant. Many marine taxa are widely distributed and cerning which species will successfully invade which geographically distinct. Terrestrial systems have also community (Rejma nek, 1995; Reichard and Hamilton, been subjected to introduction rates that are occurring 1997). , and (or a at three or more orders of magnitude greater than the combination of some or all) may drive a species into a major paleontological invasions such as the Great narrow niche in its native range, once released from this American Interchange (Williamson, 1996). the species may become more common in its new habi- In addition to human-mediated transportation, chan- tat. Additionally, a species that is rare in its native ging global climate can also signi®cantly increase habitat may become more common with increasing migration rates. For marine systems, near-shore tem- amount of favorable habitat in its new range. New perature is a major limiting factor in species distribu- habitat can include prey species with which they have tions; increased temperatures in these systems will no previous evolutionary contact so that no defenses are facilitate dispersal. For example, the interaction encountered. Conversely, a species may ®nd increased between Mytilus galloprovinicialis and M. trossolus may competition, predation and parasitism and less favor- be further complicated by warming of northern Paci®c able habitat in the new region lowering its ®tness. waters allowing M. galloprovinicialis to spread north- One of the potential consequences of hybridization is ward (Suchanek et al., 1998). that the hybrid may be able to invade that its Migration and ®tness may also be altered by di€er- parental species cannot, thus the total population size ences in production and . The invading may be increased due to new resource availability. species may genetically ``swamp'' the native by produ- Spartina anglica's occupation of lower regions of the cing large numbers of (i.e. or by intertidal zone is an example that is consistent with this males) and increased fertility in the expanded range. scenario (Thompson, 1991). A possible limitation to the Many rare plant populations contain few individuals model is that it does not allow for hybrids to reproduce (Levin et al., 1996). Low population size results in vegetatively. Sterile hybrids may expand their range and increased susceptibility for rare species to genetic spread via vegetative growth, but there is no evidence assimilation and species displacement due to inter- for this. breeding. This is an important factor of species As to the relative ®tness of hybrids, there are only a as well. For example, introgression has been cited as a limited number of documented cases of overdominance. substantial contributing factor for three (the Tecopa Endler (1986) lists only six examples. However, this may pup®sh, nevadensis; the Amista gambusia, be due to the lack of solid data testing for this phe- Gambusia amistadensis; and the longjaw cisco, Cor- nomenon, but with improving genetic techniques this egonus alpenae) of the 13 species that have become will become easier to test. Blossey and NoÈ tzold (1995) extinct since the creation of the Act suggested that the of increased competitive (Rhymer and Simberlo€, 1996). ability can result from shifts in resource allocation pat- An increasing source of migration of large numbers of terns due to selective forces in the new habitat. This may individuals is the introduction of biological control lead to rapid changes in relative ®tness of the invader agents and genetically engineered genes (Howarth, 1991; and any hybrids. In a test of this hypothesis, Blossey Klinger and Ellstrand, 1994; Simberlo€ and Stiling, and Kamil (1996) found that introduced sali- 1996). plants are a large source of engineered caria (purple loosestrife) grew better in identical condi- genes and the spread of these genes into wild popula- tions than it did in its native range. Similarly, Strong tions has been documented in several cases (Klinger and (pers. comm.) has found that introduced Spartina alter- Ellstrand, 1994; Bergelson et al., 1998). Bergelson et al. ni¯ora populations in Washington State grows rapidly, (1998) recently demonstrated that engineered genes in but has lost many of its defenses to herbivores. Levin et crop plants may have greater risks of spread than wild- al. (1996) further suggested that hybrids might perform genes in weedy forms. Additionally, many biologi- best under conditions not favored by either . cal control agents have very narrow range of hosts, Similarly, Floate et al. (1993) found that herbivory has however, hybrids between these non-native species and greatest in hybrid zones relative to ``pure'' zones. natives may allow for a broadening of hosts or host 150 G.R. Huxel / Biological Conservation 89 (1999) 143±152 switching by the hybrids. This potential hybridization is Furthermore, introgression may lead to the develop- usually not considered when selecting for biological ment of a hybrid swarm consisting of a large number of control agents. One the above mentioned species that hybrid types due to large numbers of loci. The intro- became extinct after the creation of the Endangered gression between the native Pecos pup®sh (Cyprinodon Species Act, Gambusia amistadensis, was in part due to pecosensis) and the introduced sheepheads minnow (C. two conspeci®cs, G. anis and G. holbrooki, introduced variegatus) generated a hybrid swarm. C. variegatus was for biological control of . Additionally, other introduced, by sport ®shers, as a bait®sh. Within 5 years endangered or vunerable Gambusia species hybridize of introduction of the sheepheads minnow, the native with the ®sh, G. anis (Minckley et al., 1991). had been excluded from approximately half its original range and all remaining individuals were hybrids 3.3. Number of loci (Echelle and Connor, 1989). Thus, multiple loci seem to enhance the number of hybrid types and genetic mixing In many cases of hybridization, the species may not and have sped the diminution of the ``pure'' native be sister species so that segregation between many loci types. Also, large numbers of loci essentially reduce the can frequently occur during recombination. Segregation probability of a ``pure'' individual of either parental can in¯uence interactions between genes and lead to lineage from being produced by two hybrid individuals, hybrids being phenotypically closer to one of the par- an event that is common in the single-locus models. ents. In a study of interactions in hybrid specia- Displacement holds, in model systems, for the in®nite tion, Rieseberg et al. (1996) found that selection to a loci case and may exaggerate the in¯uence of introgres- large extent has governed past hybrid species forma- sion due to the large number of potential hybrid com- tions. They also stated that nonrandom rates of intro- binations. Thus, one would expect that genetic gression and signi®cant associations among unlinked assimilation would be more common with increased, genetic markers of three synthesized hybrid lineages but ®nite, numbers of loci, preserving some of the implied that interactions between coadapted parental natives' alleles in the hybrids (however unfavorable speices' genes constrain the genomic composition of genomic interactions will limit the number of hybrid hybrid species. In many cases, reduced hybrid fertility types; Rieseberg et al., 1996). One then can assume that or sterility is due to unfavorable genomic interactions. the selection di€erences among genotypes are dependent However, successful origin of new species via hybridi- upon a relatively small number of loci. Given even a zation implies that this is not always the case. The small number of loci, a greater number of hybrid types selection process will weed out unfavorable combina- will be produced than in the single locus model and the tions while favorable ones are preserved creating new likelihood that one will be able to outcompete both the genotypes (or possibly new species) or introducing new native and the non-native is increased. Without intro- alleles into one or both of the parental species. gression these hybrids may quickly form a new species In a theoretical study of relative roles of migration as the hybrids are reproductively isolated, but with and selection in the introduction of new alleles, Kon- introgression this may be slowed as backcrosses with drashov (1992) compared a single locus system with a parental lineages occurs. model using an in®nite number of loci. He found that both migration and selection were important factors 3.4. Mating and that the coexistence of genotypes is more likely to occur with in®nite loci. Yet in both model systems, dis- While my models assume random mating, non-ran- placement occurs even in the extreme case of lethal dom mating can greatly in¯uence the results. In the case hybrids. While Kondrashov (1992) examined models of of the Pecos pup®sh, mate preference for males extreme numbers of loci, either one or in®nite, most of other species may have played a role in the rapidity systems will involve an intermediate number of loci. of the spread of exotic genotype and the loss of the Crow et al. (1990) found in models of two to nine loci ``pure'' native (Echelle and Connor, 1989). In the case that with interbreeding, ®xation of the invading geno- of the introduction of into the Columbia type could occur at high rates of two-way migration (the and Klamath Rivers, the lack of introgression created more conservative case compared to one-way migra- an advantage for the more numerous introduced species tion) and moderate rates of ®tness of the invader. The (Leary et al., 1993). However for species invading a new critical migration rate for the ®xation of the non-native habitat, mating is likely to occur with any potential genotype for ! ˆ 1 increases to 0.5 in the in®nite loci mates. case, up from 0.18 in the single locus model. However, Species that are most at risk to hybridization are ones for presence of the non-native alleles, the migration rate that have external fertilization (e.g. as broadcast could be several orders of magnitude lower (0.005 in spawning and outcrossing plants). the case of a triple dominate genotype in a three loci Wind pollined taxa such as have high rates of model). introgression. Hybridization is more likely in groups G.R. Huxel / Biological Conservation 89 (1999) 143±152 151 that have extended breeding cycles (Rhymer and Sim- tion rates to be increasing. Albuquerque et al. (1996) berlo€, 1996). found that species that are sympatric may have greater Associated with random mating is the assumption of barriers to interbreeding than species (or populations) large population size that does not vary. This has con- that have evolved allopatically. These results suggest sequences, as discussed above, in the sterile hybrid that more empirical studies need to be carried out to model and for newly evolved species and/or hybrids that examine the genetic structure of populations that are have slightly di€erent ecological requirements. In the being invaded and determine whether hybridization and latter, the of the system may be introgression are possible. Additionally, the information increased. Further, habitat segregation and selection on the relative ®tness provides better predictive power. have been found to limit random mating in studies of This information will allow for predictions of whether two or three patches (Holt, 1987; Holt and Gaines, displacement is likely. However, due to the rapidity of 1992) and in (Levins, 1969; Hedrick displacement under many conditions of the models, it is and Gilpin, 1997; Peacock and Smith, 1997). best to prevent biological invasions from occurring when possible.

4. Conclusions Acknowledgements Hybridization with introgression can exacerbate spe- I would like to thank Dan Simberlo€, Bernd Blossey, cies displacement rates under the assumptions of the Susan Harrison, Alan Hastings, Kevin McCann, models presented here. Hybridization with sterile o€- spring seems to have little e€ect on displacement. Donald Strong, Alisa Swann, David Cutler, Amy and two anonymous reviewers for suggestions, com- Introgression enhances displacement at low immigra- ments and references. Support for this work was pro- tion rates, but impedes it when the native has a large vided by a NSF Research Training Grant (BIR-960226) selective advantage and at higher rates of immigration. and a NSF Population Biology Grant (DEB-9629236). However, because of increased frequency of hybrids with introgression, the native is still heavily impacted and its likelihood of extinction is greatly increased. References Varying the ®tness of the hybrid demonstrated that at low !AB, displacement is enhanced and at greater values Abernethy, K., 1994. The establishment of a hybrid zone between red of ! , displacement is impeded. But again, because the and ( ). Molecular Ecology 3, 551±562. AB Albuquerque, G.S., Tauber, C.A., Tauber, M.J., 1996. Postmating increased frequency of hybrids, the native species is between quadripunctata and Chry- susceptible to genetic assimilation or extinction. This is sopa slossonae: mechanisms and geographic variation. Evolution 50, especially important because the taxa that are most 1598±1606. Arnold, M.L., 1997. Natural hybridization and evolution. Oxford threatened by introgression and hybridization have low University Press, New York. population sizes and restricted ranges (Levin et al., Bergelson, J., Purrington, C.B., Wichmann, G., 1998. Promiscuity in 1996). This includes the potential loss of genetic integ- transgenic plants. 395, 25. Blossey, B., Kamil, J., 1996. What determines increased competitive rity of native populations through selective stocking of ability of invasive non-indigenous plants? In: Moran, V.C., Ho€- non-native individuals (LargiadeÁ r and Scholl, 1996). man, J.H. (Eds.) Proceedings of the IX International Symposium on As Kondrashov (1992) pointed out, both immigration Biological Control of Weeds, 19±26 January 1996. Stellenbosch, South Africa, pp. 3±9. and selection are important in species displacement. For Blossey, B., NoÈ tzold, R., 1995. Evolution of increased competitive invasive species, both can play important roles when ability in invasive nonindigenous species: a hypothesis. J. of Ecol. immigration occurs from long distances at frequent 83, 887±889. Carlton, J.T., 1979. Introduced invertebrates of San Francisco Bay. intervals leaving ``enemies'' behind (or new niche space In: Conomos, T.J. (Ed.), San Francisco Bay: an urbanized estuary. is available) and maintained at a high rate of immigra- California Academy of Science, San Francisco, pp. 427±442. tion. Because of rapidity of species displacement under Carlton, J.T., 1989. Man's role in changing the face of the : biological invasions and implications for conservation of nearshore conditions of high ! and m, limiting opportunity for environments. Cons. Biol. 3, 265±273. species invasions is critical. The loss of natve species due Carlton, J.T., 1996. Biological invasions and crytogenic species. Ecol- to a closely related introduced species may not just be a ogy 77, 1653±1655. Carlton, J.T., Geller, J.B., 1993. Ecological roulette: the global trans- simple ecological or evolutionary trade-o€. Further port of non-indigenous marine organisms. Science 261, 78±82. extinctions due to unrelated species result in a greater Case, T.J., 1996. Global patterns in the establishment and distribution loss of genetic information as some genetic information of exotic birds. 78, 69±96. Crow, J.F., Engels, W.R., Denniston, C., 1990. Phase three of of the native is assimilated into the invader. In the Wright's shifting-balance theory. Evolution 44, 233±247. models presented here, the invader always becomes Dowling, T.E., DeMarais, B.D., 1993. Evolutionary signi®cance of established and increases in frequency when immigra- introgressive hybridization in cyprinid ®shes. Nature 362, 444±446. Echelle, A.A., Connor, P.J., 1989. Rapid, geographically extensive tion is greater than zero. Given the rate of species genetic introgression after between two pup®sh movement by human activity one can expect immigra- species (Cyprinodon, Cyprinodontidae). Evolution 43, 717±727. 152 G.R. Huxel / Biological Conservation 89 (1999) 143±152

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