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Research Article
Pempheris gasparinii, a new species of sweeper fish from Trindade Island, southwestern Atlantic (Teleostei, Pempheridae)
expand article infoHudson T. Pinheiro, Giacomo Bernardi, Luiz A. Rocha§
‡ Department of Ecology and Evolutionary Biology University of California, Santa Cruz, United States of America
§ California Academy of Sciences, San Francisco, United States of America
Open Access

Abstract

Pempheris gasparinii sp. n. is described from five specimens, 59.1–68.0 mm in standard length. It is only known to occur in the shallow reefs of Trindade Island, 1200 km east of the Brazilian coast, in the southwestern Atlantic. Pempheris gasparinii is the third recognized species of Pempheris in the Atlantic Ocean. This new species is morphologically similar to its close relative, P. poeyi, differing by the number of lateral-line scales (51–54 in P. gasparinii vs. 47–49 in P. poeyi), scales below lateral line (10–11 vs. 9), circumpeduncular scales (11–12 vs. 13), head and caudal peduncle lengths (2.7–3.3 vs 3.5–4.0 in head length). Moreover, Pempheris gasparinii shows a 4% genetic divergence from P. poeyi at the cytochrome oxidase I locus (COI), consistent with a lineage split at the beginning of the Pleistocene. This new species represents the 12th endemic fish species from Trindade Island.

Keywords

Endemism, COI, Vitória-Trindade Chain, oceanic island, Brazil, reef fish

Introduction

The genus Pempheris Cuvier contains 69 valid species (Randall and Victor 2015), with two species known from the Atlantic Ocean: Pempheris poeyi Bean 1885 and P. schomburgkii Müller & Troschel, 1848. Pempheris species generally display similar body shapes, however, these two species strongly differ by coloration (P. poeyi is silvery while P. schomburgkii is yellowish) and number of anal-fin rays (22–24 in P. poeyi vs. 31–34 in P. schomburgkii). Pempheris schomburgkii is widely distributed in the western Atlantic, from Bermuda (32°N) to Santa Catarina, Brazil (29°S). In contrast, a disjunct distribution has been previously assigned to Pempheris poeyi, with populations occurring in the Greater Caribbean and in Trindade Island, Brazil (Pinheiro et al. 2015), at least 5,000 km apart.

Pempheris poeyi was described from Cuba in 1885 (Bean 1885), and since then few specimens have been collected from localities such as the Bahamas, Grenada, Trinidad and Tobago, and Venezuela. Specimens identified as P. poeyi were found at Trindade Island in the early 20th century (Miranda Ribeiro 1919), and rediscovered 90 years later by Pinheiro et al. (2009). There is overlap in counts of dorsal- and anal-fin rays between the Greater Caribbean and Trindade populations, a common observation among Pempheris species (Mooi and Randall 2014), which likely explains why the new Trindade species described herein was misidentified in two recent checklists (Simon et al. 2013, Pinheiro et al. 2015, Randall and Victor 2015). Recent publications revealed that there is an abundance of undescribed cryptic species in Pempheris (Koeda et al. 2013, Mooi and Randall 2014, Randall and Bineesh 2014, Randall and Victor 2014, Randall et al. 2014). In this study, the use of genetic tools allowed us to revisit the Trindade specimens and update their taxonomic status. Thus, herein we describe a third Atlantic Ocean Pempheris species, so far only known from Trindade Island, at the end of the Vitória-Trindade Chain, 1200 km off the Brazilian coast.

Methods

All specimens were collected using hand nets. Counts were performed using a microscope, and morphological characters were measured to the nearest 0.1 mm following Mooi and Randall (2014). Morphometric and meristic data for the type series are presented in Table 1. In the description, meristic values for the holotype are provided first, followed by the range of counts of paratypes in parentheses. Type specimens were deposited in the fish collections of the Universidade Federal do Espírito Santo (CIUFES), California Academy of Sciences(CAS), and Universidade Estadual de Campinas(ZUEC).

Table 1.

Counts and measurements of selected type specimens of Pempheris gasparinii sp. n. and comparative specimens of P. poeyi and P. schomburgkii (data range) as percentages of standard length. “Circumped” = circumcaudal peduncular.

Holotype Paratypes Pempheris poeyi Pempheris schomburgkii
CIUFES 3127 CAS 238409 CAS 238410 CIUFES 2432 ZUEC PIS 11233
LL Scales 54LR 51L,52R 53L,54R 53L,52R 52LR 47–49 56–59
Scales above LL 2 2 2 2 2 1 3
Scales below 11 11 10 11 10 8–9 15–17
Circumped scales 12 11 11 12 12 13 14–17
Gill rakers 25 24 24 23 25 24 24–25
Dorsal fin IV 8 IV 8 IV 9 IV 8 IV 9 IV 7–8 IV 8
Anal fin III 24 III 24 III 24 III 24 III 25 III 24–26 III 31–34
Pectoral fin 15 15 15 15 15 14–15 I 15
Pelvic rays I 5 I 5 I 5 I 5 I 5 I 5 I 5
SL (mm) 64.5 68.0 60.5 64.6 59.1 28.6–52.7 91.6–101.9
Body depth 36.5 37.1 37.2 37.3 36.9 36.2–41.0 41.4–48.4
Body width 14.1 13.5 15.0 14.2 15.2 14.6–17.1 15.0–16.6
Head length 31.5 27.2 30.6 31.4 31.3 32.1–36.1 26.3–33.3
Snout length 5.4 3.4 3.7 5.0 4.1 4.3–6.1 4.0–5.2
Orbit diameter 11.8 14.3 13.9 13.3 13.7 12.9–14.8 13.4–13.9
Interorbital width 12.6 12.7 9.8 9.4 8.5 8.4–11.2 8.5–9.3
Caudal-penducle depth 9.6 10.0 10.5 10.5 10.9 8.4–10.2 8.7–9.0
Caudal penducle length 7.1 10.1 8.1 7.7 9.1 6.6–9.7 7.9–8.5
Predorsal length 41.2 40.6 43.1 42.9 41.6 38.9–45.1 36.4–42.3
Pre-anal length 58.8 54.3 58.7 55.4 59.9 53.5–60.5 44.7–48.6
Prepelvic length 39.1 34.9 37.4 35.1 38.1 36.4–38.6 27.3–28.6
Base of dorsal fin 15.6 15.0 16.9 16.3 17.4 16.4–18.2 15.0–16.6
First dorsal spine 4.9 4.1 4.4 4.5 3.9 3.5–3.8 3.0–7.3
Fourth dorsal spine 17.1 16.5 21.7 18.2 17.7 16.6–18.9 18.5–20.9
Longest dorsal ray 22.0 19.5 22.3 23.1 21.8 17.6–21.9 20.3–23.3
Base of anal fin 35.0 34.9 35.0 34.3 37.6 33.5–42.6 47.2–47.8
First anal spine intern intern intern intern intern intern 1.9–2.7
Third anal spine 4.3 3.2 4.5 4.3 3.6 4.5–7.6 8.9–11.5
Longest anal ray 9.1 8.8 9.8 7.6 9.0 8.1–11.8 10.6–12.2
Caudal fin length 28.5 22.9 25.3 broken broken broken 25.4–29.6
Caudal concavity 17.1 17.1 17 broken broken broken 8.6–9.5
Pectoral-fin length 24.5 23.3 24.4 25.9 24.2 25.8–31.8 25.5–27.5
Pelvic-spine length 9.5 9.4 8.1 8.7 9.1 10.2–11.7 9.7–10.5
Pelvic fin length 14.9 13.2 13.7 13.0 14.0 13.1–18.5 10.5–13.6
Upper jaw length 16.1 18.4 16.8 17.5 18.8 15.9–18.4 15.3–17.4

Mitochondrial Cytochrome c oxidase subunit I (COI) DNA was analyzed for the new species. DNA extraction and PCR amplification of the COI were performed following Weigt et al. (2012). DNA sequences were then compared to those of the other two Atlantic Pempheris (P. poeyi and P. schomburgkii) downloaded from GenBank. Phylogenetic relationships were assessed by Maximum Likelihood (ML, GARLI software, Zwickl 2006), and Neighbor-Joining (MP, PAUP* software, Swofford 2003) methods. For Maximum Likelihood topologies, we conducted 10 independent runs in GARLI, using default settings and the automated stopping criterion, terminating the search when the ln score remained constant for 20,000 consecutive generations. Statistical confidence in nodes was evaluated using 1,000 non-parametric bootstrap replicates (Felsenstein 1985) for the NJ method, and 100 replicates for ML in GARLI, using the automated stopping criterion set at 10,000 generations. Parapriacanthus is the only other genus of Pempheridae and was used as an outgroup as in Azzurro et al. (2015) (sequence from GenBank, accession number JF494087). Pempheris sequences are from Azzurro et al. (2015), except for P. poeyi, which is from this study. GenBank access numbers are KJ609406 (Pempheris gasparinii sp. n.), KT634057 (Pempheris poeyi), and KJ609388.1 and KJ609389.1 (Pempheris schomburgkii).

Results

Pempheris gasparinii sp. n.

Figs 1, 2, Trindade sweeper

Pempheris poeyi: Miranda-Ribeiro 1919: 173

Pempheris poeyi: Pinheiro et al. 2009: 49

Pempheris poeyi: Simon et al. 2013: 2121

Pempheris poeyi: Pinheiro et al. 2015: 20

Type locality

Trindade Island, Espírito Santo State, Brazil.

Holotype

CIUFES 2432, 64.5 mm SL, GenBank KJ609406, Parcel pool, Trindade Island, Espírito Santo, Brazil. 20°30'S, 29°20'W, depth 1 m, collected by HT Pinheiro and JL Gasparini, 25 Jun 2009 (Figure 2).

Paratypes

CAS 238409, 68.0 mm SL, CAS 238410, 60.5 mm SL, CIUFES 2432, 64.6 mm SL, ZUEC PIS 11233, 59.1 SL. Same data as holotype.

Comparative material

Pempheris poeyi: CAS 238411 (one specimen, 52.7 mm SL, Curaçao), USNM 318952 (two specimens, 34.6 and 39.1 mm SL, Tobago), USNM 354575 (two specimens, 28.6 and 29.0 mm SL, Tobago); Pempheris schomburgkii: CAS 1595 (one specimen, 92.7 mm SL, Bahia, Brazil), CAS 32060 (two specimens, 48.7 and 39.7 mm SL, Barbados), CAS 236600 (one specimen, 99.2 mm SL, Curaçao), CAS 236604 (one specimen, 103.4 mm SL, Curaçao).

Diagnosis

Pempheris gasparinii differs from its congeners by the following combination of character states: Head 3.2–3.7 in SL; body depth 2.7 in SL; head length 3.2–3.7 in SL; orbit diameter 1.9–2.7 in HL; caudal-peduncle depth 2.7–3.3 in HL; dorsal rays IV, 8–9; anal-fin rays III, 24–25; pectoral rays 15; lateral-line scales 51–54; scales below the lateral line 10–11; circumpeduncular scales 11–12; and gill rakers 23–25. Color in life mostly silvery, darker from mid-body to the lateral line and greenish above; fins are translucent with a darker tail. Color in alcohol light brown to silvery with darker dorsum and translucent fins; caudal fin darker. Additionally, mitochondrial DNA COI sequences show a divergence of at least 4% from all Atlantic congeners.

Description

Dorsal-fin rays IV, 8 (IV, 8–9), all segmented rays branched; anal rays III, 24 (III, 24–25), first internal, all segmented rays branched; pectoral rays 15, the first rudimentary, second unbranched, remaining rays branched; pelvic rays I V (I V); principal caudal rays 9+9 (9–10+9), the median 16 branched (16–17); upper+lower procurrent caudal rays 6+6 (6–8+5–6), the most posterior of each side segmented distally; lateral-line scales 54 (51–53) to the base of the caudal fin, pored scales continuing to the end of the fin; gill rakers 6+19 = 25 (4–6+19–21).

Body moderately deep and compressed. Depth 2.7 (2.7) in SL and width 2.6 (2.4–2.7) in body depth; head length 3.2 (3.2–3.7) in SL and dorsal profile of head moderately convex; snout very short, 5.8 (6.3–8.2) in HL; orbit diameter 2.7 (1.9–2.4) in HL; interorbital width 2.5 (2.1–3.7) in HL; caudal-peduncle depth 3.3 (2.7–3.1) in HL; caudal-peduncle length 4.5 (2.7–4.1) in HL.

Mouth oblique, forming ~60°angle to horizontal axis of body; lower jaw slightly protruding when mouth fully closed; maxilla expanding posteriorly to a width two-thirds pupil diameter; upper jaw teeth very small, sharp, incurved, in two irregular rows anteriorly, narrowing to a single row posteriorly; lower jaw teeth small, in a patch with three to four irregular rows, outer one or two rows sharply nodular, inner two rows strongly recurved and narrowly sharp; vomer with expanded V-shaped patch (three to four irregular rows) of very small nodular teeth; palatines with a long and narrow patch (two irregular rows anteriorly to one posteriorly) of very small and medially curved teeth; tongue diamond shaped, upper surface with small papillae.

Gill rakers long, longest gill filaments two-thirds the length of longest gill raker. Gill opening extending dorsally, near level of center of orbit. Margin of preopercle smooth. Anterior and posterior nostril apertures vertically oval, positioned in front of dorsal edge of pupil, and separated by narrow septum; no membranous flap on nostril edges. Most scales cycloid, except finely ctenoid posteriorly in interorbital area, on nape, on dorsal area posteriorly to dorsal fin, and above lateral line and chest. Small scales covering slightly more than basal half of anal fin and slightly less than half of caudal fin.

Origin of dorsal fin posterior to vertical alignment of rear base of pectoral fin; predorsal length 2.4 (2.3–2.5) in SL; dorsal-fin base 6.4 (5.7–6.7) in SL; first dorsal spine short, 6.4 (6.6–8.0) in HL; fourth dorsal spine longest, 1.8 (1.4–1.8) in HL; first or second dorsal segmented rays longest, 1.4 (1.4) in HL; origin of anal fin aligned with end of dorsal fin base, preanal length 1.7 (1.7–1.8) in SL; anal-fin base short, 2.9 (2.7–2.9) in SL; first anal spine internal and very short; third anal spine short, 7.3 (6.7–8.8) in HL; longest anal segmented ray 3.4 (3.1–3.5) in HL; caudal-fin length 3.5 (4.0–4.4) in SL; caudal concavity 1.8 (1.6–1.8) in HL; second or third branched pectoral ray usually longest, 4.1 (3.9–4.3) in SL; origin of pelvic fins slightly posterior to rear base of pectoral fins, prepelvic length 2.6 (2.6–2.9) in SL; pelvic spine 3.3 (2.9–3.8) in HL; pelvic-fin length 2.1 (2.1–2.4) in HL.

Color in life

Body mostly silvery, darker from mid-body to lateral line and greenish above; fins translucent with a darker tail (Figure 1).

Figure 1. 

Underwater picture of Pempheris gasparinii sp. n. at the Parcel Pool, Trindade Island (top; photo J.L. Gasparini), and a specimen shortly after death (bottom; photo T. Simon).

Color in alcohol

Body light brown, darker dorsally; fins pale except caudal fin with basal melanophores (Figure 2).

Figure 2. 

Pempheris gasparinii sp. n., preserved holotype, 64.5 mm SL, CIUFES 3127 (photo A. Barber).

Etymology

The specific name honors our ichthyologist colleague and friend João Luiz Rosetti Gasparini, one of the pioneers on the study of taxonomy and biodiversity of reef fishes in Brazil and Trindade Island. “Gaspa” has contributed to nearly half of the descriptions of reef-fish species from Brazilian waters in the last two decades. To be treated as a noun in apposition.

Distribution and habitat

Pempheris gasparinii sp. n. is known only from the type locality, Trindade Island, Espírito Santo, Brazil. It has only been found schooling in the very shallow waters of the rocky Parcel pools (Figure 3).

Figure 3. 

Parcel Pool, Trindade Island, Brazil, type locality of Pempheris gasparinii sp. n. (photo H.T. Pinheiro).

Genetic data

A maximum likelihood phylogenetic reconstruction of Atlantic Pempheris, based on the mitochondrial cytochrome oxidase 1 (CO1) marker, is presented in Figure 4. The Kimura-2 genetic distance between Pempheris gasparinii sp. n. and its closest relative (P. poeyi) is 4%.

Figure 4. 

Maximum Likelihood tree of Atlantic Pempheris based on the mitochondrial cytochrome oxidase 1 (CO1) marker. Labels correspond to sample names (following Azzurro et al. 2015), species names (when identified), collection locality, and biogeographic region. Bootstrap support (1000 replicates) for Neighbor-Joining and Maximum Likelihood are given at the node, in this order. The new species, P. gasparinii, is labeled in red.

Comparative remarks

Pempheris gasparinii differs from its Atlantic Ocean congeners by the smaller number of soft anal-fin rays (24–25) compared to P. schomburgkii (31–34), and greater number of lateral-line scales (51–54) and scales below the lateral line (10–11) compared to P. poeyi (47–49, and 9 scales respectively). Pempheris gasparinii also has fewer circumpeduncular scales (11–12 vs 13), a smaller head (3.2–3.7 vs 2.8–3.1 in SL) and higher caudal peduncle depth (2.7–3.3 vs 3.5–4.0 in head length) compared to P. poeyi.

Discussion

As stated by Mooi and Randall (2014), assignments of original or new names to Pempheris species is remarkably difficult because: 1) the poor condition and descriptions of type material; and 2) traditional meristics (e.g. fin ray counts) are not very informative at the species level due either to too little or too much character variability. For instance, because of its similarity to P. poeyi, P. gasparinii is misidentified in the most recent biodiversity checklists of Trindade Island (Pinheiro et al. 2009, 2015, Simon et al. 2013).

A phylogenetic tree of Pempheris of the Atlantic based on COI placed P. poeyi and P. gasparinii as sister species (Figure 4). The two species show a 4% sequence divergence at this locus, which is consistent with a speciation process initiated in the beginning of the Pleistocene. With only one sequence from each of the two species and thus no information on intraspecific genetic divergences, we cannot definitively use the genetic data to separate the two species. However, assuming that intraspecific divergence is low, as it is in P. schomburgkii from Panama and Curacao (Fig. 4), the combined genetic and morphological data easily distinguish the two species. The disjunct distribution associated with the genetic divergence of the species suggests that P. gasparinii might be a relict species. Similarly to other recently described species from Trindade Island (Pinheiro et al. 2010, Rocha et al. 2010), P. gasparinii seems to have been preserved in the Vitória-Trindade Chain while the Pleistocene sea-level changes extirpated the lineages along the adjacent Brazilian coast. This species represents the 12th endemic fish from Trindade Island. Thus, following the diversity reported by Pinheiro et al. (2015) and criteria of reef fishes established by Floeter et al. (2008), the proportion of endemics found in the Vitória-Trindade Chain (191 species) and Trindade Island (137 species) today is 6% and 9% respectively.

Acknowledgements

We thank the Brazilian Navy (Marinha do Brasil–1° Distrito Naval), TAMAR/ICMBio Project, and Substation Curaçao for logistical support; the California Academy of Sciences for financial support; Flamar, Windive, Voz da Natureza and Fauna for diving support; R. Santos, T. Simon and R. Andrade for collaboration on dives and collecting specimens; D. Catania, J.C. Joyeux, I. Sazima, and J. Williams for helping access CAS, CIUFES, ZUEC, and USNM collections, respectively. We are especially grateful to T. Simon and A. Barber for photographs. CNPq provided a doctoral fellowship for HTP (Ciência sem Fronteiras; GDE 202475/ 2011-5). This paper is part of the projects “Vitória—Trindade Chain: testing the theory for stepping-stone connectivity in reef fishes” (CNPq grant 470725/2009-5) and “Reef fishes of the insular complex Trindade—Martin Vaz, Vitória, ES: status, recruitment and evolution of assemblages” (CNPq grant 557043/2009-3).

References

  • Azzurro E, Goren M, Diamant A, Galil B, Bernardi G (2015) Establishing the identity and assessing the dynamics of invasion in the Mediterranean Sea by the dusky sweeper, Pempheris rhomboidea Kossmann & Räuber, 1877 (Pempheridae, Perciformes). Biological Invasions 17: 815–826. doi: 10.1007/s10530-014-0836-5
  • Bean TH (1885) Description of a new species of Pempheris (Pempheris poeyi) from Cuba. Proceedings of the United States National Museum 8: 229–230. doi: 10.5479/si.00963801.8-516.229
  • Felsenstein J (1985) Confidence Limits on Phylogenies: An Approach Using the Bootstrap. Evolution 39: 783–791. doi: 10.2307/2408678
  • Floeter SR, Rocha LA, Robertson DR, Joyeux JC, Smith-Vaniz WF, Wirtz P, Edwards AJ, Barreiros JP, Ferreira CEL, Gasparini JL, Brito A, Falcón JM, Bowen BW, Bernardi G (2008) Atlantic reef fish biogeography and evolution. Journal of Biogeography 35: 22–47. doi: 10.1111/j.1365-2699.2007.01790.x
  • Koeda K, Yoshino T, Tachihara K (2013) Pempheris ufuagari sp. nov., a new species in the genus Pempheris (Perciformes, Pempheridae) from the oceanic islands of Japan. Zootaxa 3609: 231–238. doi: 10.11646/zootaxa.3609.2.9
  • Miranda Ribeiro A (1919) A fauna vertebrada da Ilha da Trindade. Archivos do Museu Nacional 22: 171–194.
  • Mooi RD, Randall JE (2014) Pempheris bexillon, a new species of sweeper (Teleostei: Pempheridae) from the Western Indian Ocean. Zootaxa 3780: 388–398. doi: 10.11646/zootaxa.3780.2.10
  • Pinheiro HT, Camilato V, Gasparini JL, Joyeux J (2009) New records of fishes for Trindade-Martin Vaz oceanic insular complex, Brazil. Zootaxa 2298: 45–54.
  • Pinheiro HT, Gasparini JL, Sazima I (2010) Sparisoma rocha, a new species of parrotfish (Actinopterygii: Labridae) from Trindade Island, South-Western Atlantic. Zootaxa 2493: 59–65.
  • Pinheiro HT, Mazzei E, Moura RL, Amado-Filho GM, Carvalho-Filho A, Braga AC, Costa PAS, Ferreira BP, Ferreira CEL, Floeter SR, Francini-Filho RB, Gasparini JL, Macieira RM, Martins AS, Olavo G, Pimentel CR, Rocha LA, Sazima I, Simon T, Teixeira JB, Xavier LB, Joyeux J-C (2015) Fish biodiversity of the Vitória-Trindade Seamount Chain, southwestern Atlantic: an updated database. PLoS ONE 10: e0118180. doi: 10.1371/journal.pone.0118180
  • Randall JE, Bineesh KK (2014) Review of the fishes of the genus Pempheris (Perciformes: Pempheridae) of India, with description of a new species and a neotype for P. mangula Cuvier. Journal of the Ocean Science Foundation 10: 20–40.
  • Randall JE, Victor BC (2014) Four new fishes of the genus Pempheris (Perciformes : Pempheridae) from the western Indian Ocean. Journal of the Ocean Science Foundation 12: 61–83.
  • Randall JE, Victor BC (2015) Descriptions of thirty-four new species of the fish genus Pempheris (Perciformes: Pempheridae), with a key to the species of the western Indian Ocean. Journal of the Ocean Science Foundation 18: 1–77.
  • Randall JE, Victor BC, Alpermann TJ, Bogorodsky SV, Mal AO, Satapoomin U, Bineesh KK (2014) Rebuttal to Koeda et al. (2014) on the Red Sea fishes of the perciform genus Pempheris. Zootaxa 3887: 377–392. doi: 10.11646/zootaxa.3887.3.5
  • Rocha LA, Pinheiro HT, Gasparini JL (2010) Description of Halichoeres rubrovirens, a new species of wrasse (Labridae: Perciformes) from the Trindade and Martin Vaz Island group, southeastern Brazil, with a preliminary mtDNA molecular phylogeny of New World Halichoeres. Zootaxa 2422: 22–30.
  • Simon T, Macieira RM, Joyeux J-C (2013) The shore fishes of the Trindade-Martin Vaz insular complex: an update. Journal of Fish Biology 82: 2113–27. doi: 10.1111/jfb.12126
  • Swofford DL (2003) PAUP*. Phylogenetic Analysis Using Parsimony (*and Other Methods). Version 4.0a136. Sinauer Associates, Sunderland, Massachusetts.
  • Weigt LA, Baldwin CC, Driskell A, Smith DG, Ormos A, Reyier EA (2012) Using DNA barcoding to assess Caribbean reef fish biodiversity: Expanding taxonomic and geographic coverage. PLoS ONE 7. doi: 10.1371/journal.pone.0041059
  • Zwickl DJ (2006) Genetic algorithm approaches for the phylogenetic analysis of large biological sequence datasets under the maximum likelihood criterion. Ph.D. dissertation, The University of Texas at Austin.
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