Title

Schrödinger Equations On ℝ 3 × M With Non-Separable Potential

Keywords

Cytogenetics; Electric organ; Gymnotiformes; Reproductive isolation

Abstract

We describe chromosomal and electric signal diversity in three sympatric species of Gymnotus (Gymnotidae) fish from the Central Amazon Floodplain. Gymnotus arapaima presents a karyotype of 2n = 44 (24 m-sm + 20st-a), G. mamiraua 2n = 54 (42 m-sm + 12st-a), and G. jonasi 2n = 52 (12 m-sm + 40st-a). No evidence for a chromosomal sexual system was observed in two species for which both males and females were analyzed (G. mamiraua and G. arapaima). In all three species the constitutive heterochromatin is located primarily in pericentromeric regions, but also at some other sites. G. arapaima and G. mamiraua exhibit simple nucleolar organizing regions (NORs) on short arms of chromosome pairs 19 and 24, respectively. Gymnotus jonasi exhibits a multiple interstitial NOR on the long arm of pairs 9 and 10, and on the short arm of pair 11. G. arapaima and G. mamiraua exhibit several additional similarities in their karyotypic formulas-reflecting the phylogenetic proximity of these species within a G. carapo group clade (based on molecular phylogenetic evidence). The chromosomal differences among these three sympatric species imply complete post-zygotic reproductive isolation. A prominent pattern of partitioning of the peak power frequency of the electric organ discharge of these three species indicates pre-zygotic reproductive isolation of mate attraction signals. We conclude by discussing the evolutionary events that may have promoted signal divergence and reproductive isolation in Gymnotus of the Central Amazon, and the role that chromosomal rearrangements may place in diversification. © 2011 Springer Science+Business Media B.V.

Publication Date

6-1-2012

Publication Title

Journal of Mathematical Chemistry

Volume

50

Issue

2

Number of Pages

1420-1436

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s10910-012-9981-1

Socpus ID

84860722361 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84860722361

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