PACo: a novel procrustes application to cophylogenetic analysis

Abstract

We present Procrustean Approach to Cophylogeny (PACo), a novel statistical tool to test for congruence between phylogenetic trees, or between phylogenetic distance matrices of associated taxa. Unlike previous tests, PACo evaluates the dependence of one phylogeny upon the other. This makes it especially appropriate to test the classical coevolutionary model that assumes that parasites that spend part of their life in or on their hosts track the phylogeny of their hosts. The new method does not require fully resolved phylogenies and allows for multiple host-parasite associations. PACo produces a Procrustes superimposition plot enabling a graphical assessment of the fit of the parasite phylogeny onto the host phylogeny and a goodness-of-fit statistic, whose significance is established by randomization of the host-parasite association data. The contribution of each individual host-parasite association to the global fit is measured by means of jackknife estimation of their respective squared residuals and confidence intervals associated to each host-parasite link. We carried out different simulations to evaluate the performance of PACo in terms of Type I and Type II errors with respect to two similar published tests. In most instances, PACo performed at least as well as the other tests and showed higher overall statistical power. In addition, the jackknife estimation of squared residuals enabled more elaborate validations about the nature of individual links than the ParaFitLink1 test of the program ParaFit. In order to demonstrate how it can be used in real biological situations, we applied PACo to two published studies using a script written in the public-domain statistical software R.

Figure 1. Method overview of PACo.

(1) The phylogenetic information encapsulated by the host-parasite (H-P) tanglegram gives way to two distance matrices of host and parasites, and a binary matrix of host-parasite (H-P) links. (2) The distance matrices are transformed by Principal Coordinates. (3) The H-P link matrix (A) is converted into an identity matrix to account for multiple host-parasite associations. (4) Rows in the Principal Component matrices are duplicated (arched arrows) following the order dictated by the identity matrix. (5) The extended Principal Coordinate matrices (X and Y) are centred by mean column vectors and subjected to Procrustes analysis, where the parasite configuration is rotated and scaled to fit the host configuration. The fit can be visualised in a Procrustes superimposition plot. (6) The analysis yields a global goodness-of-fit statistic (), whose significance can be established by a randomization procedure, and individual link residuals that can be further analysed to establish the contribution of each H-P link to the global fit.

Figure 2. Phylogenetic trees of pocket gophers (left) and chewing lice (right).

Blue lines represent host-parasite associations observed in nature. Gopher species abbreviations: Ccas: Cratogeomys castanops; Cmer: C. merriami; GburA: Geomys bursarius halli; GburB: G. bursarius majusculus; Gbre: G. breviceps; Gpers: G. personatus; Ocav: Orthogeomys cavator; Oche: O. cherriei; Ohet: O. heterodus; Ohis: O. hispidus; Ound: O. underwoodii; Pbul: Pappogeomys bulleri; Ztri: Zygogeomys trichopus; Tbot: Thomomys bottae; Ttal: T. talpoides. Louse species abbreviations: Gact: Geomydoecus actuosi; Gcha: G. chapini; Gche: G. cherriei; Gcos: G. costaricensis; Gewi; G. ewingi; Gexp: G. expansus; Ggeo: G. geomydis; Gnad: G. nadleri; Gokl: G. oklahomensis; Gpan: G. panamensis; Gpero: G. perotensis; Gset: G. setzeri; Gtex: G. texanus; Gtho: G. thomomyus; Gtri: G. trichopi; Tbar: Thomomydoecus barbarae; Tmin: T.minor.

Figure 3. Tanglegram depicting the associations between 20 fishes and 51 Dactylogyrus spp (Monogenea).

Lineages 1–3 of Dactylogyrus correspond to those recognized by Šimková et al. . Fish species abbreviations: Aalb: Alburnus alburnus; Aasp: Aspius aspius; Abra: Abramis brama; Bbal: Ballerus ballerus; Bbar: Barbus barbus; Bbjo: Blicca bjoerkna; Bsap: Ballerus sapa; Caur: Carassius auratus; Ccar: Cyprinus carpio; Cide: Ctenopharyngodon idella; Cnas: Chondrostoma nasus; Gcer: Gymnocephalus cernua; Ggob: Gobio gobio; Lidu: Leuciscus idus; Ppar: Pseudorasbora parva; Ppho: Phoxinus phoxinus; Ralb: Romanogobio albipinnatus; Rrut: Rutilus rutilus; Scep: Squalius cephalus; Sery: Scardinius erythrophthalmus. Dactylogyrus – specific-name abbreviations: achm: achmerovi; alat: alatus; amph: amphibothrium; anch: anchoratus; auri: auriculatus; bore: borealis; caba: caballeroi; carp: carpathicus; chon: chondrostomi; chra: chranilowi; corn: cornoides; coru: cornu; cruc: crucifer; cryp: cryptomeres; difd: difformoides; diff: difformis; dist: distinguendus; dulk: dulkeiti; dyki: dyki; erge: ergensi; exte: extensus; falc: falcatus; fall: fallax; fini: finitimus; folk: folkmanovae; form: formosus; frat: fraternus; hemi: hemiamphibothrium; inex: inexpectatus; inte: intermedius; izju: izjumovae; lame: lamellatus; mall: malleus; mino: minor; nano: nanoides; nanu: nanus; parv: parvus; prop: propinquus; pros: prostae; ramu: ramulosus; rari: rarissimus; ruti: rutili; simi: similis; sphy: sphyrna; squa: squameus; tuba: tuba; vast: vastator; vist: vistulae; vran: vranoviensis; wund: wunderi; zand: zandti.

Figure 4. Statistical power for simulations under Approach 1 (Random links added).

A, B: 10 host-10 parasite simulations; C, D: 20 host-20 parasite simulations. PACo (present study): circles (solid line); HCT : crosses (dotted line); Parafit : triangles (dashed line).

Figure 5. Statistical power for simulations under Approach 2 (Coevolutionary links replaced).

A, B: 10 host-10 parasite simulations; C, D: 20 host-20 parasite simulations. PACo (present study): circles (solid line); HCT : crosses (dotted line); Parafit : triangles (dashed line).

Figure 6. Statistical power for simulations under Approach 3 (Partly congruent trees).

A, B: 10 host-10 parasite simulations; C, D: 20 host-20 parasite simulations. PACo (present study): circles (solid line); HCT : crosses (dotted line); Parafit : triangles (dashed line).

Figure 7. Procrustean superimpostion plot of pocket gophers and chewing lice.

The ordinations of gopher and lice are Principal Correspondence Coordinates of patristic distances. The lice configuration (dots) has been rotated and scaled to fit the gopher ordination (arrow tips). Length of arrows represents the projection of residuals onto the first two axes. See Fig. 6 for species abbreviations.

Figure 8. Pocket gophers and chewing lice: contributions of individual host-parasite links to the Procrustean fit.

Jacknifed squared residuals (bars) and upper 95% confidence intervals (error bars) resulting from applying PACo to (A) patristic and (B) genetic distances. Asterisks identify links significantly supported (α <0.05) by ParaFitLink1 . To ease comparisons the median squared residual value is shown (dashed line). See Fig. 2 for species abbreviations.

Figure 9. Fish and Dactylogyrus spp.: contributions of individual host-parasite links to the Procrustean fit.

Jacknifed squared residuals (bars) and upper 95% confidence intervals (error bars) resulting from applying PACo to patristic distances. Results of the ParaFitLink1 analysis for each link are indicated by the bar colour. To ease comparisons the median squared residual value is shown (red dashed line). See Fig. 3 for species abbreviations.