Euphorbia polycarpa (Euphorbia subg. Chamaesyce sect. Anisophyllum) is one of the most common species of the Sonoran Desert. It exhibits a wide range of morphological variation and has been considered as a taxonomic complex. Since the late nineteenth century more than seven varieties have been described for the complex, some with very restricted distributions. Because of morphological intergrades present in the complex, there has been much confusion among taxonomists, and it became necessary to clarify the taxonomy of this complex using molecular phylogenetic evidence in addition to morphology alone. In this paper we reconstruct the phylogenetic relationships for the E. polycarpa complex based on molecular information from the psbA-trnH and ITS spacers, using Bayesian inference. Morphology was compared with phylogenetic results, and we also explored geographic patterns of the varieties of the complex, as well as closely related species of Euphorbia sect. Anisophyllum. Taking into account the results obtained, we propose that E. polycarpa is treated as a single, highly variable species. Given the incongruities among morphology, geography, and evolutionary history inferred from molecular data, we do not recognize any of the varieties proposed previously. The phylogeny presented shows three well-supported putative lineages and suggest a complex evolutionary history within E. polycarpa.

#### POLY_ITS_gN_FINAL

NEXUS file for ITS matrix aligned.

#### POLY_PSB_gN_iC_FINAL

NEXUS file for psbA-trnH data aligned

#### Figure S1

FIG. S1. Phylogenetic reconstruction using the majority rule consensus from Bayesian analyses of the nuclear region ITS and chloroplast region psbA-trnH concatenated. Numbers above the branches are Bayesian posterior probabilities (PP).

#### Figure S2

FIG. S2. Ancestral state reconstruction for the character: “Leaves of two different sizes”, on the phylogenetic hypothesis based on psbA-trnH. Circles denote the state and circles in the nodes show the proportional likelihood visually.

#### Figure S3

FIG. S3. Ancestral state reconstruction for the character: “Leaves of two different sizes”, on the phylogenetic hypothesis based on ITS. Circles denote the state and circles in the nodes show the proportional likelihood visually.

#### Figure S4

FIG. S4. Ancestral state reconstruction for the character: “Leaf shape”, on the phylogenetic hypothesis based on psbA-trnH. Circles denote the state and circles in the nodes show the proportional likelihood visually.

#### Figure S5

FIG. S5. Ancestral state reconstruction for the character: “Leaf shape”, on the phylogenetic hypothesis based on ITS. Circles denote the state and circles in the nodes show the proportional likelihood visually.

#### Figure S6

FIG. S6. Ancestral state reconstruction for the character: “Stipule shape”, on the phylogenetic hypothesis based on psbA-trnH. Circles denote the state and circles in the nodes show the proportional likelihood visually.

#### Figure S7

FIG. S7. Ancestral state reconstruction for the character: “Stipule shape”, on the phylogenetic hypothesis based on ITS. Circles denote the state and circles in the nodes show the proportional likelihood visually.

#### Figure S8

FIG. S8. Ancestral state reconstruction for the character: “Glandular tricomes on the peduncle”, on the phylogenetic hypothesis based on psbA-trnH. Circles denote the state and circles in the nodes show the proportional likelihood visually.

#### Figure S9

FIG. S9. Ancestral state reconstruction for the character: “Glandular tricomes on the peduncle”, on the phylogenetic hypothesis based on ITS. Circles denote the state and circles in the nodes show the proportional likelihood visually.

#### Figure S10

FIG. S10. Ancestral state reconstruction for the character: “Pubescence on vegetative parts”, on the phylogenetic hypothesis based on psbA-trnH. Circles denote the state and circles in the nodes show the proportional likelihood visually.

#### Figure S11

FIG. S11. Ancestral state reconstruction for the character: “Pubescence on vegetative parts”, on the phylogenetic hypothesis based on ITS. Circles denote the state and circles in the nodes show the proportional likelihood visually.

#### Figure S12

FIG. S12. Ancestral state reconstruction for the character: “Appendage margin”, on the phylogenetic hypothesis based on psbA-trnH. Circles denote the state and circles in the nodes show the proportional likelihood visually.

#### Figure S13

FIG. S13. Ancestral state reconstruction for the character: “Appendage margin”, on the phylogenetic hypothesis based on ITS. Circles denote the state and circles in the nodes show the proportional likelihood visually.

#### Figure S14

FIG. S14. Ancestral state reconstruction for the character: “Zigzag steams”, on the phylogenetic hypothesis based on psbA-trnH. Circles denote the state and circles in the nodes show the proportional likelihood visually.

#### Figure S15

FIG. S15. Ancestral state reconstruction for the character: “Zigzag steams”, on the phylogenetic hypothesis based on ITS. Circles denote the state and circles in the nodes show the proportional likelihood visually.

#### Figure S16

FIG. S16. Ancestral state reconstruction for the character: “Appendages long (mm)”, on the phylogenetic hypothesis based on psbA-trnH. Circles denote the state and circles in the nodes show the proportional likelihood visually.

#### Figure S17

FIG. S17. Ancestral state reconstruction for the character: “Appendages long (mm)”, on the phylogenetic hypothesis based on ITS. Circles denote the state and circles in the nodes show the proportional likelihood visually.

#### Figure S18

FIG. S18. Ancestral state reconstruction for the character: “Relation between the width of the appendage and width of the gland”, on the phylogenetic hypothesis based on psbA-trnH. Circles denote the state and circles in the nodes show the proportional likelihood visually.

#### Figure S19

FIG. S19. Ancestral state reconstruction for the character: “Relation between the width of the appendage and width of the gland”, on the phylogenetic hypothesis based on ITS. Circles denote the state and circles in the nodes show the proportional likelihood visually.

#### Figure S20

FIG. S20. Ancestral state reconstruction for the character: “Sonoran biome and adjacent areas”, on the phylogenetic hypothesis based on psbA-trnH. Circles denote the state and circles in the nodes show the proportional likelihood visually.

#### Figure S21

FIG. S21. Ancestral state reconstruction for the character: “Sonoran biome and adjacent areas”, on the phylogenetic hypothesis based on ITS. Circles denote the state and circles in the nodes show the proportional likelihood visually.