Seed and capsule morphology of Iranian perennial species of Euphorbia (Euphorbiaceae) and its phylogenetic application

Of the 480 species of Euphorbia subgenus Esula, c. 290 occur in the Mediterranean and Irano‐Turanian regions. Turkey and Iran are the most species‐rich countries in Asia with 83 and 74 species, respectively. Following our previous paper on annual species of Iranian Euphorbia, we studied the quantitative and qualitative macro‐ and micromorphological traits of seeds and capsules of 47 perennial species, including E . ferdowsiana sp. nov. , E . sulphurea sp. nov. and E. glareosa, as a first report from Iran. A key for all Iranian perennial Euphorbia spp. based on seed and capsule morphology is provided. The phylogenetic relationships of Iranian species based on internal transcribed spacer (ITS) nuclear and ndhF plastid regions are updated and used for the characterization of the synapomorphies of each clade. Capsule shape, seed shape, seed surface and shape of the caruncle have been found to be homoplastic, whereas the presence or absence of granulate elements on seed surfaces represents a phylogenetically important trait for section delimitation. The capsule surface is synapomorphic for several sections, including Helioscopia (tuberculate‐verrucose), Myrsiniteae (vesiculate) and Esula (granulate), and seed shape is synapomorphic for sections Helioscopia (ellipsoidal), Myrsiniteae (ovoid‐quadrangular) and Herpetorrhizae (pseudo‐hexahedral). Reversals have also taken place in some features, including capsule surface (E. mazandaranica, E. altissima) and seed shape (E. densa, E. aleppica). It seems that ecarunculate seeds are plesiomorphic in sections Helioscopia (E. eriophora) and Herpetorrhizae (E. consanguinea and E. turczaninowii). © 2015 The Linnean Society of London, Botanical Journal of the Linnean Society, 2015, 00 , 000–000.     

A model of HIV-1 infection with two time delays: mathematical analysis and comparison with patient data

Mathematical models have made considerable contributions to our understanding of HIV dynamics. Introducing time delays to HIV models usually brings challenges to both mathematical analysis of the models and comparison of model predictions with patient data. In this paper, we incorporate two delays, one the time needed for infected cells to produce virions after viral entry and the other the time needed for the adaptive immune response to emerge to control viral replication, into an HIV-1 model. We begin model analysis with proving the positivity and boundedness of the solutions, local stability of the infection-free and infected steady states, and uniform persistence of the system. By developing a few Lyapunov functionals, we obtain conditions ensuring global stability of the steady states. We also fit the model including two delays to viral load data from 10 patients during primary HIV-1 infection and estimate parameter values. Although the delay model provides better fits to patient data (achieving a smaller error between data and modeling prediction) than the one without delays, we could not determine which one is better from the statistical standpoint. This highlights the need of more data sets for model verification and selection when we incorporate time delays into mathematical models to study virus dynamics.