Distinctive Convergence in Australian Floral Colours Seen Through the Eyes of Australian Birds

We used a colour-space model of avian vision to assess whether a distinctive bird pollination syndrome exists for floral colour among Australian angiosperms. We also used a novel phylogenetically based method to assess whether such a syndrome represents a significant degree of convergent evolution. About half of the 80 species in our sample that attract nectarivorous birds had floral colours in a small, isolated region of colour space characterized by an emphasis on long-wavelength reflection. The distinctiveness of this 'red arm' region was much greater when colours were modelled for violet-sensitive (VS) avian vision than for the ultraviolet-sensitive visual system. Honeyeaters (Meliphagidae) are the dominant avian nectarivores in Australia and have VS vision. Ancestral state reconstructions suggest that 31 lineages evolved into the red arm region, whereas simulations indicate that an average of five or six lineages and a maximum of 22 are likely to have entered in the absence of selection. Thus, significant evolutionary convergence on a distinctive floral colour syndrome for bird pollination has occurred in Australia, although only a subset of bird-pollinated taxa belongs to this syndrome. The visual system of honeyeaters has been the apparent driver of this convergence.

Squared Extrapolation Methods (SQUAREM): A New Class of Simple and Efficient Numerical Schemes for Accelerating the Convergence of the EM Algorithm

We derive a new class of iterative schemes for accelerating the convergence of the EM algorithm, by exploiting the connection between fixed point iterations and extrapolation methods. First, we present a general formulation of one-step iterative schemes, which are obtained by cycling with the extrapolation methods. We, then square the one-step schemes to obtain the new class of methods, which we call SQUAREM. Squaring a one-step iterative scheme is simply applying it twice within each cycle of the extrapolation method. Here we focus on the first order or rank-one extrapolation methods for two reasons, (1) simplicity, and (2) computational efficiency. In particular, we study two first order extrapolation methods, the reduced rank extrapolation (RRE1) and minimal polynomial extrapolation (MPE1). The convergence of the new schemes, both one-step and squared, is non-monotonic with respect to the residual norm. The first order one-step and SQUAREM schemes are linearly convergent, like the EM algorithm but they have a faster rate of convergence. We demonstrate, through five different examples, the effectiveness of the first order SQUAREM schemes, SqRRE1 and SqMPE1, in accelerating the EM algorithm. The SQUAREM schemes are also shown to be vastly superior to their one-step counterparts, RRE1 and MPE1, in terms of computational efficiency. The proposed extrapolation schemes can fail due to the numerical problems of stagnation and near breakdown. We have developed a new hybrid iterative scheme that combines the RRE1 and MPE1 schemes in such a manner that it overcomes both stagnation and near breakdown. The squared first order hybrid scheme, SqHyb1, emerges as the iterative scheme of choice based on our numerical experiments. It combines the fast convergence of the SqMPE1, while avoiding near breakdowns, with the stability of SqRRE1, while avoiding stagnations. The SQUAREM methods can be incorporated very easily into an existing EM algorithm. They only require the basic EM step for their implementation and do not require any other auxiliary quantities such as the complete data log likelihood, and its gradient or hessian. They are an attractive option in problems with a very large number of parameters, and in problems where the statistical model is complex, the EM algorithm is slow and each EM step is computationally demanding.

Glycoprotein VI is a major collagen receptor for platelet activation: it recognizes the platelet-activating quaternary structure of collagen, whereas CD36, glycoprotein IIb/IIIa, and von Willebrand factor do not

Simple collagen-related peptides (CRPs) containing a repeat Gly-Pro-Hyp sequence are highly potent platelet agonists. Like collagen, they must exhibit tertiary (triple-helical) and quaternary (polymeric) structure to activate platelets. Platelet signaling events induced by the peptides are the same as most of those induced by collagen. The peptides do not recognize the alpha 2 beta 1 integrin. To identify the signaling receptor involved, we have evaluated the response to the CRP, Gly-Lys-Hyp(Gly-Pro-Hyp)10-Gly-Lys-Hyp-Gly of platelets with defined functional deficiencies. These studies exclude a primary recognition role for CD36, von Willebrand factor (vWF), or glycoprotein (GP) IIb/IIIa. Thus, both CD36 and vWF-deficient platelets exhibited normal aggregation, normal fibrinogen binding, and normal expression of CD62 and CD63, measured by flow cytometry, in response to the peptide, and there was normal expression of CD62 and CD63 on thrombasthenic platelets. In contrast, GPVI-deficient platelets were totally unresponsive to the peptide, indicating that this receptor recognizes the Gly-Pro-Hyp sequence in collagen. GPVI-deficient platelets showed some fibrinogen binding in response to collagen but failed to aggregate and to express CD62 and CD63. Collagen, but not CRP-XL, contains binding sites for alpha 2 beta 1. Therefore, it is possible that collagen still induces some signaling via alpha 2 beta 1, leading to activation of GPIIb/IIIa. Our findings are consistent with a two-site, two-step model of collagen interaction with platelets involving recognition of specific sequences in collagen by an adhesive receptor such as alpha 2 beta 1 to arrest platelets under flow and subsequent recognition of another specific collagen sequence by an activatory receptor, namely GPVI.