Periodic time series modeling of environmental proxy records with guaranteed positive growth rate estimation

Identifying a periodic time-series model from environmental records, without imposing the positivity of the growth rate, does not necessarily respect the time order of the data observations. Consequently, subsequent observations, sampled in the environmental archive, can be inversed on the time axis, resulting in a non-physical signal model. In this paper an optimization technique with linear constraints on the signal model parameters is proposed that prevents time inversions. The activation conditions for this constrained optimization are based upon the physical constraint of the growth rate, namely, that it cannot take values smaller than zero. The actual constraints are defined for polynomials and first-order splines as basis functions for the nonlinear contribution in the distance-time relationship. The method is compared with an existing method that eliminates the time inversions, and its noise sensitivity is tested by means of Monte Carlo simulations. Finally, the usefulness of the method is demonstrated on the measurements of the vessel density, in a mangrove tree, Rhizophora mucronata, and the measurement of Mg/Ca ratios, in a bivalve, Mytilus trossulus.

Complex history of a chromosomal paralogy region: insights from amphioxus aromatic amino acid hydroxylase genes and insulin-related genes

Aromatic amino acid hydroxylase (AAAH) genes and insulin-like genes form part of an extensive paralogy region shared by human chromosomes 11 and 12, thought to have arisen by tetraploidy in early vertebrate evolution. Cloning of a complementary DNA (cDNA) for an amphioxus (Branchiostoma floridae) hydroxylase gene (AmphiPAH) allowed us to investigate the ancestry of the human chromosome 11/12 paralogy region. Molecular phylogenetic evidence reveals that AmphiPAH is orthologous to vertebrate phenylalanine (PAH) genes; the implication is that all three vertebrate AAAH genes arose early in metazoan evolution, predating vertebrates. In contrast, our phylogenetic analysis of amphioxus and vertebrate insulin-related gene sequences is consistent with duplication of these genes during early chordate ancestry. The conclusion is that two tightly linked gene families on human chromosomes 11 and 12 were not duplicated coincidentally. We rationalize this paradox by invoking gene loss in the AAAH gene family and conclude that paralogous genes shared by paralogous chromosomes need not have identical evolutionary histories.