Forking in simple theories and CM-triviality

[cat] Aquesta tesi té tres objectius. En primer lloc, estudiem generalitzacions de la jerarquia no ample relatives a una família de tipus parcials. Aquestes jerarquies en permeten classificar la complexitat del “forking” respecte a una família de tipus parcials. Si considerem la família de tipus algebraics, aquestes generalitzacions corresponen a la jerarquia ordinària, on el primer i el segon nivell corresponen a one-basedness i a CM-trivialitat, respectivament. Fixada la família de tipus regulars “no one-based”, el primer nivell d'una d'aquestes possibles jerarquies no ample ens diu que el tipus de la base canònica sobre una realització és analitzable en la família. Demostrem que tota teoria simple amb suficients tipus regulars pertany al primer nivell de la jerarquia dèbil relativa a la família de tipus regulars no one-based. Aquest resultat generalitza una versió dèbil de la “Canonical Base Property” estudiada per Chatzidakis i Pillay. En segon lloc, discutim problemes d'eliminació de hiperimaginaris assumint que la teoria és CM-trivial, en tal cas la independència del “forking” té un bon comportament. Més concretament, demostrem que tota teoria simple CM-trivial elimina els hiperimaginaris si elimina els hiperimaginaris finitaris. En particular, tota teoria petita simple CM-trivial elimina els hiperimaginaris. Cal remarcar que totes les teories omega-categòriques simples que es coneixen són CM-trivials; en particular, aquelles teories obtingudes mitjançant una construcció de Hrushovski. Finalment, tractem problemes de classificació en les teories simples. Estudiem la classe de les teories simples baixes; classe que inclou les teories estables i les teories supersimples de D-rang finit. Demostrem que les teories simples amb pes finit acotat també pertanyen a aquesta classe. A més, provem que tota teoria omega-categòrica simple CM-trivial és baixa. Aquest darrer fet resol parcialment una pregunta formulada per Casanovas i Wagner.[eng] The development of first-order stable theories required two crucial abstract notions: forking independence, and the related notion of canonical base. Forking independence generalizes the linear independence in vector spaces and the algebraic independence in algebraically closed fields. On the other hand, the concept of canonical base generalizes the field of definition of an algebraic variety. The general theory of independence adapted to simple theories, a class of first-order theories which includes all stable theories and other interesting examples such as algebraically closed fields with an automorphism and the random graph. Nevertheless, in order to obtain canonical bases for simple theories, the model-theoretic development of hyperimaginaries --equivalence classes of arbitrary tuple modulo a type-definable (without parameters) equivalence relation-- was required. In the present thesis we deal with topics around the geometry of forking in simple theories. Our first goal is to study generalizations of the non ample hierarchy which will code the complexity of forking with respect to a family of partial types. We introduce two hierarchies: the non (weak) ample hierarchy with respect to a fixed family of partial types. If we work with respect to the family of bounded types, these generalizations correspond to the ordinary non ample hierarchy. Recall that in the ordinary non ample hierarchy the first and the second level correspond to one-basedness and CM-triviality, respectively. The first level of the non weak ample hierarchy with respect to some fixed family of partial types states that the type of the canonical base over a realization is analysable in the family. Considering the family of regular non one-based types, the first level of the non weak ample hierarchy corresponds to the weak version of the Canonical Base Property studied by Chatzidakis and Pillay. We generalize Chatzidakis' result showing that in any simple theory with enough regular types, the canonical base of a type over a realization is analysable in the family of regular non one-based types. We hope that this result can be useful for the applications; for instance, the Canonical Base Property plays an essential role in the proof of Mordell-Lang for function fields in characteristic zero and Manin-Mumford due to Hrushovski. Our second aim is to use combinatorial properties of forking independence to solve elimination of hyperimaginaries problems. For this we assume the theory to be simple and CM-trivial. This implies that the forking independence is well-behaved. Our goal is to prove that any simple CM-trivial theory which eliminates finitary hyperimaginaries --hyperimaginaries which are definable over a finite tuple-- eliminates all hyperimaginaries. Using a result due to Kim, small simple CM-trivial theories eliminate hyperimaginaries. It is worth mentioning that all currently known omega-categorical simple theories are CM-trivial, even those obtained by an ab initio Hrushovski construction. To conclude, we study a classification problem inside simple theories. We study the class of simple low theories, which includes all stable theories and supersimple theories of finite D-rank. In addition, we prove that it also includes the class of simple theories of bounded finite weight. Moreover, we partially solve a question posed by Casanovas and Wagner: Are all omega-categorical simple theories low? We solve affirmatively this question under the assumption of CM-triviality. In fact, our proof exemplifies that the geometry of forking independence in a possible counterexample cannot come from finite sets

Microsatellite markers reveal shallow genetic differentiation between cohorts of the common sea urchin Paracentrotus lividus (Lamarck) in northwest Mediterranean

Temporal variability was studied in the common sea urchin Paracentrotus lividus through the analysis of the genetic composition of three yearly cohorts sampled over two consecutive springs in a locality in northwestern Mediterranean. Individuals were aged using growth ring patterns observed in tests and samples were genotyped for five microsatellite loci. No reduction of genetic diversity was observed relative to a sample of the adult population from the same location or within cohorts across years. FST and amova results indicated that the differentiation between cohorts is rather shallow and not significant, as most variability is found within cohorts and within individuals. This mild differentiation translated into estimates of effective population size of 90-100 individuals. When the observed excess of homozygotes was taken into account, the estimate of the average number of breeders increased to c. 300 individuals. Given our restricted sampling area and the known small-scale heterogeneity in recruitment in this species, our results suggest that at stretches of a few kilometres of shoreline, large numbers of progenitors are likely to contribute to the larval pool at each reproduction event. Intercohort variation in our samples is six times smaller than spatial variation between adults of four localities in the western Mediterranean. Our results indicate that, notwithstanding the stochastic events that take place during the long planktonic phase and during the settlement and recruitment processes, reproductive success in this species is high enough to produce cohorts genetically diverse and with little differentiation between them. Further research is needed before the link between genetic structure and underlying physical and biological processes can be well established

To denoise or to cluster? That is not the question. Optimizing pipelines for COI metabarcoding and metaphylogeography

Background: The recent blooming of metabarcoding applications to biodiversity studies comes with some relevant methodological debates. One such issue concerns the treatment of reads by denoising or by clustering methods, which have been wrongly presented as alternatives. It has also been suggested that denoised sequence variants should replace clusters as the basic unit of metabarcoding analyses, missing the fact that sequence clusters are a proxy for species-level entities, the basic unit in biodiversity studies. We argue here that methods developed and tested for ribosomal markers have been uncritically applied to highly variable markers such as cytochrome oxidase I (COI) without conceptual or operational (e.g., parameter setting) adjustment. COI has a naturally high intraspecies variability that should be assessed and reported, as it is a source of highly valuable information. We contend that denoising and clustering are not alternatives. Rather, they are complementary and both should be used together in COI metabarcoding pipelines. Results: Using a COI dataset from benthic marine communities, we compared two denoising procedures (based on the UNOISE3 and the DADA2 algorithms), set suitable parameters for denoising and clustering, and applied these steps in diferent orders. Our results indicated that the UNOISE3 algorithm preserved a higher intra-cluster variability. We introduce the program DnoisE to implement the UNOISE3 algorithm taking into account the natural variability (measured as entropy) of each codon position in protein-coding genes. This correction increased the number of sequences retained by 88%. The order of the steps (denoising and clustering) had little infuence on the fnal outcome. Conclusions: We highlight the need for combining denoising and clustering, with adequate choice of stringency parameters, in COI metabarcoding. We present a program that uses the coding properties of this marker to improve the denoising step. We recommend researchers to report their results in terms of both denoised sequences (a proxy for haplotypes) and clusters formed (a proxy for species), and to avoid collapsing the sequences of the latter into a single representative. This will allow studies at the cluster (ideally equating species-level diversity) and at the intra-cluster level, and will ease additivity and comparability between studies

Low genetic diversity and recent demographic expansion in the red starfish Echinaster sepositus (Retzius 1816)

16 páginas, 5 tablas, 7 figuras.Understanding the phylogeography and genetic structure of populations and the processes responsible of patterns therein is crucial for evaluating the vulnerability of marine species and developing management strategies. In this study, we explore how past climatic events and ongoing oceanographic and demographic processes have shaped the genetic structure and diversity of the Atlanto- Mediterranean red starfish Echinaster sepositus. The species is relatively abundant in some areas of the Mediterranean Sea, but some populations have dramatically decreased over recent years due to direct extraction for ornamental aquariums and souvenir industries. Analyses across most of the distribution range of the species based on the mitochondrial cytochrome c oxidase subunit I gene and eight microsatellite loci revealed very low intraspecific genetic diversity. The species showed a weak genetic structure within marine basins despite the a priori low dispersal potential of its lecithotrophic larva. Our results also revealed a very recent demographic expansion across the distribution range of the species. The genetic data presented here indicate that the species might be highly vulnerable, due to its low intraspecific genetic diversity.This study was supported by a FPI-MICINN PhD fellowship (BES-2011-044154) to AGC, a ‘Juan de la Cierva’ contract from the Spanish Government to RPP, and the Spanish government research projects BENTHOMICS (CTM2010-22218-C02-) and CHALLENGEN (CTM2103-48163). This paper is a contribution of the Consolidated Research Group 2009SRG665 supported by the Generalitat de Catalunya.Peer reviewe

DNA metabarcoding of littoral hard-bottom communities: high diversity and database gaps revealed by two molecular markers

Biodiversity assessment of marine hard-bottom communities is hindered by the high diversity and size-ranges of the organisms present. We developed a DNA metabarcoding protocol for biodiversity characterization of structurally complex natural marine hard-bottom communities. We used two molecular markers: the "Leray fragment" of mitochondrial cytochrome c oxidase (COI), for which a novel primer set was developed, and the V7 region of the nuclear small subunit ribosomal RNA (18S). Eight different shallow marine littoral communities from two National Parks in Spain (one in the Atlantic Ocean and another in the Mediterranean Sea) were studied. Samples were sieved into three size fractions from where DNA was extracted separately. Bayesian clustering was used for delimiting molecular operational taxonomic units (MOTUs) and custom reference databases were constructed for taxonomic assignment. Despite applying stringent filters, we found high values for MOTU richness (2,510 and 9,679 MOTUs with 18S and COI, respectively), suggesting that these communities host a large amount of yet undescribed eukaryotic biodiversity. Significant gaps are still found in sequence reference databases, which currently prevent the complete taxonomic assignment of the detected sequences. In our dataset, 85% of 18S MOTUs and 64% of COI MOTUs could be identified to phylum or lower taxonomic level. Nevertheless, those unassigned were mostly rare MOTUs with low numbers of reads, and assigned MOTUs comprised over 90% of the total sequence reads. The identification rate might be significantly improved in the future, as reference databases are further completed. Our results show that marine metabarcoding, currently applied mostly to plankton or sediments, can be adapted to structurally complex hard bottom samples. Thus, eukaryotic metabarcoding emerges as a robust, fast, objective and affordable method to comprehensively characterize the diversity of marine benthic communities dominated by macroscopic seaweeds and colonial or modular sessile metazoans. The 18S marker lacks species-level resolution and thus cannot be recommended to assess the detailed taxonomic composition of these communities. Our new universal primers for COI can potentially be used for biodiversity assessment with high taxonomic resolution in a wide array of marine, terrestrial or freshwater eukaryotic communities

Long telomeres are associated with clonality in wild populations of the fissiparous starfish Coscinasterias tenuispina

elomeres usually shorten during an organism's lifespan and have thus been used as an aging and health marker. When telomeres become sufficiently short, senescence is induced. The most common method of restoring telomere length is via telomerase reverse transcriptase activity, highly expressed during embryogenesis. However, although asexual reproduction from adult tissues has an important role in the life cycles of certain species, its effect on the aging and fitness of wild populations, as well as its implications for the long-term survival of populations with limited genetic variation, is largely unknown. Here we compare relative telomere length of 58 individuals from four populations of the asexually reproducing starfish Coscinasterias tenuispina. Additionally, 12 individuals were used to compare telomere lengths in regenerating and non-regenerating arms, in two different tissues (tube feet and pyloric cecum). The level of clonality was assessed by genotyping the populations based on 12 specific microsatellite loci and relative telomere length was measured via quantitative PCR. The results revealed significantly longer telomeres in Mediterranean populations than Atlantic ones as demonstrated by the Kruskal-Wallis test (K=24.17, significant value: P-value<0.001), with the former also characterized by higher levels of clonality derived from asexual reproduction. Telomeres were furthermore significantly longer in regenerating arms than in non-regenerating arms within individuals (pyloric cecum tissue: Mann-Whitney test, V=299, P-value<10−6; and tube feet tissue Student's t=2.28, P-value=0.029). Our study suggests that one of the mechanisms responsible for the long-term somatic maintenance and persistence of clonal populations is telomere elongation