Life amidst singularities

"Adaptive dynamics" is the study of evolution driven by rare mutations with small effects. The essential tool is the "invasion fitness", the expected number of offspring for a rare mutant in a resident community at equilibrium. The first part of this thesis starts by generalising the "canonical equation of adaptive dynamics", a first-order approximation of the speed of change of multidimensional traits under directional selection, so that it holds for general physiologically structured (i.e., arbitrarily complex) population models. Secondly, it proves that near evolutionary singularities and up to second-order terms, such models have the same invasion fitness as the much simpler Lotka-Volterra models (but third-order terms can differ). Thirdly, it combines those results in a recipe for studying analytically the complete dynamics of evolutionary models with limited mutational effects. A prerequisite for models of sympatric speciation to work is the evolution of assortative mating, which has never been validated against alternatives. Therefore the second part compares in a general setting the relative probabilities of the evolution of assortative mate choice to that of dominance interactions, and the conditions favouring each one. This part also shows that allowing for the possibility of sexual dimorphism makes sympatric speciation much less likely.NWO-ALW PhD grant 809.34.002. NWO Dutch-Hungarian exchange grant 048.011.039. ERTN ModLife funding through HPRN-CT-2000-00051 EU grant. NWO-Veni grant for co-author Tom Van Dooren (2 chapters). OTKA T049689 and TS049885 research and travel grants for co-author Geza Meszena (1 chapter).UBL - phd migration 201

Evolutionary branching in a stochastic population model with discrete mutational steps

Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a trait, and also by population sizes, and that mutations lead to small changes in trait value. Then, traditionally, the evolutionary dynamics is studied in the limit of vanishing mutational step sizes. In the present approach, small but non-negligible mutational steps are considered. By means of theoretical analysis in the limit of infinitely large populations, as well as computer simulations, we demonstrate how discrete mutational steps affect the patterns of evolutionary branching. We also argue that the average time to the first branching depends in a sensitive way on both mutational step size and population size.Comment: 12 pages, 8 figures. Revised versio

The purification and characterisation of novel dipeptidyl peptidase IV-like activity from bovine serum

The discovery of a potentially novel proline-specific peptidase from bovine serum is presented which is capable of cleaving the dipeptidyl peptidase IV (DPIV) substrate Gly-Pro-MCA. The enzyme was isolated and purified with the use of Phenyl Sepharose Hydrophobic Interaction, Sephacryl S300 Gel Filtration, and Q-Sephacryl Anion Exchange, producing an overall purification factor of 257. SDS PAGE resulted in a monomeric molecular mass of 158 kDa while Size Exclusion Chromatography generated a native molecular mass of 328 kDa. The enzyme remained active over a broad pH range with a distinct preference for a neutral pH range of 7-8.5. Chromatofocusing and Isoelectric Focusing revealed the enzyme’s isoelectric point to be 4.74. DPIV-like activity was not inhibited by serine protease inhibitors but was by the metallo-protease inhibitors, the phenanthrolines. The enzyme was also partially inhibited by Bestatin. Substrate Specificity studies proved that the enzyme is capable of sequential cleavage of bovine β- Casomorphin and Substance P. The peptidase cleaved the standard DPIV substrate, Gly-Pro-MCA with a KM of 38.4 μM, while Lys-Pro-MCA was hydrolysed with a KM of 103 μM. The DPIV- like activity was specifically inhibited by both Diprotin A and B, non-competitively, generating a Ki of 1.4x10-4 M for both inhibitors. Ile-Thiazolidide and Ile-Pyrrolidide both inhibited competitively with an inhibition constant of 3.7x10-7 M and 7.5x10-7 M respectively. It is concluded that bovine serum DPIV-like activity share many biochemical properties with DPIV and DPIV-like enzymes but not exclusively, suggesting that the purified peptidase may play an important novel role in bioactive oligopeptide degradation

Solvent and thermal stability, and pH kinetics, of proline-specific dipeptidyl peptidase IV-like enzyme from bovine serum

Proline-specific dipeptidyl peptidase-like (DPP IV; EC 3.4.14.5) activity in bovine serum has attracted little attention despite its ready availability and the paucity of useful proline-cleaving enzymes. Bovine serum DPP IV-like peptidase is very tolerant of organic solvents, particularly acetonitrile: upon incubation for 1 h at room temperature in 70% acetonitrile, 47% dimethylformamide, 54% DMSO and 33% tetrahydrofuran (v/v concentrations) followed by dilution into the standard assay mixture, the enzyme retained half of its aqueous activity. As for thermal performance in aqueous buffer, its relative activity increased up to 50 ◦C. Upon thermoinactivation at 71 ◦C, pH 8.0 (samples removed periodically, cooled on ice, then assayed under optimal conditions), residual activities over short times fit a first-order decay with a k-value of 0.071±0.0034 min−1. Over longer times, residual activities fit to a double exponential decay with k1 and k2 values of 0.218±0.025 min−1 (46±4% of overall decay) and 0.040±0.002 min−1 (54±4% of overall decay), respectively. The enzyme’s solvent and thermal tolerances suggest that it may have potential for use as a biocatalyst in industry. Kinetic analysis with the fluorogenic substrate Gly-Pro-7-aminomethylcoumarin over a range of pH values indicated two pK values at 6.18±0.07 and at 9.70±0.50. We ascribe the lower value to the active site histidine; the higher may be due to the active site serine or to a free amino group in the substrate

Daphnias: from the individual based model to the large population equation

The class of deterministic 'Daphnia' models treated by Diekmann et al. (J Math Biol 61: 277-318, 2010) has a long history going back to Nisbet and Gurney (Theor Pop Biol 23: 114-135, 1983) and Diekmann et al. (Nieuw Archief voor Wiskunde 4: 82-109, 1984). In this note, we formulate the individual based models (IBM) supposedly underlying those deterministic models. The models treat the interaction between a general size-structured consumer population ('Daphnia') and an unstructured resource ('algae'). The discrete, size and age-structured Daphnia population changes through births and deaths of its individuals and throught their aging and growth. The birth and death rates depend on the sizes of the individuals and on the concentration of the algae. The latter is supposed to be a continuous variable with a deterministic dynamics that depends on the Daphnia population. In this model setting we prove that when the Daphnia population is large, the stochastic differential equation describing the IBM can be approximated by the delay equation featured in (Diekmann et al., l.c.)

An open and transparent process to select ELIXIR Node Services as implemented by ELIXIR-UK

ELIXIR is the European infrastructure established specifically for the sharing and sustainability of life science data. To provide up-to-date resources and services, ELIXIR needs to undergo a continuous process of refreshing the services provided by its national Nodes. Here we present the approach taken by ELIXIR-UK to address the advice by the ELIXIR Scientific Advisory Board that Nodes need to develop “mechanisms to ensure that each Node continues to be representative of the Bioinformatics efforts within the country”. ELIXIR-UK put in place an open and transparent process to identify potential ELIXIR resources within the UK during late 2015 and early to mid-2016. Areas of strategic strength were identified and Expressions of Interest in these priority areas were requested from the UK community. A set of criteria were established, in discussion with the ELIXIR Hub, and prospective ELIXIR-UK resources were assessed by an independent committee set up by the Node for this purpose. Of 19 resources considered, 14 were judged to be immediately ready to be included in the UK ELIXIR Node’s portfolio. A further five were placed on the Node’s roadmap for future consideration for inclusion. ELIXIR-UK expects to repeat this process regularly to ensure its portfolio continues to reflect its community’s strengths

Polymorphic evolution sequence and evolutionary branching

We are interested in the study of models describing the evolution of a polymorphic population with mutation and selection in the specific scales of the biological framework of adaptive dynamics. The population size is assumed to be large and the mutation rate small. We prove that under a good combination of these two scales, the population process is approximated in the long time scale of mutations by a Markov pure jump process describing the successive trait equilibria of the population. This process, which generalizes the so-called trait substitution sequence, is called polymorphic evolution sequence. Then we introduce a scaling of the size of mutations and we study the polymorphic evolution sequence in the limit of small mutations. From this study in the neighborhood of evolutionary singularities, we obtain a full mathematical justification of a heuristic criterion for the phenomenon of evolutionary branching. To this end we finely analyze the asymptotic behavior of 3-dimensional competitive Lotka-Volterra systems

Evolution of Assortative Mating in a Population Expressing Dominance

In this article, we study the influence of dominance on the evolution of assortative mating. We perform a population-genetic analysis of a two-locus two-allele model. We consider a quantitative trait that is under a mixture of frequency-independent stabilizing selection and density- and frequency-dependent selection caused by intraspecific competition for a continuum of resources. The trait is determined by a single (ecological) locus and expresses intermediate dominance. The second (modifier) locus determines the degree of assortative mating, which is expressed in females only. Assortative mating is based on similarities in the quantitative trait (‘magic trait’ model). Analytical conditions for the invasion of assortment modifiers are derived in the limit of weak selection and weak assortment. For the full model, extensive numerical iterations are performed to study the global dynamics. This allows us to gain a better understanding of the interaction of the different selective forces. Remarkably, depending on the size of modifier effects, dominance can have different effects on the evolution of assortment. We show that dominance hinders the evolution of assortment if modifier effects are small, but promotes it if modifier effects are large. These findings differ from those in previous work based on adaptive dynamics