An adaptive Newton-method based on a dynamical systems approach

The traditional Newton method for solving nonlinear operator equations in Banach spaces is discussed within the context of the continuous Newton method. This setting makes it possible to interpret the Newton method as a discrete dynamical system and thereby to cast it in the framework of an adaptive step size control procedure. In so doing, our goal is to reduce the chaotic behavior of the original method without losing its quadratic convergence property close to the roots. The performance of the modified scheme is illustrated with various examples from algebraic and differential equations.

The genomic substrate for adaptive radiation in African cichlid fish

Cichlid fishes are famous for large, diverse and replicated adaptive radiations in the Great Lakes of East Africa. To understand the molecular mechanisms underlying cichlid phenotypic diversity, we sequenced the genomes and transcriptomes of five lineages of African cichlids: the Nile tilapia (Oreochromis niloticus), an ancestral lineage with low diversity; and four members of the East African lineage: Neolamprologus brichardi/pulcher (older radiation, Lake Tanganyika), Metriaclima zebra (recent radiation, Lake Malawi), Pundamilia nyererei (very recent radiation, Lake Victoria), and Astatotilapia burtoni (riverine species around Lake Tanganyika). We found an excess of gene duplications in the East African lineage compared to tilapia and other teleosts, an abundance of non-coding element divergence, accelerated coding sequence evolution, expression divergence associated with transposable element insertions, and regulation by novel microRNAs. In addition, we analysed sequence data from sixty individuals representing six closely related species from Lake Victoria, and show genome-wide diversifying selection on coding and regulatory variants, some of which were recruited from ancient polymorphisms. We conclude that a number of molecular mechanisms shaped East African cichlid genomes, and that amassing of standing variation during periods of relaxed purifying selection may have been important in facilitating subsequent evolutionary diversification.

Contemporary ecotypic divergence during a recent range expansion was facilitated by adaptive introgression

Although rapid phenotypic evolution during range expansion associated with colonization of contrasting habitats has been documented in several taxa, the evolutionary mechanisms that underlie such phenotypic divergence have less often been investigated. A strong candidate for rapid ecotype formation within an invaded range is the three-spine stickleback in the Lake Geneva region of central Europe. Since its introduction only about 140 years ago, it has undergone a significant expansion of its range and its niche, now forming phenotypically differentiated parapatric ecotypes that occupy either the pelagic zone of the large lake or small inlet streams, respectively. By comparing museum collections from different times with contemporary population samples, we here reconstruct the evolution of parapatric phenotypic divergence through time. Using genetic data from modern samples, we infer the underlying invasion history. We find that parapatric habitat-dependent phenotypic divergence between the lake and stream was already present in the first half of the twentieth century, but the magnitude of differentiation increased through time, particularly in antipredator defence traits. This suggests that divergent selection between the habitats occurred and was stable through much of the time since colonization. Recently, increased phenotypic differentiation in antipredator defence traits likely results from habitat-dependent selection on alleles that arrived through introgression from a distantly related lineage from outside the Lake Geneva region. This illustrates how hybridization can quickly promote phenotypic divergence in a system where adaptation from standing genetic variation was constrained.

Adaptive, convergent origins of the pygmy phenotype in African rainforest hunter-gatherers

Tropical rainforest hunter-gatherer populations worldwide share the pygmy phenotype, or small human body size. The evolutionary history of this phenotype is largely unknown. Here we studied DNA from the Batwa, a rainforest hunter-gatherer population from east central Africa, to identify regions of the Batwa genome that underlie the pygmy phenotype. We then performed population genomic analyses to study the evolution of these regions, including comparisons with the Baka, a west central African rainforest hunter-gatherer population. We conclude that the pygmy phenotype likely arose due to positive natural selection and that it arose possibly multiple times within Africa. These results support longstanding anthropological hypotheses that small body size confers an important selective advantage for human rainforest hunter-gatherers.

Explosive speciation rates and unusual species richness in haplochromine cichlid fishes: Effects of sexual selection

Ancient lakes are often unusually species rich, mostly as a result of radiation and species-flock formation having taken place in only one or a few of many taxa present. Understanding why some taxa radiate and others do not is at the heart of understanding biodiversity. In this chapter I discuss possible explanations for disproportionally large species numbers in some cichlid fish lineages in East African Great Lakes: the halochromine cichlid fishes in Lakes Victoria and Malawi. I show that speciation rates in this group are higher than in any other lacustrine fish radiation. Against this background, I review hypotheses put forward to explain diversity in cichlid species flocks. The evolution of species diversity requires three processes: speciation, ecological radiation and anatomical diversification, and it is wrong to consider hypotheses that are relevant to different processes as alternatives to each other. The African cichlid species flocks show unusually high ecological species packing in several phylogenetic groups and unusually high speciation rates in haplochromines. Therefore, it maybe concluded that at least two evolutionary models are required to explain the difference between cichlid diversity and other fish diversity in East African Lakes: one for speciation in haplochromines and one for coexistence. Subsequently I review work on speciation in haplochromines, and in particular studies aimed at testing the hypothesis of speciation by sexual selection. Haplochromines have a polygynous mating system, conducive to sexual selection, but other polygynous cichlids are not particularly species rich. This suggests that more than just strong sexual selection is required to explain haplochromine species richness. Recent palaeoecological evidence undermines the previously popular hypotheses that explained the species richness of Lake Victoria in terms of speciation under varying natural or sexual selection regimes in satellite lakes or in isolated lake basins. I summarize experimental and comparative studies, which provide evidence for two mechanisms of sympatric speciation by disruptive sexual selection on polymorphic coloration. Such modes of speciation may explain (i) the high speciation rates in colour polymorphic lineages of haplochromine cichlids under conditions where colour variation is visible in clear water, and (ii) in combination with factors that affect population survival, the unusual species richness in haplochromine species flocks. I argue that sexual selection, if disruptive, can accelerate the pace of adaptive radiation because the resultant genetic population fragmentation allows a much increased rate of differential response to disruptive natural selection. Hence, the ecological pattern of diversity resembles that produced by disruptive natural selection, with the difference that disruptive sexual selection continues to cause (gross) speciation even after niche space is saturated. This may explain the unusually high numbers of very closely related and ecologically similar species in haplochromine species flocks. The role of disruptive sexual selection is twofold: it not only causes speciation, but also maintains reproductive isolation in sympatry between species that have evolved in sympatry or allopatry. Therefore, the maintenance of diversity in species flocks that originated through sexual selection depends on the persistence of the selection regime within the environmental signal space under which that diversity evolved.