Jan Eisner

Do clones degenerate over time? Explaining the genetic variability of asexuals through population genetic models

BackgroundQuest for understanding the nature of mechanisms governing the life span of clonal organisms lasts for several decades. Phylogenetic evidence for recent origins of most clones is usually interpreted as proof that clones suffer from gradual age-dependent fitness decay (e.g. Mullers ratchet). However, we have shown that a neutral drift can also qualitatively explain the observed distribution of clonal ages. This finding was followed by several attempts to distinguish the effects of neutral and non-neutral processes. Most recently, Neiman et al. 2009 (Ann N Y Acad Sci.:1168:185-200.) reviewed the distribution of asexual lineage ages estimated from a diverse array of taxa and concluded that neutral processes alone may not explain the observed data. Moreover, the authors inferred that similar types of mechanisms determine maximum asexual lineage ages in all asexual taxa. In this paper we review recent methods for distinguishing the effects of neutral and non-neutral processes and point at methodological problems related with them.Results and DiscussionWe found that contemporary analyses based on phylogenetic data are inadequate to provide any clear-cut answer about the nature and generality of processes affecting evolution of clones. As an alternative approach, we demonstrate that sequence variability in asexual populations is suitable to detect age-dependent selection against clonal lineages. We found that asexual taxa with relatively old clonal lineages are characterised by progressively stronger deviations from neutrality.ConclusionsOur results demonstrate that some type of age-dependent selection against clones is generally operational in asexual animals, which cover a wide taxonomic range spanning from flatworms to vertebrates. However, we also found a notable difference between the data distribution predicted by available models of sequence evolution and those observed in empirical data. These findings point at the possibility that processes affecting clonal evolution differ from those described in recent studies, suggesting that theoretical models of asexual populations must evolve to address this problem in detail.ReviewersThis article was reviewed by Isa Schön (nominated by John Logsdon), Arcady Mushegian and Timothy G. Barraclough (nominated by Laurence Hurst).

Smooth continuation of solutions and eigenvalues for variational inequalities based on the implicit function theorem

The implicit function theorem is applied in a nonstandard way to abstract variational inequalities depending on a (possibly infinite-dimensional) parameter. In this way, results on smooth continuation of solutions as well as of eigenvalues and eigenvectors are established under certain particular assumptions. The abstract results are applied to a linear second order elliptic eigenvalue problem with nonlocal unilateral boundary conditions (Schrodinger operator with the potential as the parameter).

Smooth bifurcation for variational inequalities based on the implicit function theorem

Abstract We present a certain analog for variational inequalities of the classical result on bifurcation from simple eigenvalues of Crandall and Rabinowitz. In other words, we describe the existence and local uniqueness of smooth families of nontrivial solutions to variational inequalities, bifurcating from a trivial solution family at certain points which could be called simple eigenvalues of the homogenized variational inequality. If the bifurcation parameter is one-dimensional, the main difference between the case of equations and the case of variational inequalities (when the cone is not a linear subspace) is the following: For equations two smooth half-branches bifurcate, for inequalities only one. The proofs are based on scaling techniques and on the implicit function theorem. The abstract results are applied to a fourth order ODE with pointwise unilateral conditions (an obstacle problem for a beam with the compression force as the bifurcation parameter).

Spatial Patterns for reaction-diffusion systems with conditions described by inclusions

We consider a reaction-diffusion system of the activator-inhibitor type with boundary conditions given by inclusions. We show that there exists a bifurcation point at which stationary but spatially nonconstant solutions (spatial patterns) bifurcate from the branch of trivial solutions. This bifurcation point lies in the domain of stability of the trivial solution to the same system with Dirichlet and Neumann boundary conditions, where a bifurcation of this classical problem is excluded.

Global Bifurcation for a Reaction-Diffusion System with Inclusions

We consider a reaction-diffusion system exhibiting diffusion driven instability if supplemented by Dirichlet-Neumann boundary conditions. We impose unilateral conditions given by inclusions on this system and prove that global bifurcation of spatially nonhomogeneous stationary solutions occurs in the domain of parameters where bifurcation is excluded for the original mixed boundary value problem. Inclusions can be considered in one of the equations itself as well as in boundary conditions. The proof is based on the degree theory for multivalued mappings (jump of the degree implies bifurcation). We show how the degree for a class of multivalued maps including those corresponding to a weak formulation of our problem can be calculated.

Location of Bifurcation Points for a Reaction-Diffusion System with Neumann-Signorini Conditions

Abstract We consider a reaction-diffusion system of activator-inhibitor or substrate-depletion type in one space dimension which is subject to diffusion-driven instability. We determine the change of bifurcation when a pure Neumann condition is supplemented with a Signorini condition. We show that this change differs essentially from the known case when also Dirichlet conditions are assumed.

Sperm-dependent parthenogens delay the spatial expansion of their sexual hosts.

It has been known for long time that asexual organisms may affect the distribution of sexual taxa. In fact, such phenomenon is inherent in the concept of geographical parthenogenesis. On the other hand, it was generally hypothesized that sperm-dependent asexuals may not exercise the same effect on related sexual population, due to their dependence upon them as sperm-donors. Recently, however, it became clear that sperm-dependent asexuals may directly or indirectly affect the distribution of their sperm-hosts, but rather in a small scale. No study addressed the large-scale biogeographic effect of the coexistence of such asexuals with the sexual species. In our study we were interested in the effect of sexual-asexual coexistence on the speed of spatial expansion of the whole complex. We expand previously published Lotka-Volterra model of the coexistence of sexual and gynogenetic forms of spined loach (Cobitis; Teleostei) hybrid complex by diffusion. We show that presence of sperm-dependent parthenogens is likely to negatively affect the spatial expansion of sexuals, and hence the whole complex, compared to pure sexual population. Given that most of the known sperm-dependent asexual complexes are distributed in areas prone to climate-induced colonization/extinction events, we conclude that such mechanism may be an important agent in determining the biogeography of sexual taxa and therefore requires further attention including empirical tests.

Bifurcation of Solutions to Reaction-Diffusion Systems with Jumping Nonlinearities

Bifurcation of stationary solutions to reaction-diffusion systems of activator-inhibitor type with jumping nonlinearities are located. The result can be understood as a certain destabilizing effect of jumping terms.

BIFURCATION DIRECTION AND EXCHANGE OF STABILITY FOR AN ELLIPTIC UNILATERAL BVP

The direction of bifurcation of nontrivial solutions to the elliptic boundary value problem involving unilateral nonlocal boundary conditions is shown in a neighbourhood of bifurcation points of a certain type. Moreover, the stability and instability of bifurcating solutions as well as of the trivial solution is described in the sense of minima of the potential. In particular, an exchange of stability is observed.