Adaptive Walks on Changing Landscapes: Levins' Approach Extended

The assumption that trade-offs exist is fundamental in evolutionary theory. Levins (Am. Nat. 96 (1962) 361-372) introduced a widely adopted graphical method for analyzing evolution towards an optimal combination of two quantitative traits, which are traded off. His approach explicitly excluded the possibility of density- and frequency-dependent selection. Here we extend Levins method towards models, which include these selection regimes and where therefore fitness landscapes change with population state. We employ the same kind of curves Levins used: trade-off curves and fitness contours. However, fitness contours are not fixed but a function of the resident traits and we only consider those that divide the trait space into potentially successful mutants and mutants which are not able to invade ('invasion boundaries'). The developed approach allows to make a priori predictions about evolutionary endpoints and about their bifurcations. This is illustrated by applying the approach to several examples from the recent literature

The Evolution of Simple Life-Histories: Step Towards Classification

We present a classification of the evolutionary dynamics for a class of simple life-history models. The model class considered is characterised by discrete time population dynamics, density-dependent population growth, by the assumption that individuals can occur in two states, and that two evolving traits are coupled by a trade-off. Individual models differ in the choice of traits that are presumed to evolve and in the way population regulation is incorporated. The classification is based on a fitness measure that is sign equivalent to invasion fitness but algebraically simpler. We classify models according to curvature properties of the fitness landscape and whether the evolutionary dynamics can be analysed by means of an optimisation criterion. The first classification allows us to infer whether trait combinations that are characterised by a zero fitness gradient are susceptible to invasion by similar trait combinations. The second classification distinguishes models where evolutionary change is frequency-independent from models that give rise to frequency dependence. Given certain symmetry assumptions we can extend the classification in the latter case by splitting selection into a density-dependent and a frequency-dependent component. We apply our approach to several simple life-history models and demonstrate how our classification facilitates an analytical analysis. We conclude by discussing some general patterns that emerge from our analysis and by hinting at several possible extensions

The Evolution of Resource Specialization through Frequency-Dependent and Frequency-Independent Mechanisms

Levin's fitness set approach has shaped the intuition of many evolutionary ecologists about resource specialization: if the set of possible phenotypes is convex, a generalist is favored, while either of the two specialists is predicted for concave phenotype sets. An important aspect of Levins approach is that it explicitly excludes frequency-dependent selection. Frequency-dependence emerged in a series of models that studied the degree of character displacement of two consumers coexisting on two resources. Surprisingly, the evolutionary dynamics of a single consumer type under frequency-dependence has not been studied in detail yet. We analyze a model of one evolving consumer feeding on two resources and show that, depending on the trait considered to be subject to evolutionary change, selection is either frequency-independent or frequency-dependent. This difference is explained by the effects different foraging traits have on the consumer-resource interactions. If selection is frequency-dependent, then the population can become dimorphic through evolutionary branching at the trait value of the generalist. Those traits with frequency-independent selection, however, do indeed follow the predictions based on Levin's fitness set approach. This dichotomy in the evolutionary dynamics of traits involved in the same foraging process was not previously recognized

Grensverleggend huisvesten van melkvee

Rapport over vernieuwende ideeën met betrekking tot huisvesting van melkvee. Er is gekeken naar vernieuwende stalconcepten in binnen- en buitenland die praktisch toepasbaar zij

Local Linearizations of Rational Matrices with Application to Rational Approximations of Nonlinear Eigenvalue Problems

This paper presents a definition for local linearizations of rational matrices and studies their properties. This definition allows us to introduce matrix pencils associated to a rational matrix that preserve its structure of zeros and poles in subsets of any algebraically closed field and also at infinity. Moreover, such definition includes, as particular cases, other definitions that have been used previously in the literature. In this way, this new theory of local linearizations captures and explains rigorously the properties of all the different pencils that have been used from the 1970's until 2019 for computing zeros, poles and eigenvalues of rational matrices. Particular attention is paid to those pencils that have appeared recently in the numerical solution of nonlinear eigenvalue problems through rational approximation.Comment: 49 page