On the evolution of the timing of reproduction with non-equilibrium resident dynamics.

We study the evolution of an individual's reproductive strategy in a mechanistic modeling framework. We assume that the total number of juveniles one adult individual can produce is a finite constant, and we study how this number should be distributed during the season, given the types of inter-individual interactions and mortality processes included in the model. The evolution of the timing of reproduction in this modeling framework has already been studied earlier in the case of equilibrium resident dynamics, but we generalize the situation to also fluctuating population dynamics. We find that, as in the equilibrium case, the presence or absence of inter-juvenile aggression affects the functional form of the evolutionarily stable reproductive strategy. If an ESS exists, it can have an absolutely continuous part only if inter-juvenile aggression is included in the model. If inter-juvenile aggression is not included in the model, an ESS can have no continuous parts, and only Dirac measures are possible.

The Allee effect in mechanistic models based on inter-individual interaction processes.

Recently, Eskola and Geritz (Bull. Math. Biol. 69:329-346, 2007) showed that several discrete-time population models can be derived mechanistically within a single ecological framework by varying the within-season patterns of reproduction and inter-individual aggression. However, these models do not have the Allee effect. In this paper, we modify the original modelling framework by adding different mate finding processes, and thus derive mechanistically several population models with the Allee effect.

On the evolution of the timing of reproduction.

In this paper, we study the evolution of the per capita rate of reproduction as a function of time in the modelling framework introduced by Eskola and Geritz [Eskola, H.T.M., Geritz, S.A.H., 2007. On the mechanistic derivation of various discrete-time population models, Bull. Math. Biol. 69, 329-346]. We assume that the total number of juveniles one adult individual can produce is a finite constant, and we study how this number should be distributed during the season, when certain interaction and mortality processes are also included in the model. If aggressive interactions between the juveniles are not included in the model, evolution is simply optimizing, and the optimal reproductive strategy is always a single Dirac delta-peak within the season. If aggressive interactions between the juveniles are included, an evolutionarily stable strategy can consist of not only one or two delta-peaks, but also of continuous reproduction during the season. Using this approach, we have also derived conditions under which the classical population dynamical models of Beverton and Holt [Beverton, R.J.H., Holt, S.J., 1957. On the dynamics of exploited fish populations. Fisheries Investigations, Ser. 219], Hassell [Hassell, M.P., 1975. Density-dependence in single-species populations. J. Animal Ecology 44, 283-295] and Ricker [Ricker, W.E., 1954. Stock and recruitment. J. Fisheries Res. Board Can. 11, 559-623] are evolutionarily stable.

Investigation of Feshbach resonances in ultracold 40K spin mixtures.

Magnetically tunable Feshbach resonances are an indispensable tool for experiments with atomic quantum gases. We report on 37 thus far unpublished Feshbach resonances and four further probable Feshbach resonances in spin mixtures of ultracold fermionic 40K with temperatures well below 100 nK. In particular, we locate a broad resonance at B = 389.7G with a magnetic width of 26.7 G. Here 1 G = 10-4 T. Furthermore, by exciting low-energy spin waves, we demonstrate a means to precisely determine the zero crossing of the scattering length for this broad Feshbach resonance. Our findings allow for further tunability in experiments with ultracold 40K quantum gases.

On the mechanistic underpinning of discrete-time population models with Allee effect.

The Allee effect means reduction in individual fitness at low population densities. There are many discrete-time population models with an Allee effect in the literature, but most of them are phenomenological. Recently, Geritz and Kisdi [2004. On the mechanistic underpinning of discrete-time population models with complex dynamics. J. Theor. Biol. 228, 261-269] presented a mechanistic underpinning of various discrete-time population models without an Allee effect. Their work was based on a continuous-time resource-consumer model for the dynamics within a year, from which they derived a discrete-time model for the between-year dynamics. In this article, we obtain the Allee effect by adding different mate finding mechanisms to the within-year dynamics. Further, by adding cannibalism we obtain a higher variety of models. We thus present a generator of relatively realistic, discrete-time Allee effect models that also covers some currently used phenomenological models driven more by mathematical convenience.

On the mechanistic derivation of various discrete-time population models.

We present a derivation of various discrete-time population models within a single unifying mechanistic context. By systematically varying the within-year patterns of reproduction and aggression between individuals we can derive various discrete-time population models. These models include classical examples such as the Ricker model, the Beverton-Holt model, the Skellam model, the Hassell model, and others. Some of these models until now lacked a good mechanistic interpretation or have been derived in a different context. By using this mechanistic approach, the model parameters can be interpreted in terms of individual behavior.