Journal of Mathematical Biology

 We analyze the evolution of spatially inhomogeneous perturbations in a lattice gas model for a prey-predator population. Starting with the master equation of the model, decoupled by means of a mean field approximation, spatial instabilities are seen to take place in a region of the phase diagram. This is in qualitative agreement with local oscillations already observed in computer simulations. We determine the transition line that separates the homogeneous region from the inhomogeneous region and we study the spatio-temporal self-organized structures that appear inside the inhomogeneous region.

The energy cost of offspring is important in the conversion of resources allocated to reproduction to numbers of offspring, and in obtaining energy budget parameters from quantities that are easy to measure. An efficient numerical procedure is presented to obtain this cost for eggs and foetusses in the context of the dynamic energy budget theory, which specifies that birth occurs when maturity exceeds a threshold value and maternal effects determine the reserve density at birth. This paper extends previous work to arbitrary values of the ratio of the maturity and somatic maintenance costs. I discuss the body size scaling implications for the relative size and age at birth and conclude that the size at birth, contrary to the age at birth, covaries with the maintenance ratio. Apart from evolutionary adaptation of the maturity at birth, this covariation might explain some of the observed scatter in the relative length at birth. The theory can be used to evaluate the effects of the separation of cells in e.g. the two-cell stage of embryonic development, and of the removal of initial egg mass. If cell separation hardly affects energy parameters, body size scaling relationships imply that cell separation can only occur successfully in species with sufficiently large maximum body length (as adult); i.e. some two times that of Daphnia magna. Toxic compounds that increase the cost of synthesis of structure, decrease the allocation to reproduction indirectly via the life cycle, because food uptake is linked to size. They can also decrease the egg size, however, such that the reproduction rate is stimulated at low concentrations. The present theory offers a possible explanation for this well-known phenomenon.

In the spreading of infectious diseases, an important number to determine is how many other people will be infected on average by anyone who has become infected themselves. This is known as the reproduction number. This paper describes a non-parametric inverse method for extracting the full transfer function of infection, of which the reproduction number is the integral. The method is demonstrated by applying it to the timeline of hospitalisation admissions for covid-19 in the Netherlands up to May 20 2020, which is publicly available from the site of the Dutch National Institute of Public Health and the Environment (rivm.nl).

By introducing linear cross-diffusion for a two-component reaction-diffusion system with activator-depleted reaction kinetics (Gierer and Meinhardt, Kybernetik 12:30–39, 1972; Prigogine and Lefever, J Chem Phys 48:1695–1700, 1968; Schnakenberg, J Theor Biol 81:389–400, 1979), we derive cross-diffusion-driven instability conditions and show that they are a generalisation of the classical diffusion-driven instability conditions in the absence of cross-diffusion. Our most revealing result is that, in contrast to the classical reaction-diffusion systems without cross-diffusion, it is no longer necessary to enforce that one of the species diffuse much faster than the other. Furthermore, it is no longer necessary to have an activator–inhibitor mechanism as premises for pattern formation, activator–activator, inhibitor–inhibitor reaction kinetics as well as short-range inhibition and long-range activation all have the potential of giving rise to cross-diffusion-driven instability. To support our theoretical findings, we compute cross-diffusion induced parameter spaces and demonstrate similarities and differences to those obtained using standard reaction-diffusion theory. Finite element numerical simulations on planary square domains are presented to back-up theoretical predictions. For the numerical simulations presented, we choose parameter values from and outside the classical Turing diffusively-driven instability space; outside, these are chosen to belong to cross-diffusively-driven instability parameter spaces. Our numerical experiments validate our theoretical predictions that parameter spaces induced by cross-diffusion in both the $$u$$ and $$v$$ components of the reaction-diffusion system are substantially larger and different from those without cross-diffusion. Furthermore, the parameter spaces without cross-diffusion are sub-spaces of the cross-diffusion induced parameter spaces. Our results allow experimentalists to have a wider range of parameter spaces from which to select reaction kinetic parameter values that will give rise to spatial patterning in the presence of cross-diffusion.

A population genetic two-locus model with additive, directional selection and recombination is considered. It is assumed that recombination is weaker than selection; i.e., the recombination parameter r is smaller than the selection coefficients. This assumption is appropriate for describing the effects of two-locus selection at the molecular level. The model is formulated in terms of ordinary differential equations (ODES) for the gamete frequencies x = (x 1, x 2, x 3, x 4), defined on the simplex S 4. The ODEs are analyzed using first a regular pertubation technique. However, this approach yields satisfactory results only if r is very small relative to the selection coefficients and if the initial values x(0) are in the interior part of S 4. To cope with this problem, a novel two-scale perturbation method is proposed which rests on the theory of averaging of vectorfields. It is demonstrated that the zeroth-order solution of this two-scale approach approximates the numerical solution of the model well, even if recombination rate is on the order of the selection coefficients.

The paper models the maintenance of ecological networks in forest environments, built from bioreserves, patches and corridors, when these grids are subject to random processes such as extreme natural events. It also outlines a management plan to support the optimized results. After presenting the random graph-theoretic framework, we apply the stochastic optimal control to the graph dynamics. Our results show that the preservation of the network architecture cannot be achieved, under stochastic control, over the entire duration. It can only be accomplished, at the cost of sacrificing the links between the patches, by increasing the usage of the control devices. This would have a negative effect on the species migration by causing congestion among the channels left at their disposal. The optimal scenario, in which the shadow price is at its lowest and all connections are well-preserved, occurs at half of the course, be it the only optimal stopping moment found on the stochastic optimal trajectories. In such a scenario, the optimal forestry management policy has to integrate agility, integrated response, and quicker response time.