Simulation of Different Age Distributions for the Analysis of the Aging Curve of a Population of “S. cerevisiae”

: Newly developed microfluidic devices (“Mother Machines”) have improved data gathering for the study of aging in unicellular models, and thereby the understanding of this process. Each device has different features that cause them to have certain advantages or disadvantages. This has the advantage of not using mechanical pressure to trap the cells, but as it starts with a mixed age population it does not guarantee that the cells studied are virgin. One of the basic outputs in these studies is the aging curve, which shows how the fraction of viable cells varies with respect to time. From this it can be deduced how fast or slow the population ages. For devices where it is not possible to work with virgin cells, the age distribution is assumed, but changes in this distribution could affect the analysis of the data. Therefore, the present work seeks to carry out a series of simulations to find the different age distributions that could be present and determine the corresponding changes in the aging curve. We propose two population growth models, synchronous and asynchronous. For each model we will start with the possible age distributions and determine the various curves that can be obtained and then compare these computational results with the experimental data to propose a better interpretation of the data obtained from mother machine devices.

Stability in terms of two measures for population growth models with impulsive perturbations

In this paper, we establish some criteria for the stability of trivial solution of population growth models with impulsive perturbations. The working tools are based on the theory of generalized ordinary differential equations. Here, the conditions concerning the functions are more general than the classical ones.

The shape of density dependence and the relationship between population growth, intraspecific competition and equilibrium population density

The logistic growth model is one of the most frequently used formalizations of density dependence affecting population growth, persistence and evolution. Ecological and evolutionary theory and applications to understand population change over time often include this model. However, the assumptions and limitations of this popular model are often not well appreciated.Here, we briefly review past use of the logistic growth model and highlight limitations by deriving population growth models from underlying consumer-resource dynamics. We show that the logistic equation likely is not applicable to many biological systems. Rather, density-regulation functions are usually non-linear and may exhibit convex or both concave and convex curvatures depending on the biology of resources and consumers. In simple cases, the dynamics can be fully described by the continuous-time Beverton-Holt model. More complex consumer dynamics show similarities to a Maynard Smith-Slatkin model.Importantly, we show how population-level parameters, such as intrinsic rates of increase and equilibrium population densities are not independent, as often assumed. Rather, they are functions of the same underlying parameters. The commonly assumed positive relationship between equilibrium population density and competitive ability is typically invalid. As a solution, we propose simple and general relationships between intrinsic rates of increase and equilibrium population densities that capture the essence of different consumer-resource systems.Relating population level models to underlying mechanisms allows us to discuss applications to evolutionary outcomes and how these models depend on environmental conditions, like temperature via metabolic scaling. Finally, we use time-series from microbial food chains to fit population growth models and validate theoretical predictions.Our results show that density-regulation functions need to be chosen carefully as their shapes will depend on the study system’s biology. Importantly, we provide a mechanistic understanding of relationships between model parameters, which has implications for theory and for formulating biologically sound and empirically testable predictions.

Pollen limitation and its effect on seed germination

In nature, fruit and seed production in many plants have been shown to be pollen limited. Pollen limitation is demonstrated when open-pollinated plants that are hand-supplemented (Ps) with outcross pollen produce more fruits and/or seeds than open-pollinated controls that are not hand-pollinated (Po). There are three categories of results in such studies: Ps> Po, Ps= Poand Ps< Po, in which case pollen limitation indices are positive, zero and negative, respectively. In an index widely used to calculate pollen limitation, 1 – (Po/Ps), the bounds for Ps≥ Poare 0 to + 1, whereas the bounds for Ps< Poare 0 to –∞. The first aim of this review was to show how the pollen limitation index can be modified so that the bounds of Ps< Poare 0 and –1, whereupon the index gives equal weight to the best performer (Psor Po) and worst performer (Psor Po). In addition to seed quantity, pollen supplementation can affect seed quality, including germinability. Thus, our second aim was to summarize the results of studies that have also tested the effect of pollen limitation on seed germination. In short, the 30 case studies in 15 families, 16 genera and 18 species that we identified show that seed germination percentage increased, was not affected or decreased by pollen supplementation in 12, 11 and seven cases, respectively. The effect of pollen limitation on seed germination, which can be quite large, has not been considered in developing population growth models to determine the effect of pollen limitation on λ.