Biology subjects

Gerlee, P.

Publications and source records attributed to Gerlee, P..

6 recordsLinked to original sources

bioRxiv2018

Extinction times in diffusive public good population dynamics

The co-evolutionary dynamics of competing populations can be strongly affected by frequency-dependent selection and population structure in space. As co-evolving populations grow into a spatial domain, their initial spatial arrangement, as well as their growth rate differences determine the dynamics. Here, we are interested in the dynamics of producers and free-rider co-evolution in the context of an ecological public good that is produced by a sub-population but evokes growth benefits to all individuals. We consider the spatial growth dynamics in one, two and three dimensions by modeling producer cell, free-rider cell and public good densities in space, driven by birth, death and diffusion. Typically, one population goes extinct. We find that uncorrelated initial spatial structures do not influence the time to extinction in comparison to the well-mixed system. We derive a slow manifold solution in order to estimate the time to extinction of either free-riders or producers. For invading populations, i.e. for populations that are initially highly segregated, we observe a traveling wave, whose speed can be calculated to improve the extinction time estimate by a simple superposition of the two times. Our results show that local effects of spatial dynamics evolve independently of the dynamics of the mean populations. Our considerations provide quantitative predictions for the transient dynamics of cooperative traits under pressure of extinction, and a potential experiment to derive elusive details of the fitness function of an ecological public goods game through extinction time observations.\n\nAuthor SummaryEcological public goods (PG) relationships emerge in growing cellular populations, for example between bacteria and cancer cells. We study the eco-evolutionary dynamics of a PG in populations that grow in space. In our model, public good-producer cells and free-rider cells can grow according to their own birth and death rates. Co-evolution occurs due to public good-driven surplus in the intrinsic growth rates and a cost to producers. A net growth rate benefit to free-riders leads to the well-known tragedy of the commons in which producers go extinct. What is often omitted from discussions is the time scale on which this extinction can occur, especially in spatial populations. We derive analytical estimates of the time to extinction in different spatial settings, and identify spatial scenarios in which extinction takes long enough such that the tragedy of the commons never occurs within the lifetime of the populations. Using numerical simulations we analyze the deviations from analytical predictions. Our results have direct implications for inferring ecological public good game properties from in vitro and in vivo experimental observations.

ecology↗

bioRxiv2018

Inferring rates of metastatic dissemination using stochastic network models

The formation of metastases is driven by the ability of cancer cells to disseminate from the site of the primary tumour to target organs. The process of dissemination is constrained by anatomical features such as the flow of blood and lymph in the circulatory system. We exploit this fact in a stochastic network model of metastasis formation, in which only anatomically feasible routes of dissemination are considered. By fitting this model to two different clinical datasets (tongue & ovarian cancer) we show that incidence data can be modelled using a small number of biologically meaningful parameters. The fitted models reveal site specific relative rates of dissemination and also allow for patient-specific predictions of metastatic involvement based on primary tumour location and stage. Applied to other data sets this type of model could yield insight about seed-soil effects, and could also be used in a clinical setting to provide personalised predictions about the extent of metastatic spread. AUTHOR SUMMARYFor most cancer patients the occurrence of metastases equals incurable disease. Despite this fact our quantitative knowledge about the process of metastatic dissemination is limited. In this manuscript we improve on a previously published mathematical model by incorporating known biological facts about metastatic spread and also consider the temporal dimension of dissemination. The model is fit to two different cancer types with very different patterns of spread, which highlights the versatility of our framework. Properly parametrised this type of model can be used for making personalised predictions about metastatic burden.

cancer biology↗

bioRxiv2018

Finite size effects in diffusive public goods games

A particular challenge in the co-evolutionary dynamics of growing populations is to determine the effects of population assortment on growth advantage of cooperative traits. Here we study the coevolution of cooperators that are public good producers and consumers, and free riders that are only public good consumers. Using an individual-based model and its continuum limit we show that the differential growth rate between producers and free-riders depends on the spatial Fourier decomposition of their respective densities. Further, we derive a finite-size correction, which scales as the cell size, which accurately describes the dynamics of a randomly assorted population. Using this result we are also able to derive an effective benefit to cost relation, which provides a criterion that relates the parameters of the model (e.g. diffusion constant of the public good, decay rate and cost) to the long-term persistence of cooperation. Our findings provide a powerful tool for the analysis of diffusive public goods games, and can explain commonly observed patterns of cooperation, rather than the tragedy of the commons, based on the derived finite-size correction.

ecology↗

bioRxiv2018

Neighborhood size-effects in nonlinear public goods games

Ecological and evolutionary dynamics can be strongly affected by population assortment and frequency-dependent selection. In growing populations, a particular challenge is to disentangle global ecological effects from local frequency-dependent effects. Here we implement a logistic growth and death model on the global scale, coupled to frequency-dependent growth rates influenced by a public goods game between cooperators and defectors. For each individual, the public good is only effective within a neighborhood of other individuals, and the public good-growth rate relationship can be nonlinear. At low numbers of cooperators, increases of public good accumulate synergistically; at high numbers, increases in public good only provide diminishing returns-the inflection point of this pattern is given by the strength of frequency-dependent selection in relation to the background fitness effect. We observed complex critical behavior in the evolutionary dynamics equilibria, determined by the relative magnitude of frequency-dependent to constant (background) growth benefits. We predict neighborhood-size-driven state changes, hysteresis between polymorphic and monomorphic equilibria, and observed that type-dependent differences in neighborhood sizes can destabilize monomorphic cooperative states but increase coexistence of cooperators and defectors. Stochastic neighborhood size fluctuations also led to coexistence and could stabilize the purely cooperative equilibrium. Our results quantify the role of assortment through neighborhood-size effects and nonlinearity of the gains function in eco-evolutionary dynamics, which is relevant for a variety of microbial and cellular public goods games.

ecology↗

bioRxiv2018

Using neural networks to bridge scales in cancer: Mapping signaling pathways to phenotypes

Cancer is an evolving system subject to mutation and selection. Selection is driven by the microenvironment that the cancer cells are growing in and acts on the cell phenotype, which is in turn modulated by intracellular signaling pathways regulated by the cell genotype. Integrating all of these processes requires bridging different biological scales. We present a mathematical model that uses a neural network as a means to connecting these scales. In particular, we consider the mapping from intracellular pathway activity to phenotype under different microenvironmental conditions.

cancer biology↗

bioRxiv2017

Extinction Times In Tumor Public Goods Games

Cancer evolution and progression are shaped by cellular interactions and Darwinian selection. Evolutionary game theory incorporates both of these principles, and has been proposed as a framework to understand tumor cell population dynamics. A cornerstone of evolutionary dynamics is the replicator equation, which describes changes in the relative abundance of different cell types, and is able to predict evolutionary equilibria. Typically, the replicator equation focuses on differences in relative fitness. We here show that this framework might not be sufficient under all circumstances, as it neglects important aspects of population growth. Standard replicator dynamics might miss critical differences in the time it takes to reach an equilibrium, as this time also depends on cellular turnover in growing but bounded populations. As the system reaches a stable manifold, the time to reach equilibrium depends on cellular death and birth rates. These rates shape the timescales, in particular in co-evolutionary dynamics of growth factor producers and free-riders. Replicator dynamics might be an appropriate framework only when birth and death rates are of similar magnitude. Otherwise, population growth effects cannot be neglected when predicting the time to reach an equilibrium, and cell type specific rates have to be accounted for explicitly.

cancer biology↗