TY - JOUR AB - We investigate the evolutionary dynamics of an age-structured population subject to weak frequency-dependent selection. It turns out that the weak selection is affected in a non-trivial way by the life-history trait. We disentangle the dynamics, based on the appearance of different time scales. These time scales, which seem to form a universal structure in the interplay of weak selection and life-history traits, allow us to reduce the infinite dimensional model to a one-dimensional modified replicator equation. The modified replicator equation is then used to investigate cooperation (the prisoner's dilemma) by means of adaptive dynamics. We identify conditions under which age structure is able to promote cooperation. At the end we discuss the relevance of our findings. AU - John, S. AU - Müller, J. C1 - 68263 C2 - 54794 CY - Ste 800, 230 Park Ave, New York, Ny 10169 Usa TI - Age structure, replicator equation, and the prisoner's dilemma. JO - Math. Biosci. VL - 365 PB - Elsevier Science Inc PY - 2023 SN - 0025-5564 ER - TY - JOUR AB - The authors regret that the original publication was inaccurately categorized as a "Review". This corrigendum seeks to clarify that the article is an "Original Research" article. The authors would like to apologise for any inconvenience caused. AU - Okolie, A.* AU - Müller, J. C1 - 67933 C2 - 54411 CY - Ste 800, 230 Park Ave, New York, Ny 10169 Usa TI - Corrigendum to "Exact and approximate formulas for contact tracing on random trees" [Mathematical Biosciences 321 (2020) 108320]. JO - Math. Biosci. VL - 364 PB - Elsevier Science Inc PY - 2023 SN - 0025-5564 ER - TY - JOUR AB - Due to the relevance for conservation biology, there is an increasing interest to extend evolutionary genomics models to plant, animal or microbial species. However, this requires to understand the effect of life-history traits absent in humans on genomic evolution. In this context, it is fundamentally of interest to generalize the replicator equation, which is at the heart of most population genomics models. However, as the inclusion of life-history traits generates models with a large state space, the analysis becomes involving. We focus, here, on quiescence and seed banks, two features common to many plant, invertebrate and microbial species. We develop a method to obtain a low-dimensional replicator equation in the context of evolutionary game theory, based on two assumptions: (1) the life-history traits are per se neutral, and (2) frequency-dependent selection is weak. We use the results to investigate the evolution and maintenance of cooperation based on the Prisoner's dilemma and the snowdrift game. We first consider the generalized replicator equation, and then refine the investigation using adaptive dynamics. It turns out that, depending on the structure and timing of the quiescence/dormancy life-history trait, cooperation in a homogeneous population can be stabilized. We finally discuss and highlight the relevance of these results for plant, invertebrate and microbial communities. AU - Müller, J. AU - Tellier, A.* C1 - 65033 C2 - 52650 TI - Life-History traits and the replicator equation. JO - Math. Biosci. VL - 349 PY - 2022 SN - 0025-5564 ER - TY - JOUR AB - We consider a stochastic susceptible-infected-recovered (SIR) model with contact tracing on random trees and on the configuration model. On a rooted tree, where initially all individuals are susceptible apart from the root which is infected, we are able to find exact formulas for the distribution of the infectious period. Thereto, we show how to extend the existing theory for contact tracing in homogeneously mixing populations to trees. Based on these formulas, we discuss the influence of randomness in the tree and the basic reproduction number. We find the well known results for the homogeneously mixing case as a limit of the present model (tree-shaped contact graph). Furthermore, we develop approximate mean field equations for the dynamics on trees, and - using the message passing method - also for the configuration model. The interpretation and implications of the results are discussed. AU - Okolie, A.* AU - Müller, J. C1 - 58467 C2 - 48178 CY - Ste 800, 230 Park Ave, New York, Ny 10169 Usa TI - Exact and approximate formulas for contact tracing on random trees. JO - Math. Biosci. VL - 321 PB - Elsevier Science Inc PY - 2020 SN - 0025-5564 ER - TY - JOUR AB - Despite the wealth of empirical and theoretical studies, the origin and maintenance of cooperation is still an evolutionary riddle. In this context, ecological life-history traits which affect the efficiency of selection may play a role despite being often ignored. We consider here species such as bacteria, fungi, invertebrates and plants which exhibit resting stages in the form of a quiescent state or a seed bank. When quiescent, individuals are inactive and reproduce upon activation, while under seed bank parents produce offspring remaining dormant for different amount of time. We assume weak frequency-dependent selection modeled using game-theory and the prisoner's dilemma (cooperation/defect) as payoff matrix. The cooperators and defectors are allowed to evolve different quiescence or dormancy times. By means of singular perturbation theory we reduce the model to a one-dimensional equation resembling the well known replicator equation, in which the gain functions are scaled with lumped parameters reflecting the time scale of the resting state of the cooperators and defectors. If both time scales are identical cooperation cannot persist in a homogeneous population. If, however, the time scale of the cooperator is distinctively different from that of the defector, cooperation may become a locally asymptotically stable strategy. Interestingly enough, in the seed bank case the cooperator needs to become active faster than the defector, while in the quiescent case the cooperator has to be slower. We use adaptive dynamics to identify situations where cooperation may evolve and form a convergent stable ESS. We conclude by highlighting the relevance of these results for many non-model species and the maintenance of cooperation in microbial, invertebrate or plant populations. AU - Sellinger, T.* AU - Müller, J. AU - Hösel, V.* AU - Tellier, A.* C1 - 57260 C2 - 47656 CY - Ste 800, 230 Park Ave, New York, Ny 10169 Usa TI - Are the better cooperators dormant or quiescent? JO - Math. Biosci. VL - 318 PB - Elsevier Science Inc PY - 2019 SN - 0025-5564 ER - TY - JOUR AB - We consider a model for an infectious disease in the onset of an outbreak. We introduce contact tracing incorporating a tracing delay. The effect of randomness in the delay and the effect of the length of this delay in comparison to the infectious period of the disease respectively to a latency period on the effect of tracing, given e.g. by the change of the reproduction number, is analyzed. We focus particularly on the effect of randomness in the tracing delay. AU - Müller, J. AU - Koopmann, B.* C1 - 49844 C2 - 40975 CY - New York SP - 204-214 TI - The effect of delay on contact tracing. JO - Math. Biosci. VL - 282 PB - Elsevier Science Inc PY - 2016 SN - 0025-5564 ER - TY - JOUR AB - We consider the uptake of various carbon sources by microorganisms based on four fundamental assumptions: (1) the uptake of nutrient follows a saturation characteristics (2) substrate processing has a benefit but comes at costs of maintaining the process chain (3) substrate uptake is controlled and (4) evolution optimized the control of substrate uptake. These assumptions result in relatively simple mathematical models. In case of two substrates, our main finding is the following: Depending on the overall topology of the metabolic pathway, three different behavioural patterns can be identified. (1) both substrates are consumed at a time, (2) one substrate is preferred and represses the uptake of the other (catabolite repression), or (3) a cell feeds exclusively on one or the other substrate, possibly leading to a population that splits in two sub-populations, each of them specialized on one substrate only. Batch-culture and retentostat data of toluene, benzoate, and acetate uptake by Geobacter metallireducens are used to demonstrate that the model structure is suited for a quantitative description of uptake dynamics. AU - Müller, J. AU - Hense, B.A. AU - Marozava, S. AU - Kuttler, C. AU - Meckenstock, R.U. C1 - 31713 C2 - 34694 CY - New York SP - 52-70 TI - Model selection for microbial nutrient uptake using a cost-benefit approach. JO - Math. Biosci. VL - 255 IS - 1 PB - Elsevier Science Inc PY - 2014 SN - 0025-5564 ER - TY - JOUR AB - In this work we present results of a detailed Bayesian parameter estimation for an analysis of ordinary differential equation models. These depend on many unknown parameters that have to be inferred from experimental data. The statistical inference in a high-dimensional parameter space is however conceptually and computationally challenging. To ensure rigorous assessment of model and prediction uncertainties we take advantage of both a profile posterior approach and Markov chain Monte Carlo sampling. We analyzed a dynamical model of the JAK2/STAT5 signal transduction pathway that contains more than one hundred parameters. Using the profile posterior we found that the corresponding posterior distribution is bimodal. To guarantee efficient mixing in the presence of multimodal posterior distributions we applied a multi-chain sampling approach. The Bayesian parameter estimation enables the assessment of prediction uncertainties and the design of additional experiments that enhance the explanatory power of the model. This study represents a proof of principle that detailed statistical analysis for quantitative dynamical modeling used in systems biology is feasible also in high-dimensional parameter spaces. AU - Hug, S. AU - Raue, A. AU - Hasenauer, J. AU - Bachmann, J.* AU - Klingmüller, U.* AU - Timmer, J.* AU - Theis, F.J. C1 - 26164 C2 - 32101 SP - 293-304 TI - High-dimensional Bayesian parameter estimation: Case study for a model of JAK2/STAT5 signaling. JO - Math. Biosci. VL - 246 IS - 2 PB - Elsevier Science PY - 2013 SN - 0025-5564 ER - TY - JOUR AB - Pseudomonas syringae is a gram-negative bacterium which lives on leaf surfaces. Its growth has been described using epifluorescence microscopy and image analysis; it was found to be growing in aggregates of a wide range of sizes. We develop a stochastic model to describe aggregate distribution and determine the mechanisms generating experimental observations. We found that a logistic birth-death model with migration (time-homogeneous Markov process) provides the best description of the observed data. We discuss how to analyze the joint distribution of the numbers of aggregates of different sizes at a given time and explore how to account for new aggregates being created, that is, the joint distribution of the family size statistics conditional on the total number of aggregates. We compute the first two moments. Through simulations we examine how the model's parameters affect the aggregate size distribution and successfully explain the quantitative experimental data available. Aggregation formation is thought to be the first step towards pathogenic behavior of this bacterium; understanding aggregate size distribution would prove useful to understand the switch from epiphytic to pathogenic behavior. AU - Pérez-Velázquez, J. AU - Schlicht, R.* AU - Dulla, G.* AU - Hense, B.A. AU - Kuttler, C.* AU - Lindow, S.E.* C1 - 8425 C2 - 28108 SP - 106-116 TI - Stochastic modeling of Pseudomonas syringae growth in the phyllosphere. JO - Math. Biosci. VL - 239 IS - 1 PB - Elsevier PY - 2012 SN - 0025-5564 ER - TY - JOUR AB - This paper focus on the quest for mechanisms that are able to create tolerance and an activation threshold in the extrinsic coagulation cascade. We propose that the interplay of coagulation inhibitor and blood flow creates threshold behavior. First we test this hypothesis in a minimal, four dimensional model. This model can be analysed by means of time scale analysis. We find indeed that only the interplay of blood flow and inhibition together are able to produce threshold behavior. The mechanism relays on a combination of raw substance supply and wash-out effect by the blood flow and a stabilization of the resting state by the inhibition. We use the insight into this minimal model to interpret the simulation results of a large model. Here, we find that the initiating steps (TF that produces together with fVII(a) factor Xa) does not exhibit threshold behavior, but the overall system does. Hence, the threshold behavior appears via the feedback loop (in that fIIa produces indirectly fXa that in turn produces fIIa again) inhibited by ATIII and blood flow. AU - Müller, J. AU - Brandt, S. AU - Mayerhofer, K.* AU - Tjardes, T.* AU - Maegele, M.* C1 - 2420 C2 - 25441 SP - 226-254 TI - Tolerance and threshold in the extrinsic coagulation system. JO - Math. Biosci. VL - 211 IS - 2 PB - American Elsevier PY - 2008 SN - 0025-5564 ER - TY - JOUR AB - We develop a simple model for the random distribution of a gene product. it is assumed that the only source of variance is due to switching transcription on and off by a random process. Under the condition that the transition rates between on and off are constant we find that the amount of mRNA follows a scaled Beta distribution. Additionally, a simple positive feedback loop is considered. The simplicity of the model allows for an explicit solution also in this setting. These findings in turn allow, e.g., for easy parameter scans. We find that bistable behavior translates into bimodal distributions. These theoretical findings are in line with experimental results. AU - Müller, J.* AU - Kuttler, C. AU - Hense, B.A. AU - Zeiser, S. AU - Liebscher, V.* C1 - 2571 C2 - 25829 SP - 30-39 TI - Transcription, intercellular variability and correlated random walk. JO - Math. Biosci. VL - 216 IS - 1 PB - American Elsevier PY - 2008 SN - 0025-5564 ER - TY - JOUR AU - Blomer, R.J. C1 - 41911 C2 - 35368 SP - 163-173 TI - Decomposition of compartment transition functions by means of the Pade approximation. JO - Math. Biosci. VL - 19 IS - 1-2 PY - 1974 SN - 0025-5564 ER -