On the variations of the principal eigenvalue with respect to a parameter in growth-fragmentation models

Campillo, Fabien; Champagnat, Nicolas; Fritsch, Coralie

doi:10.4310/cms.2017.v15.n7.a1

Cited by 12 publications

(17 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that in the present study, we inflate the growth speed by a factor that depends on each individual. To finish I mention a recent study by Campillo, Champagnat and Fritsch [6]: for growthfragmentation-death models, they focus on the variations of the first eigenvalue with respect to a parameter involved in both the growth speed and the birth and death rates, with a nice mixing of deterministic and stochastic techniques. Table 1.…”

Section: 22mentioning

confidence: 99%

“…Proposition 9 (Second derivative at point 0). Consider Model (A+V) with Specifications (5), (6) and ρ(v, dv ) = ρ α (v )dv defined by (12),…”

Section: Proof Introduce the Operatormentioning

confidence: 99%

“…Thus we want to investigate the behaviour of the Malthus parameter λ B,ρα -which is a perturbation of λ B,v -for small value of α.Theorem 5. Consider Model (A+V) with Specifications (5),(6) and ρ(v, dv ) = ρ α (v )dv with ρ α defined in(12). Then α ; λ B,ρα is twice differentiable and the Malthus parameter λ B,ρα defined by (11) satisfies…”

mentioning

confidence: 99%

See 2 more Smart Citations

How does variability in cell aging and growth rates influence the Malthus parameter?

Olivier¹

2017

Kinetic &Amp; Related Models

View full text Add to dashboard Cite

The aim of this study is to compare the growth speed of different cell populations measured by their Malthus parameter. We focus on both the age-structured and size-structured equations. A first population (of reference) is composed of cells all aging or growing at the same ratev. A second population (with variability) is composed of cells each aging or growing at a rate v drawn according to a non-degenerated distribution ρ with meanv. In a first part, analytical answers -based on the study of an eigenproblem -are provided for the age-structured model. In a second part, numerical answers -based on stochastic simulations -are derived for the size-structured model. It appears numerically that the population with variability proliferates more slowly than the population of reference (for experimentally plausible division rates). The decrease in the Malthus parameter we measure, around 2% for distributions ρ with realistic coefficients of variations around 15-20%, is determinant since it controls the exponential growth of the whole population.

show abstract

Section: 22mentioning

confidence: 99%

“…Proposition 9 (Second derivative at point 0). Consider Model (A+V) with Specifications (5), (6) and ρ(v, dv ) = ρ α (v )dv defined by (12),…”

Section: Proof Introduce the Operatormentioning

confidence: 99%

See 1 more Smart Citation

How does variability in cell aging and growth rates influence the Malthus parameter?

Olivier¹

2017

Kinetic &Amp; Related Models

View full text Add to dashboard Cite

show abstract

“…There has been a continued interest in this eigenvalue for linear models of cell division since and we refer to [6] in particular for a detailed study of the monotonicity of the Perron eigenvalue with respect to parameters of a structured model for cell division. In a stochastic framework for growth and fragmentation, [4] establishes a similar monotonicity property. In this context, the Perron eigenvalue is seen as the cell growth rate, and this is why its dependence in the model parameters is important.…”

Section: (Sstp)mentioning

confidence: 87%

Sharp seasonal threshold property for cooperative population dynamics with concave nonlinearities

Ji¹,

Strugarek²

2018

Bulletin des Sciences Mathématiques

View full text Add to dashboard Cite

We consider a biological population whose environment varies periodically in time, exhibiting two very different "seasons": one is favorable and the other one is unfavorable. For monotone differential models with concave nonlinearities, we address the following question: the system's period being fixed, under what conditions does there exist a critical duration for the unfavorable season? By "critical duration" we mean that above some threshold, the population cannot sustain and extincts, while below this threshold, the system converges to a unique periodic and positive solution. We term this a "sharp seasonal threshold property" (SSTP, for short).Building upon a previous result, we obtain sufficient conditions for SSTP in any dimension and apply our criterion to a two-dimensional model featuring juvenile and adult populations of insects.

show abstract

“…This trait will then characterize the "best" population growth. Following the argument of substrate concentration at the stationary state and using a mathematical result previously proved in Campillo et al (2016b), we have proposed a more efficient simulation method to determine the invasion possibilities. In fact, we have drawn the PIP by computing, for each resident and mutant trait, first, the stationary state of the resident population and second, the growth rate of the mutant population in this stationary state.…”

Section: Discussionmentioning

confidence: 99%

A numerical approach to determine mutant invasion fitness and evolutionary singular strategies

Fritsch

Campillo

Ovaskainen

2017

Theoretical Population Biology

Self Cite

View full text Add to dashboard Cite

We propose a numerical approach to study the invasion fitness of a mutant and to determine evolutionary singular strategies in evolutionary structured models in which the competitive exclusion principle holds. Our approach is based on a dual representation, which consists of the modeling of the small size mutant population by a stochastic model and the computation of its corresponding deterministic model. The use of the deterministic model greatly facilitates the numerical determination of the feasibility of invasion as well as the convergence-stability of the evolutionary singular strategy. Our approach combines standard adaptive dynamics with the link between the mutant survival criterion in the stochastic model and the sign of the eigenvalue in the corresponding deterministic model. We present our method in the context of a mass-structured individual-based chemostat model. We exploit a previously derived mathematical relationship between stochastic and deterministic representations of the mutant population in the chemostat model to derive a general numerical method for analyzing the invasion fitness in the stochastic models. Our method can be applied to the broad class of evolutionary models for which a link between the stochastic and deterministic invasion fitnesses can be established.

show abstract

On the variations of the principal eigenvalue with respect to a parameter in growth-fragmentation models

Cited by 12 publications

References 20 publications

How does variability in cell aging and growth rates influence the Malthus parameter?

How does variability in cell aging and growth rates influence the Malthus parameter?

Sharp seasonal threshold property for cooperative population dynamics with concave nonlinearities

A numerical approach to determine mutant invasion fitness and evolutionary singular strategies

Contact Info

Product

Resources

About