Eddy Kwessi

Competition models with Allee effects

In this paper, we study a generalized two-species contest-competition model with an Allee effect. We provide a complete analysis of the global dynamics of the system. In particular, we determine all the invariant manifolds, the extinction, the exclusion and the coexistence regions. We use tools from topology and dynamical systems to show that all orbits must converge to one of the equilibrium points of the system. The analysis shows that there are several potential scenarios including competition coexistence, exclusion and extinction.

Allee effects and resilience in stochastic populations

Allee effects, or positive functional relationships between a population’s density (or size) and its per unit abundance growth rate, are now considered to be a widespread if not common influence on the growth of ecological populations. Here we analyze how stochasticity and Allee effects combine to impact population persistence. We compare the deterministic and stochastic properties of four models: a logistic model (without Allee effects), and three versions of the original model of Allee effects proposed by Vito Volterra representing a weak Allee effect, a strong Allee effect, and a strong Allee effect with immigration. We employ the diffusion process approach for modeling single-species populations, and we focus on the properties of stationary distributions and of the mean first passage times. We show that stochasticity amplifies the risks arising from Allee effects, mainly by prolonging the amount of time a population spends at low abundance levels. Even weak Allee effects become consequential when the ubiquitous stochastic forces affecting natural populations are accounted for in population models. Although current concepts of ecological resilience are bound up in the properties of deterministic basins of attraction, a complete understanding of alternative stable states in ecological systems must include stochasticity.

A discrete-time host–parasitoid model with an Allee effect

We introduce a discrete-time host–parasitoid model with a strong Allee effect on the host. We adapt the Nicholson–Bailey model to have a positive density dependent factor due to the presence of an Allee effect, and a negative density dependence factor due to intraspecific competition. It is shown that there are two scenarios, the first with no interior fixed points and the second with one interior fixed point. In the first scenario, we show that either both host and parasitoid will go to extinction or there are two regions, an extinction region where both species go to extinction and an exclusion region in which the host survives and tends to its carrying capacity. In the second scenario, we show that either both host and parasitoid will go to extinction or there are two regions, an extinction region where both species go to extinction and a coexistence region where both species survive.

Hierarchical competition models with Allee effects

We consider a two-species hierarchical competition model with a strong Allee effect. The Allee effect is assumed to be caused by predator saturation. Moreover, we assume that there is a ‘silverback’ species x that gets first choice of the resources and where growth is limited by its own intraspecific competition, while the second ‘inferior’ species y gets whatever is left. Both species x and y are assumed to have the property of strong Allee effect. In this paper we determine the impact of the presence of the Allee effect on the global dynamics of both species.

A Note on Multiplication and Composition Operators in Lorentz Spaces

we revisit the Lorentz spaces 𝐿(𝑝,𝑞) for 𝑝>1,𝑞>0 defined by G. G. Lorentz in the nineteen fifties and we show how the atomic decomposition of the spaces 𝐿(𝑝,1) obtained by De Souza in 2010 can be used to characterize the multiplication and composition operators on these spaces. These characterizations, though obtained from a completely different perspective, confirm the various results obtained by S. C. Arora, G. Datt and S. Verma in different variants of the Lorentz Spaces.

Hierarchical competition models with the Allee effect II: the case of immigration

ABSTRACT This is part II of an earlier paper that dealt with hierarchical models with the Allee effect but with no immigration. In this paper, we greatly simplify the proofs in part I and provide a proof of the global dynamics of the non-hyperbolic cases that were previously conjectured. Then, we show how immigration to one of the species or to both would, drastically, change the dynamics of the system. It is shown that if the level of immigration to one or to both species is above a specified level, then there will be no extinction region where both species go to extinction.

Characterization of lacunary functions in weighted Bergman–Besov–Lipschitz spaces

We consider the weighted Bergman–Besov–Lipschitz space B ρ of analytic functions F in the unit disc 𝔻 = {z ∈ ℂ, |z| ≤ 1} for which and we show that a lacunary function belongs to B ρ if and only if the sequence a n satisfies , where I n are diadic intervals defined by I n  = {k ∈ ℕ : 2 n−1 ≤ k < 2 n }, ρ belongs to a certain class of weights and K(n, ρ) > 0 is a function of n and ρ.

A stochastic modified Beverton–Holt model with the Allee effect

In this paper, we consider a discrete stochastic Beverton–Holt model with the Allee effect. We study the effects of demographic and environmental fluctuations on the dynamics of the model. Moreover, we investigate the potential function, the attainment time and quasi-stationary distributions of the system.

Increased Risk of Autism Development in Children Whose Mothers Experienced Birth Complications or Received Labor and Delivery Drugs.

Autism spectrum disorder (ASD) is a perplexing and pervasive developmental disorder characterized by social difficulties, communicative deficits, and repetitive behavior. The increased rate of ASD diagnosis has raised questions concerning the genetic and environmental factors contributing to the development of this disorder; meanwhile, the cause of ASD remains unknown. This study surveyed mothers of ASD and non-ASD children to determine possible effects of labor and delivery (L&D) drugs on the development of ASD. The survey was administered to mothers; however, the results were analyzed by child, as the study focused on the development of autism. Furthermore, an independent ASD dataset from the Southwest Autism Research and Resource Center was analyzed and compared. Indeed, L&D drugs are associated with ASD (p = .039). Moreover, the Southwest Autism Research and Resource Center dataset shows that the labor induction drug, Pitocin, is significantly associated with ASD (p = .004). We also observed a synergistic effect between administrations of L&D drugs and experiencing a birth complication, in which both obstetrics factors occurring together increased the likelihood of the fetus developing ASD later in life (p = .0003). The present study shows the possible effects of L&D drugs, such as Pitocin labor-inducing and analgesic drugs, on children and ASD.

Generalised signed-rank estimation for nonlinear models with multidimensional indices

We consider a nonlinear regression model when the index variable is multidimensional. Such models are useful in signal processing, texture modelling, and spatio-temporal data analysis. A generalised form of the signed-rank estimator of the nonlinear regression coefficients is proposed. This general form of the signed-rank (SR) estimator includes estimators and hybrid variants. Sufficient conditions for strong consistency and asymptotic normality of the estimator are given. It is shown that the rate of convergence to normality can be different from . The sufficient conditions are weak in the sense that they are satisfied by harmonic-type functions for which results in the current literature may not apply. A simulation study shows that certain generalised SR estimators (e.g. signed rank) perform better in recovering signals than others (e.g. least squares) when the error distribution is contaminated or is heavy-tailed.