Papers by Sergei Pilyugin
Ecosphere, Aug 1, 2016
The protection of predators inside marine reserves is expected to generate trophic cascades with ... more The protection of predators inside marine reserves is expected to generate trophic cascades with predator density increasing but prey density decreasing; however, predators and prey often both increase inside reserves. This mismatch between the expected and observed change in prey density has been explained because prey also are harvested; that is, the protection of prey compensates for the additional predation inside the reserve. Here, we show that this mechanism alone cannot increase densities of predator and prey; other mechanisms are required, and we hypothesized that movement of predator and/or prey might provide such a mechanism. We therefore built two spatially implicit two-patch predator-prey models with movement of predator and prey between reserve and fishing grounds. We show that post-settlement movement of predators (but not prey) altered the strength of trophic cascades and could increase densities of both predator and focal prey. We further built a more general model that shows that predator post-settlement movement can reinforce and even supplement the effect of two previously investigated mechanisms producing trophic cascades: a prey size refuge and predator density-dependent mortality. Our study increases understanding of mechanisms that can alter the strength (and direction) of prey responses inside marine reserves and highlights the importance of movement in human-induced heterogeneous systems.
An animal's movement rate (mobility) and its ability to perceive fitness gradients (fitness s... more An animal's movement rate (mobility) and its ability to perceive fitness gradients (fitness sensitivity) determine how well it can exploit resources. Previous models have examined mobility and fitness sensitivity separately and found that mobility, modelled as random movement, prevents animals from staying in high-quality patches, leading to a departure from an ideal free distribution (IFD). However, empirical work shows that animals with higher mobility can more effectively collect environmental information and better sense patch quality, especially when the environment is frequently changed by human activities. Here, we model, for the first time, this positive correlation between mobility and fitness sensitivity and measure its consequences for the populations of a consumer and its resource. In the absence of consumer demography, mobility alone had no effect on system equilibria, but a positive correlation between mobility and fitness sensitivity could produce an IFD. In the p...
An animal's movement rate (mobility) and its ability to perceive fitness gradients (fitness s... more An animal's movement rate (mobility) and its ability to perceive fitness gradients (fitness sensitivity) determine how well it can exploit resources. Previous models have examined mobility and fitness sensitivity separately and found that mobility, modelled as random movement, prevents animals from staying in high-quality patches, leading to a departure from an ideal free distribution (IFD). However, empirical work shows that animals with higher mobility can more effectively collect environmental information and better sense patch quality, especially when the environment is frequently changed by human activities. Here, we model, for the first time, this positive correlation between mobility and fitness sensitivity and measure its consequences for the populations of a consumer and its resource. In the absence of consumer demography, mobility alone had no effect on system equilibria, but a positive correlation between mobility and fitness sensitivity could produce an IFD. In the presence of consumer demography, lower levels of mobility prevented the system from approaching an IFD due to the mixing of consumers between patches. However, when positively correlated with fitness sensitivity, high mobility led to an IFD. Our study demonstrates that the expected covariation of animal movement attributes can drive broadly theorized consumer–resource patterns across space and time and could underlie the role of consumers in driving spatial heterogeneity in resource abundance.
arXiv (Cornell University), Apr 15, 2022
First Passage (FP) processes are utilized widely to model phenomena in many areas of mathematical... more First Passage (FP) processes are utilized widely to model phenomena in many areas of mathematical applications, from biology to computer science. Introducing a mechanism to restart the parent process can alter the first passage characteristics, and the properties of the resulting First Passage Under Restart (FPUR) process have been subject to much recent investigation. Here we seek to more fully characterize whether a discrete FP process can have its mean hitting time reduced through the implementation of restart by analyzing a construct we call the restart sequence, which is determined solely by the distribution of the FP process. I. THE INITIAL FRAMEWORK
Mathematic proof for the stability of equations without consumer demography and the uniqueness of... more Mathematic proof for the stability of equations without consumer demography and the uniqueness of the solution; This is the numerical simulation to reveal the relationship among mobility, fitness sensitivity and the time to reach equlibrium without considering consumer's demography; Mathematic proof about the relationship between fitness sensitivity and system equlibrium without considering consumer demography; Mathematic proof about the correlation between fitness sensitivity and regional resource density without considering consumer demography
We consider a chemostat model of phytoplankton competing for nitrogen taking into account effects... more We consider a chemostat model of phytoplankton competing for nitrogen taking into account effects of both intraand interspecific crowding. Crowding can be modeled as an additive density-dependent mortality rate. Crowding effects may be classified into intraand interspecific crowding depending on whether the additional mortality is caused by the same or alternate species. We analyze the existence and local and global stability of single species and coexistence equilibria using the linearization and stability method of Lyapunov. A numerical example illustrating that the crowding effects may lead to the bistable coexistence of two phytoplankton species. We demonstrate that the crowding affects the outcome of exploitative competition for a single resource and promote coexistence. This work was published in [1]. To consider of the spatial homogeneity, lattice dynamical systems are proposed here.The lattice dynamical systems can be viewed as a model for patchy environment. In this study, ...
In recent years, it has been well-established that adding a restart mechanism can alter the first... more In recent years, it has been well-established that adding a restart mechanism can alter the first passage statistics of a stochastic processes in useful and interesting ways. Though different mechanisms have been investigated, we derive a probability generating function for a discrete-time First Passage process Under Restart and use it to examine two examples, including a biased random walk on the non-negative integers.
Theoretical Population Biology, 2016
Marine protected areas (MPAs) are regions in the ocean where fishing is restricted or prohibited.... more Marine protected areas (MPAs) are regions in the ocean where fishing is restricted or prohibited. Although several measures for MPA performance exist, here we focus on a specific one, namely the ratio of the steady state fish densities inside and outside the MPA. Several 2 patch models are proposed and analyzed mathematically. One patch represents the MPA, whereas the second patch represents the fishing ground. Fish move freely between both regions in a diffusive manner. Our main objective is to understand how fish mobility affects MPA performance. We show that MPA effectiveness decreases with fish mobility for single species models with logistic growth, and that densities inside and outside the MPA tend to equalize. This suggests that MPA performance is highest for the least mobile species. We then consider a 2 patch Lotka-Volterra predator-prey system. When one of the species moves, and the other does not, the ratio of the moving species first remains constant, and ultimately decreases with increased fish mobility, again with a tendency of equalization of the density in both regions. This suggests that MPA performance is not only highest for slow, but also for moderately mobile species. The discrepancy in MPA performance for single species models and for predator-prey models, confirms that MPA design requires an integrated, ecosystem-based approach. The mathematical approaches advocated here complement and enhance the numerical and theoretical approaches that are commonly applied to more complex models in the context of MPA design.
We investigate an epidemic model of two diseases. The primary disease is assumed to be a slowly p... more We investigate an epidemic model of two diseases. The primary disease is assumed to be a slowly progressing disease and the density of individuals infected with it is structured by age since infection. Hosts that are already infected with the primary disease can become coinfected with a secondary disease. We show that in addition to the disease-free equilibrium, there exists a unique dominance equilibrium corresponding to each disease. Without coinfection there are no coexistence equilibria, however, with coinfection the number of coexistence equilibria may vary. For some parameter values, there exist two coexistence equilibria. We also observe competitor mediated oscillatory coexistence. Furthermore, weakly subthreshold (which occur when exactly one of the reproduction numbers is below one) and strongly subthreshold (which occur when both reproduction numbers are below one) coexistence equilibria may exist. Some of those are a result of a two-parameter backward bifurcation. Bistabi...
International Journal of Biomathematics
We consider a deterministic model of Zika and Dengue viruses co-circulating in a human population... more We consider a deterministic model of Zika and Dengue viruses co-circulating in a human population. We study the system of differential equations modeling the dynamics of the diseases that can either be transmitted directly (host-to-host) or indirectly (host-vector-host). We use an SIR model for hosts and an SI model for vectors in the homogeneous populations. The stability of the model has been analyzed both qualitatively and quantitatively.
Ecology
Theoretical studies of marine protected areas (MPAs) suggest that more mobile species should exhi... more Theoretical studies of marine protected areas (MPAs) suggest that more mobile species should exhibit reduced local effects (defined as the ratio of the density inside vs. outside of the MPA). However, empirical studies have not supported the expected negative relationship between the local effect and mobility. We propose that differential, habitat-dependent movement (i.e., a higher movement rate in the fishing grounds than in the MPA) might explain the disparity between theoretical expectations and empirical results. We evaluate this hypothesis by building two-patch box and stepping-stone models and show that increasing disparity in the habitat-specific movement rates shifts the relationship between the local effect and mobility from negative (the previous theoretical results) to neutral or positive (the empirical pattern). This shift from negative to positive occurs when differential movement offsets recruitment and mortality differences between the two habitats. Thus, local effects of MPAs might be caused by behavioral responses via differential movement rather than by, or in addition to, reductions in mortality. In addition, the benefits of MPAs, in terms of regional abundance and fishing yields, can be altered by the magnitude of differential movement. Thus, our study points to a need for empirical investigations that disentangle the interactions among mobility, differential movement, and protection.
Proceedings of the International Joint Conference on Neural Networks, 2003., 2000
W e present a new method of analyzing the dynamics of a biological relevant system with different... more W e present a new method of analyzing the dynamics of a biological relevant system with different time scales based on the theory of p o w invariance. We are able to show the conditions under which the solutions of such a system aTe bounded being less restrictive than with the K-monotone theory, singular peTtUTbatiOn theory, or those based on supervised synaptic learning. W e prove the existence and the uniqueness of the equilibrium. A strict Lyapunov junction for the pow of a competitive neural system with diflerent time scales is given and based on it we are able to prove the global exponential stability of the equilibrium point.
2004 IEEE International Joint Conference on Neural Networks (IEEE Cat. No.04CH37541), 2004
ABSTRACT We present a new method of analyzing the dynamics of self-organizing neural networks wit... more ABSTRACT We present a new method of analyzing the dynamics of self-organizing neural networks with different time scales based on the theory of flow invariance. We are able to show the conditions under which the solutions of such a system are bounded being less restrictive than with the K-monotone theory, singular perturbation theory, or those based on supervised synaptic learning. We prove the existence and the uniqueness of the equilibrium. A strict Lyapunov function for the flow of a competitive neural system with different time scales is given, and based on it we are able to prove the global exponential stability of the equilibrium point.
Marine Mammal Science, 2015
SIAM Journal on Applied Mathematics, 1999
A model of the simple chemostat which allows for growth on the wall (or other marked surface) is ... more A model of the simple chemostat which allows for growth on the wall (or other marked surface) is presented as three nonlinear ordinary differential equations. The organisms which are attached to the wall do not wash out of the chemostat. This destroys the basic reduction of the chemostat equations to a monotone system, a technique which has been useful in the analysis of many chemostat-like equations. The adherence to and shearing from the wall eliminates the boundary equilibria. For a reasonably general model, the basic properties of invariance, dissipation, and uniform persistence are established. For two important special cases, global asymptotic results are obtained. Finally, a perturbation technique allows the special results to be extended to provide the rest point as a global attractor for nearby growth functions.
The CFSE dye dilution assay is widely used to determine the number of divisions a given CFSE labe... more The CFSE dye dilution assay is widely used to determine the number of divisions a given CFSE labelled cell has undergone in vitro and in vivo. In this paper, we consider how the data obtained with the use of CFSE (CFSE data) can be used to estimate the parameters determining cell division and death. For a homogeneous cell population (i.e., a population with the parameters for cell division and death being independent of time and the number of divisions cells have undergone), we consider a specific biologically based bSmith-MartinQ model of cell turnover and analyze three different techniques for estimation of its parameters: direct fitting, indirect fitting and rescaling method. We find that using only CFSE data, the duration of the division phase (i.e., approximately the S+G2+M phase of the cell cycle) can be estimated with the use of either technique. In some cases, the average division or cell cycle time can be estimated using the direct fitting of the model solution to the data ...
Different theories have been proposed to understand the growing problem of antibiotic resistance ... more Different theories have been proposed to understand the growing problem of antibiotic resistance of microbial populations. Here we investigate a model that is based on the hypothesis that senescence is a possible explanation for the existence of so-called persister cells which are resistant to antibiotic treatment. We study a chemostat model with a microbial population which is age-structured and show that if the growth rates of cells in different age classes are sufficiently close to a scalar multiple of a common growth rate, then the population will globally stabilize at a coexistence steady state. This steady state persists under an antibiotic treatment if the level of antibiotics is below a certain threshold; if the level exceeds this threshold, the washout state becomes a globally attracting equilibrium.
The simultaneous growth of multiple microbial species is a problem of fundamental ecological inte... more The simultaneous growth of multiple microbial species is a problem of fundamental ecological interest. In media containing more than one growth-limiting substrate, multiple species can coexist. The question then arises: Can single-species data predict the existence and stability of mixed-culture steady states in mixed-substrate environments? This question has been extensively studied with the help of resource-based models. These studies have shown that the single-species data required to predict mixed-culture behavior consists of the growth isoclines and consumption vectors, which in turn are determined from single-substrate data by making specific assumptions about the kinetics of mixed-substrate growth. Here, we show that these assumptions are not valid for microbial growth on mixtures of substitutable substrates. However, the theory can be developed by determining the growth isoclines and consumption vectors directly from the mixed-substrate data, thus obviating the need for spec...
Discrete and Continuous Dynamical Systems - Series B, 2014
Recent experimental studies have shown that HIV can be transmitted directly from cell to cell whe... more Recent experimental studies have shown that HIV can be transmitted directly from cell to cell when structures called virological synapses form during interactions between T cells. In this article, we describe a new withinhost model of HIV infection that incorporates two mechanisms: infection by free virions and the direct cell-to-cell transmission. We conduct the local and global stability analysis of the model. We show that if the basic reproduction number R 0 ≤ 1, the virus is cleared and the disease dies out; if R 0 > 1, the virus persists in the host. We also prove that the unique positive equilibrium attracts all positive solutions under additional assumptions on the parameters. Finally, a multi strain model incorporating cell-to-cell viral transmission is proposed and shown to exhibit a competitive exclusion principle.
Canadian Applied Mathematics Quarterly
We investigate some properties of a very general model of growth in the chemostat. In the classic... more We investigate some properties of a very general model of growth in the chemostat. In the classical models of the chemostat, the function describing cellular growth is assumed to be a constant multiple of the function modeling substrate uptake. The constant of proportionality is called the growth yield constant. Here, this assumption of a constant describing growth yield is relaxed. Instead, we assume that the relationship between uptake and growth might depend on the substrate concentration and hence that the yield is variable. We obtain criteria for the stability of equilibria and for the occurrence of a Hopf bifurcation. In particular, a Hopf bifurcation can occur if the uptake function is unimodal. Then, in this setting, we consider competition in the chemostat for a single substrate, in order to challenge the principle of competitive exclusion. We consider two examples. In the first, the function describing the growth process is monotone and in the second it is unimodal. In bot...
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Papers by Sergei Pilyugin