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1.
Objectives: Intercellular cooperation has been hypothesized to enhance cell proliferation during cancer metastasis through autocrine signalling cascades and mathematical models can provide valuable insights into underlying mechanisms of metastatic tumorigenesis. Here, we present a model that incorporates signal‐stimulated cell proliferation, and investigate influences of diffusion‐driven heterogeneity in signal concentration on proliferation dynamics. Materials and methods: Our model incorporates signal production through both autocrine and paracrine pathways, and signal diffusion and loss for a metastasizing cell population at a host site. We use the signalling pathway of IL‐6 for illustration where this signalling species forms an intermediate complex with its receptor IL‐6R. This in turn forms a heterodimeric complex with transmembrane protein gp130, ultimately resulting in production of downstream signals. Cell population dynamics are taken to follow a modified logistic equation for which the rate term is dependent on local IL‐6 concentration. Results and conclusions: Our spatiotemporal model agrees closely with experimental results. The model is also able to predict two phenomena typical of metastatic tumorigenesis – host tissue preference and long periods of proliferation dormancy. It confirms that diffusivity of the signalling species in a host tissue plays a significant role during the process. Our results show that the proliferation–apoptosis balance is tipped in favour of the former for host sites that have relatively smaller signal diffusivities. 相似文献
2.
Guanghao Li Zuyu Yang Dafei Wu Sixue Liu Xuening Li Tao Li Yawei Li Liji Liang Weilong Zou Chung-I Wu Hurng-Yi Wang Xuemei Lu 《Molecular biology and evolution》2022,39(1)
Spatial genetic and phenotypic diversity within solid tumors has been well documented. Nevertheless, how this heterogeneity affects temporal dynamics of tumorigenesis has not been rigorously examined because solid tumors do not evolve as the standard population genetic model due to the spatial constraint. We therefore, propose a neutral spatial (NS) model whereby the mutation accumulation increases toward the periphery; the genealogical relationship is spatially determined and the selection efficacy is blunted (due to kin competition). In this model, neutral mutations are accrued and spatially distributed in manners different from those of advantageous mutations. Importantly, the distinctions could be blurred in the conventional model. To test the NS model, we performed a three-dimensional multiple microsampling of two hepatocellular carcinomas. Whole-genome sequencing (WGS) revealed a 2-fold increase in mutations going from the center to the periphery. The operation of natural selection can then be tested by examining the spatially determined clonal relationships and the clonal sizes. Due to limited migration, only the expansion of highly advantageous clones can sweep through a large part of the tumor to reveal the selective advantages. Hence, even multiregional sampling can only reveal a fraction of fitness differences in solid tumors. Our results suggest that the NS patterns are crucial for testing the influence of natural selection during tumorigenesis, especially for small solid tumors. 相似文献
3.
The Moran effect for populations separated in space states that the autocorrelations in the population fluctuations equal the autocorrelation in environmental noise, assuming the same linear density regulation in all populations. Here we generalize the Moran effect to include also nonlinear density regulation with spatial heterogeneity in local population dynamics as well as in the effects of environmental covariates by deriving a simple expression for the correlation between the sizes of two populations, using diffusion approximation to the theta-logistic model. In general, spatial variation in parameters describing the dynamics reduces population synchrony. We also show that the contribution of a covariate to spatial synchrony depends strongly on spatial heterogeneity in the covariate or in its effect on local dynamics. These analyses show exactly how spatial environmental covariation can synchronize fluctuations of spatially segregated populations with no interchange of individuals even if the dynamics are nonlinear. 相似文献
4.
Heterogeneity in habitat plays a crucial role in the dynamics of spatially extended populations and is often ignored by both
empiricists and theoreticians. A common assumption made is that spatially homogeneous systems and those with slight heterogeneity
will behave similarly and, therefore, the results and data from studies of the former can be applied to the latter. Here,
we test this assumption by deriving a phase model from two weakly coupled predator-prey oscillators and analyze the effect
of spatial heterogeneity on the phase dynamics of this system. We find that even small heterogeneity between the two patches
causes substantial changes in the phase dynamics of the system which can have dramatic effects on both population dynamics
and persistence. Additionally, if the prey and predator time scales are similar, the effect of heterogeneity is much greater. 相似文献
5.
Extrapolating ecological processes from small-scale experimental systems to scales of natural populations usually entails a considerable increase in spatial heterogeneity, which may affect process rates and, ultimately, population dynamics. We demonstrate how information on the heterogeneity of natural populations can be taken into account when scaling up laboratory-derived process functions, using the technique of moment approximation. We apply moment approximation to a benthic crustacean predator-prey system, where a laboratory-derived functional response is made spatial by including correction terms for the variance in prey density and the covariance between prey and predator densities observed in the field. We also show how moment approximation may be used to incorporate spatial information into a dynamic model of the system. While the nonspatial model predicts stable dynamics, its spatial equivalent also produces bounded fluctuations, in agreement with observed dynamics. A detailed analysis shows that predator-prey covariance, but not prey variance, destabilizes the dynamics. We conclude that second-order moment approximation may provide a useful technique for including spatial information in population models. The main advantage of the method is its conceptual value: by providing explicit estimates of variance and covariance effects, it offers the possibility of understanding how heterogeneity affects ecological processes. 相似文献
6.
In the attempt to use results from small-scale studies to make large-scale predictions, it is critical that we take into account
the greater spatial heterogeneity encountered at larger spatial scales. An important component of this heterogeneity is variation
in plant quality, which can have a profound influence on herbivore population dynamics. This influence is particularly relevant
when we consider that the strength of density dependence can vary among host plants and that the strength of density dependence
determines the difference between exponential and density- dependent growth. Here, we present some simple models and analyses
designed to examine the impact of variable plant quality on the dynamics of insect herbivore populations, and specifically
the consequences of variation in the strength of density dependence among host plants. We show that average values of herbivore
population growth parameters, calculated from plants that vary in quality, do not predict overall population growth. Furthermore,
we illustrate that the quality of a few individual plants within a larger plant population can dominate herbivore population
growth. Our results demonstrate that ignoring spatial heterogeneity that exists in herbivore population growth on plants that
differ in quality can lead to a misunderstanding of the mechanisms that underlie population dynamics. 相似文献
7.
This paper deals with the study of a predator-prey model in a patchy environment. Prey individuals moves on two patches, one is a refuge and the second one contains predator individuals. The movements are assumed to be faster than growth and predator-prey interaction processes. Each patch is assumed to be homogeneous. The spatial heterogeneity is obtained by assuming that the demographic parameters (growth rates, predation rates and mortality rates) depend on the patches. On the predation patch, we use a Lotka-Volterra model. Since the movements are faster that the other processes, we may assume that the frequency of prey and predators become constant and we would get a global predator-prey model, which is shown to be a Lotka-Volterra one. However, this simplified model at the population level does not match the dynamics obtained with the complete initial model. We explain this phenomenom and we continue the analysis in order to give a two-dimensional predator-prey model that gives the same dynamics as that provided by the complete initial one. We use this simplified model to study the impact of spatial heterogeneity and movements on the system stability. This analysis shows that there is a globally asymptotically stable equilibrium in the positive quadrant, i.e. the spatial heterogeneity stabilizes the equilibrium. 相似文献
8.
The importance of environmental spatial heterogeneity and host social structure in disease transmission
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《新西兰生态学杂志》2011,30(1):147-148
[First paragraph]The spatial structure of a host population determines the spatial probability distribution of interaction between individuals, and therefore influences the spatio-temporal dynamics of disease transmission within the host population (Keeling, 1999; Gudelj and White, 2004). Nigel Barlow recognised this and included non-linear transmission in his later models (Barlow, 1991), simulating the result of spatial heterogeneity of risk in susceptible hosts. These models produced behaviour that could not be found in models with homogeneously mixed host populations: more rapid disease dynamics and a greater robustness of disease to control measures. However, in this model there was no causal mechanism driving the initial spatial heterogeneity of risk in host individuals. Environmental heterogeneity is likely to be a key factor in determining the spatial distribution of host individuals (Cronin and Reeve, 2005). We attempted to explore how environmental heterogeneity may affect disease dynamics via its influence on the spatial distribution of host individuals. We developed a spatially explicit stochastic model that incorporated spatially variable host density distributions, primarily driven by environmental heterogeneity. 相似文献
9.
Intraneoplastic diversity in human tumors is a widespread phenomenon of critical importance for tumor progression and the response to therapeutic intervention. Insights into the evolutionary events that control tumor heterogeneity would be a major breakthrough in our comprehension of cancer development and could lead to more effective prevention methods and therapies. In this paper, we design an evolutionary mathematical framework to study the dynamics of heterogeneity over time. We consider specific situations arising during tumorigenesis, such as the emergence of positively selected mutations ("drivers") and the accumulation of neutral variation ("passengers"). We perform exact computer simulations of the emergence of diverse tumor cell clones over time, and derive analytical estimates for the extent of heterogeneity within a population of cancer cells. Our methods contribute to a quantitative understanding of tumor heterogeneity and the impact of heritable alterations on this tumor trait. 相似文献
10.
Angelina Mageni Lutambi Melissa A. Penny Thomas Smith Nakul Chitnis 《Mathematical biosciences》2013,241(2):198-216
Mosquito dispersal is a key behavioural factor that affects the persistence and resurgence of several vector-borne diseases. Spatial heterogeneity of mosquito resources, such as hosts and breeding sites, affects mosquito dispersal behaviour and consequently affects mosquito population structures, human exposure to vectors, and the ability to control disease transmission. In this paper, we develop and simulate a discrete-space continuous-time mathematical model to investigate the impact of dispersal and heterogeneous distribution of resources on the distribution and dynamics of mosquito populations. We build an ordinary differential equation model of the mosquito life cycle and replicate it across a hexagonal grid (multi-patch system) that represents two-dimensional space. We use the model to estimate mosquito dispersal distances and to evaluate the effect of spatial repellents as a vector control strategy. We find evidence of association between heterogeneity, dispersal, spatial distribution of resources, and mosquito population dynamics. Random distribution of repellents reduces the distance moved by mosquitoes, offering a promising strategy for disease control. 相似文献
11.
Models of host–parasitoid dynamics often assume constant levels of spatial heterogeneity in parasitoid attack rate, which tends to stabilize the interactions. Recently, authors have questioned this assumption and shown that outcomes of simple host–parasitoid models change if spatial heterogeneity is allowed to vary with parasitoid density. Here, we allow spatial heterogeneity to vary with either parasitoid density or percent parasitism in a model designed to explain specialist parasitoid coexistence on insect hosts with various levels of refuge. By examining this model we can evaluate the effect of varying spatial heterogeneity on a more complex model in which spatial heterogeneity is not considered the primary determinant of persistence. By modeling communities with one host and two parasitoid species, we show that the probability of species persistence for the competitively inferior parasitoid depends on the assumed relationship between spatial heterogeneity and both parasitoid density and percent parasitism. The probability of parasitoid coexistence is generally lower when spatial heterogeneity varies with parasitoid demographics. We conclude that the conditions for which host refuge promote specialist parasitoid coexistence are less common that proposed by the original model. Finally, we compared a model in which spatial heterogeneity varies with percent parasitism to data from laboratory trials and find a reasonable fit. We conclude that the change in spatial heterogeneity strongly influenced the outcome of the laboratory trials, and we suggest more research is necessary before researchers can assume constant spatial heterogeneity in future models. 相似文献
12.
Cornell SJ Isham VS Grenfell BT 《Proceedings. Biological sciences / The Royal Society》2004,271(1545):1243-1250
Host-parasite systems provide powerful opportunities for the study of spatial and stochastic effects in ecology; this has been particularly so for directly transmitted microparasites. Here, we construct a fully stochastic model of the population dynamics of a macroparasite system: trichostrongylid gastrointestinal nematode parasites of farmed ruminants. The model subsumes two implicit spatial effects: the host population size (the spatial extent of the interaction between hosts) and spatial heterogeneity ('clumping') in the infection process. This enables us to investigate the roles of several different processes in generating aggregated parasite distributions. The necessity for female worms to find a mate in order to reproduce leads to an Allee effect, which interacts nonlinearly with the stochastic population dynamics and leads to the counter-intuitive result that, when rare, epidemics can be more likely and more severe in small host populations. Clumping in the infection process reduces the strength of this Allee effect, but can hamper the spread of an epidemic by making infection events too rare. Heterogeneity in the hosts' response to infection has to be included in the model to generate aggregation at the level observed empirically. 相似文献
13.
Yu Jin Frank M. Hilker Peter M. Steffler Mark A. Lewis 《Bulletin of mathematical biology》2014,76(7):1522-1565
A key problem in environmental flow assessment is the explicit linking of the flow regime with ecological dynamics. We present a hybrid modeling approach to couple hydrodynamic and biological processes, focusing on the combined impact of spatial heterogeneity and temporal variability on population dynamics. Studying periodically alternating pool-riffle rivers that are subjected to seasonally varying flows, we obtain an invasion ratchet mechanism. We analyze the ratchet process for a caricature model and a hybrid physical–biological model. The water depth and current are derived from a hydrodynamic equation for variable stream bed water flows and these quantities feed into a reaction-diffusion-advection model that governs population dynamics of a river species. We establish the existence of spreading speeds and the invasion ratchet phenomenon, using a mixture of mathematical approximations and numerical computations. Finally, we illustrate the invasion ratchet phenomenon in a spatially two-dimensional hydraulic simulation model of a meandering river structure. Our hybrid modeling approach strengthens the ecological component of stream hydraulics and allows us to gain a mechanistic understanding as to how flow patterns affect population survival. 相似文献
14.
Dengue fever is currently the most important arthropod-borne viral disease in Brazil. Mathematical modeling of disease dynamics is a very useful tool for the evaluation of control measures. To be used in decision-making, however, a mathematical model must be carefully parameterized and validated with epidemiological and entomological data. In this work, we developed a simple dengue model to answer three questions: (i) which parameters are worth pursuing in the field in order to develop a dengue transmission model for Brazilian cities; (ii) how vector density spatial heterogeneity influences control efforts; (iii) with a degree of uncertainty, what is the invasion potential of dengue virus type 4 (DEN-4) in Rio de Janeiro city. Our model consists of an expression for the basic reproductive number (R0) that incorporates vector density spatial heterogeneity. To deal with the uncertainty regarding parameter values, we parameterized the model using a priori probability density functions covering a range of plausible values for each parameter. Using the Latin Hypercube Sampling procedure, values for the parameters were generated. We conclude that, even in the presence of vector spatial heterogeneity, the two most important entomological parameters to be estimated in the field are the mortality rate and the extrinsic incubation period. The spatial heterogeneity of the vector population increases the risk of epidemics and makes the control strategies more complex. At last, we conclude that Rio de Janeiro is at risk of a DEN-4 invasion. Finally, we stress the point that epidemiologists, mathematicians, and entomologists need to interact more to find better approaches to the measuring and interpretation of the transmission dynamics of arthropod-borne diseases. 相似文献
15.
The technological changes and educational expansion have created the heterogeneity in the human species. Clearly, this heterogeneity generates a structure in the population dynamics, namely: citizen, permanent resident, visitor, and etc. Furthermore, as the heterogeneity in the population increases, the human mobility between meta-populations patches also increases. Depending on spatial scales, a meta-population patch can be decomposed into sub-patches, for examples: homes, neighborhoods, towns, etc. Members of the population can move between the sub-patches. The dynamics of human mobility in a heterogeneous and scaled structured population is still its infancy level. In this work, an attempt is made to investigate the human mobility dynamics of heterogeneous and scaled structured population. We present a two scaled human mobility model for a meta-population. The sub regions and regions are interlinked via intra-and inter regional transport network systems. Under various types of growth order assumptions on the intra and interregional residence times of the residents of a sub region, different patterns of static behavior of the mobility process is studied. In addition, the results reveal that the system has a natural tendency to quarantine itself without total breaking a link in the transportation network system. Moreover, there is a threshold point for the largest intra regional visiting time of residents of a given sub region that leads to either a total isolation of the residents from other sub regions within the region or a partial isolation of residents from some of the sub regions within the region. 相似文献
16.
K Pham A Chauviere H Hatzikirou X Li HM Byrne V Cristini J Lowengrub 《Journal of biological dynamics》2012,6(Z1):54-71
Gliomas are very aggressive brain tumours, in which tumour cells gain the ability to penetrate the surrounding normal tissue. The invasion mechanisms of this type of tumour remain to be elucidated. Our work is motivated by the migration/proliferation dichotomy (go-or-grow) hypothesis, i.e. the antagonistic migratory and proliferating cellular behaviours in a cell population, which may play a central role in these tumours. In this paper, we formulate a simple go-or-grow model to investigate the dynamics of a population of glioma cells for which the switch from a migratory to a proliferating phenotype (and vice versa) depends on the local cell density. The model consists of two reaction-diffusion equations describing cell migration, proliferation and a phenotypic switch. We use a combination of numerical and analytical techniques to characterize the development of spatio-temporal instabilities and travelling wave solutions generated by our model. We demonstrate that the density-dependent go-or-grow mechanism can produce complex dynamics similar to those associated with tumour heterogeneity and invasion. 相似文献
17.
Most human cancer types result from the accumulation of multiple genetic and epigenetic alterations in a single cell. Once the first change (or changes) have arisen, tumorigenesis is initiated and the subsequent emergence of additional alterations drives progression to more aggressive and ultimately invasive phenotypes. Elucidation of the dynamics of cancer initiation is of importance for an understanding of tumor evolution and cancer incidence data. In this paper, we develop a novel mathematical framework to study the processes of cancer initiation. Cells at risk of accumulating oncogenic mutations are organized into small compartments of cells and proliferate according to a stochastic process. During each cell division, an (epi)genetic alteration may arise which leads to a random fitness change, drawn from a probability distribution. Cancer is initiated when a cell gains a fitness sufficiently high to escape from the homeostatic mechanisms of the cell compartment. To investigate cancer initiation during a human lifetime, a 'race' between this fitness process and the aging process of the patient is considered; the latter is modeled as a second stochastic Markov process in an aging dimension. This model allows us to investigate the dynamics of cancer initiation and its dependence on the mutational fitness distribution. Our framework also provides a methodology to assess the effects of different life expectancy distributions on lifetime cancer incidence. We apply this methodology to colorectal tumorigenesis while considering life expectancy data of the US population to inform the dynamics of the aging process. We study how the probability of cancer initiation prior to death, the time until cancer initiation, and the mutational profile of the cancer-initiating cell depends on the shape of the mutational fitness distribution and life expectancy of the population. 相似文献
18.
Guiming Wang N. Thompson Hobbs Saran Twombly Randall B. Boone Andrew W. Illius Iain J. Gordon John E. Gross 《Population Ecology》2009,51(1):123-132
Variation in the abundance of animals has traditionally been explained as the outcome of endogenous forcing from density dependence
and exogenous forcing arising from variation in weather and predation. Emerging evidence suggests that the effects of density
dependence interact with external influences on population dynamics. In particular, spatial heterogeneity in resources and
the presence of capable predators may weaken feedbacks from density dependence to growth of populations. We used the Kalman
filter to analyze 23 time series of estimates of abundance of northern ungulate populations arrayed along a latitudinal gradient
(latitude range of 40°–70°N) to evaluate the influence of spatial heterogeneity in resources and predation on density dependence.
We also used contingency tables to test whether density dependence was independent of the presence of carnivores (our estimate
of predation) and multiple regressions to determine the effects of spatial heterogeneity in resources, predation, and latitude
on the strength of density dependence. Our results showed that the strength of density dependence of ungulate populations
was low in the presence of large carnivores, particularly at northern latitudes with low primary productivity. We found that
heterogeneity in elevation, which we assume acted as a surrogate for spatial heterogeneity in plant phenology, also reduced
effects of density dependence. Thus, we show that external forces created by heterogeneity in resources and predation interact
with internal feedbacks from population density to shape dynamics of populations of northern ungulates. 相似文献
19.
We study a reaction-diffusion-advection model for the dynamics of populations under biological control. A control agent is assumed to be a predator species that has the ability to perceive the heterogeneity of pest distribution. The advection term represents the predator density movement according to a basic prey taxis assumption: acceleration of predators is proportional to the prey density gradient. The prey population reproduces logistically, and the local population interactions follow the Holling Type II trophic function. On the scale of the population, our spatially explicit approach subdivides the predation process into random movement represented by diffusion, directed movement described by prey taxis, local prey encounters, and consumption modeled by the trophic function. Thus, our model allows studying the effects of large-scale predator spatial activity on population dynamics. We show under which conditions spatial patterns are generated by prey taxis and how this affects the predator ability to maintain the pest population below some economic threshold. In particular, intermediate taxis activity can stabilize predator-pest populations at a very low level of pest density, ensuring successful biological control. However, very intensive prey taxis destroys the stability, leading to chaotic dynamics with pronounced outbreaks of pest density. 相似文献
20.
Spatial and temporal heterogeneity are often described as important factors having a strong impact on biodiversity. The effect
of heterogeneity is in most cases analyzed by the response of biotic interactions such as competition of predation. It may
also modify intrinsic population properties such as growth rate. Most of the studies are theoretic since it is often difficult
to manipulate spatial heterogeneity in practice. Despite the large number of studies dealing with this topics, it is still
difficult to understand how the heterogeneity affects populations dynamics. On the basis of a very simple model, this paper
aims to explicitly provide a simple mechanism which can explain why spatial heterogeneity may be a favorable factor for production.
We consider a two patch model and a logistic growth is assumed on each patch. A general condition on the migration rates and
the local subpopulation growth rates is provided under which the total carrying capacity is higher than the sum of the local
carrying capacities, which is not intuitive. As we illustrate, this result is robust under stochastic perturbations. 相似文献