Constant Migration Rate Research Articles

Geomorphological Changes of a Migrating Sandbank: Multidecadal Analysis as a Tool for Managing Conflicts in Coastal Use

While beach erosion and sand loss are typically of great concern to the tourism industry, managing rapid morphological changes linked to large amounts of moving sediments is the challenge facing Grado, an important seaside resort in the northern Adriatic, Italy. The cause of the unusual management conflict is the presence of the Mula di Muggia Bank, a nearshore depositional system made up of relict and active migrating sandbanks extending up to 2 km seawards from the touristic beachfront. A reconstruction of the morpho-sedimentary evolution of the coastal system over a 200-year period was done using a large dataset which includes historical cartography, topographic maps, aerial photos and topo-bathymetric surveys. The results show the growth of a significant urban development aimed at creating a tourist destination by occupying the waterfront along fetch-limited coastal tracts with very shallow water and scarce hydrodynamics. Furthermore, a number of sandy dynamic landforms (longshore migrating bars, a bypass corridor, an ebb-tidal delta) and accumulation zones attest to a sediment excess which can be mostly attributed to the eastern river supplies. The progressive constant migration rate of 12.6 my−1 allowed the bank to induce the expansion of the low-energy silty backbarrier environment, characterised by abundant seagrass meadows a short distance directly in front of the tourist beaches of Grado. As a result of historical analysis and more current observations, areas with diverse morphosedimentary features and with varying tourist/recreational, ecological, and conservation values have been identified. These can be considered as basic units for future accurate planning and re-evaluation of coastal management choices to balance environmental protection and tourist use. A soft coastal defence approach is proposed which includes either the preservation of specific environments or the proper use of excess sand for beach nourishment via periodic dredging or sediment bypassing.

Global redistribution and local migration in semi-discrete host–parasitoid population dynamic models

Host–parasitoid population dynamics is often probed using a semi-discrete/hybrid modeling framework. Here, the update functions in the discrete-time model connecting year-to-year changes in the population densities are obtained by solving ordinary differential equations that mechanistically describe interactions when hosts become vulnerable to parasitoid attacks. We use this semi-discrete formalism to study two key spatial effects: local movement (migration) of parasitoids between patches during the vulnerable period; and yearly redistribution of populations across patches outside the vulnerable period. Our results show that in the absence of any redistribution, constant density-independent migration and parasitoid attack rates are unable to stabilize an otherwise unstable host–parasitoid population dynamics. Interestingly, inclusion of host redistribution (but not parasitoid redistribution) before the start of the vulnerable period can lead to stable coexistence of both species. Next, we consider a Type-III functional response (parasitoid attack rate increases with host density), where the absence of any spatial effects leads to a neutrally stable host–parasitoid equilibrium. As before, density-independent parasitoid migration by itself is again insufficient to stabilize the population dynamics and host redistribution provides a stabilizing influence. Finally, we show that a Type-III functional response combined with density-dependent parasitoid migration leads to stable coexistence, even in the absence of population redistributions. In summary, we have systematically characterized parameter regimes leading to stable/unstable population dynamics with different forms of spatial heterogeneity coupled to the parasitoid’s functional response using mechanistically formulated semi-discrete models.

食饵庇护所对斑块环境下Leslie-Gower捕食系统的影响

PDF HTML阅读 XML下载 导出引用 引用提醒 食饵庇护所对斑块环境下Leslie-Gower捕食系统的影响 DOI: 10.5846/stxb201704130654 作者: 作者单位: 河南大学 数学与统计学院 应用数学研究所 作者简介: 通讯作者: 中图分类号: Q141 基金项目: 中国博士后科学基金项目（2017M612388）；国家自然科学基金项目（31200312）；河南大学科学基金项目（yqpy20140045） The effect of prey refuge in a patchy Leslie-Gower predation system Author: Affiliation: Henan UniversityInstitute of Applied Mathematics, School of Mathematics and Information Sciences, Fund Project: 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:建立了一个显式含有空间庇护所的两斑块Leslie-Gower捕食者-食饵系统。假设只有食饵种群在斑块间以常数迁移率迁移，且在每个斑块上食饵间的迁移比局部捕食者-食饵相互作用发生的时间尺度要快。利用两个时间尺度，可以构建用来描述所有斑块总的食饵和捕食者密度的综合系统。数学分析表明，在一定条件下，存在唯一的正平衡点，并且此平衡点全局稳定。进一步，捕食者的数量随着食饵庇护所数量增加而降低；在一定条件下，食饵的数量随着食饵庇护所数量增加先增加后降低，在足够强的庇护所强度下，两物种出现灭绝。对比以往研究，利用显式含有和隐含空间庇护所的数学模型所得结论不一致，这意味着在研究庇护所对捕食系统种群动态影响时，空间结构可能起着重要作用。 Abstract:Predation is a common and important species interaction in many ecological systems. Mathematical models are important and very useful tools to understand and analyze the dynamic behavior of the predator-prey systems. Classical predator-prey models such as the Lotka-Volterra model and Leslie-Gower model can be used in a homogeneous environment. However, in general, the environment is heterogeneous and this can be represented using a set of discrete patches connected by migration. In the simplest situation, the two patches predator-prey model is used, which is composed of the local population process and the dispersal from patch to patch. Prey escaping predation in space or time is widely observed. Spatial or temporal refuges are well-known examples of this class of mechanism. Most theoretical studies have focused on how refuges add stability to the system with predator-prey interactions. The role of spatial and temporal refuges on species coexistence in communities with intraguild predation has also been investigated. These studies have two characteristics. First, most of the research is based on the Lotka-Volterra framework, only a few on the Leslie-Gower framework. Second, the traditional way to model this is to modify the functional response of predators and consider prey refuges, implicitly. The prey refuge can positively affect the growth of prey and negatively that of predators, because the decrease of predation success can lead to the reduction of prey mortality. On the other hand, the hiding behavior of prey could be either advantageous or detrimental for the involved populations. For example, the prey population in the refuges has a low or even negative growth rate because they are rarely offered feeding or mating opportunities. That is, there is a different population structure between the prey refuge and the normal habitat patch. Therefore, it is more reasonable to consider prey refuge explicitly. Based on the above consideration, this paper proposes a Leslie-Gower predator-prey model incorporating the effect of prey refuge explicitly in a two-patch environment. We assume that the prey dispersal is at a constant migration rate and is faster than the local predator-prey interaction, while the predator cannot disperse between patches. Taking advantage of the two different time scales, we use aggregation methods to obtain a reduced (aggregated) model governing the total prey and predator densities. The mathematical analysis of the aggregated model shows that there exists a unique and globally stable positive equilibrium under a certain condition. Simple mathematical analysis shows that increasing the amount of refuge can increase predator densities. As far as the prey species is concerned, under a certain condition, there exists a threshold, such that, for the prey refuge smaller than this threshold, increasing the amount of prey refuge can increase the prey densities, and if the prey refuge is larger than this threshold, increasing the amount of prey refuge can decrease the prey densities. Furthermore, prey and predator will become extinct when the effect of prey refuge is strong enough. In contrast to previous research, the effects of refuges used by the prey are different in spatially implicit and spatially explicit models. The discrepancy suggests that the spatial structure is important when refuges are included. 参考文献 相似文献 引证文献

Investigation of Headcut Erosion in Cohesive Soils

Headcut, known as knickpoint migration too, is developed due to sudden change in channel bed followed by bed scour and erosion which progressing upstream. The results are the downstream morphological change and transporting massive sediment to the downstream reservoir. Most of the past studies focus on non-cohesive soils, although many problems occur because of cohesive soils. In this study, 10 different samples of cohesive soils in long term consolidation with different composition of silt and clay were tested under different circumstances of waterfall height and flow velocity to investigate the neck migration rate and the sediment yield. Tests were continued to reach a constant migration rate. One of the effective phenomena in all tests was tensional cracks on soil surface. The size and number of these cracks have inverse relation with percent of clay. Because of these cracks, massive erosion occurs at the beginning of all tests. By reducing percent of clay, headcut, waterfall height and sediment yield were increased and by reducing waterfall height and flow velocity these parameters were reduced. In lower percent of clay, headcut erosion will occur quickly with more slants. Caving phenomenon was not observed in any tests and massive erosion rate was more quickly.

CLOSED-FORM SOLUTION TO AN ECONOMIC GROWTH LOGISTIC MODEL WITH CONSTANT MIGRATION

This paper considers a Solow-Swan economic growth model with the labor force ruled by the logistic equation added by a constant migration rate, I. We prove the global asymptotic stability of the capital and production per capita. Considering a Cobb-Douglas production function, we show this model to have a closed-form solution, which is expressed in terms of the Beta and Appell F1 special functions. We also show, through simulations, that if I>0, it implies in a smaller capital and product per capita in the short term, but in a higher capital and product per capita in the middle and long terms. In both cases, these per capita variables converge to the same steady-state given by the model without migration. If I<0 the transient behavior is the opposite. Finally, if I=0, we recover the solution for the pure logistic case, involving Gauss' Hypergeometric Function 2F1.

A prey-predator model with migrations and delays

In this paper we propose a prey-predator model in multiplepatches through the stage structured maturation time delay with migrations among patches. Focus on the case with two patches, we discuss the existence of equilibrium points and the uniform persistence. In particular, when the maturation times are the same in the patches, we study the local and global attractivity of boundary equilibrium point with general migration function and the local stability of the positive equilibrium with constant migration rate. Numerical simulations are provided to demonstrate the theoretical results, to illustrate the effect of the maturation time, the migration rate on the dynamical behavior of the system.

Closed-Form Solution for the Solow Model with Constant Migration

In this work we deal with the Solow economic growth model, when the labor force is ruled by the Malthusian law added by a constant migration rate I. Considering a Cobb-Douglas production function, we prove some stability issues and find a closed-form solution for the emigration case, involving Gauss' Hypergeometric functions. In addition, we prove that, depending on the value of the emigration rate, the economy could collapse, stabilize at a constant level, or grow more slowly than the standard Solow model. Immigration also can be analyzed by the model if the Malthusian manpower is declining.

Recently introduced invasive geckos quickly reach population genetic equilibrium dynamics

Invasive species are spreading at high rates, yet fundamental processes allowing them to progress through the stages of invasion are unclear. The establishment stage is a critical point because this is when exotic species can survive, reproduce, and begin to spread. Unfortunately, inference of population dynamics during this stage may be impossible if historical and observational data are incomplete. Nonetheless, critical inferences on population dynamics during the establishment stage can be acquired indirectly by characterizing demographic history via the population genetics of recently introduced populations. Geckos have been introduced at a global scale and are one of the most successfully establishing families of alien reptile known. Here we conduct a series of population genetic analyses among five close subpopulations of the introduced Mediterranean gecko Hemidactylus turcicus. We tested for non-equilibrium genetic signatures, a pattern expected during early stages of invasion if there were few founders or repeated introductions led to population turnover. Genetic analyses showed no evidence of non-equilibrium dynamics such as genetic bottlenecks. Moreover, we found strong support for population genetic equilibrium dynamics. The observed results may have been generated via an introduction that involved high propagule pressure. However, given the life history of H. turcicus including generation time and dispersal potential, we favor the hypothesis that the invasive metapopulation has rapidly reached the establishment stage as indicated by relatively constant effective sizes and migration rates among introduced subpopulations. The ability to rapidly pass through the establishment stage may in part explain the invasion success of these geckos.

Detection of Functional Matrix Metalloproteinases by Zymography

Matrix metalloproteinases (MMPs) are zinc-containing endopeptidases. They degrade proteins by cleavage of peptide bonds. More than twenty MMPs have been identified and are separated into six groups based on their structure and substrate specificity (collagenases, gelatinases, membrane type [MT-MMP], stromelysins, matrilysins, and others). MMPs play a critical role in cell invasion, cartilage degradation, tissue remodeling, wound healing, and embryogenesis. They therefore participate in both normal processes and in the pathogenesis of many diseases, such as rheumatoid arthritis, cancer, or chronic obstructive pulmonary disease1-6. Here, we will focus on MMP-2 (gelatinase A, type IV collagenase), a widely expressed MMP. We will demonstrate how to detect MMP-2 in cell culture supernatants by zymography, a commonly used, simple, and yet very sensitive technique first described in 1980 by C. Heussen and E.B. Dowdle7-10. This technique is semi-quantitative, it can therefore be used to determine MMP levels in test samples when known concentrations of recombinant MMP are loaded on the same gel11. Solutions containing MMPs (e.g. cell culture supernatants, urine, or serum) are loaded onto a polyacrylamide gel containing sodium dodecyl sulfate (SDS; to linearize the proteins) and gelatin (substrate for MMP-2). The sample buffer is designed to increase sample viscosity (to facilitate gel loading), provide a tracking dye (bromophenol blue; to monitor sample migration), provide denaturing molecules (to linearize proteins), and control the pH of the sample. Proteins are then allowed to migrate under an electric current in a running buffer designed to provide a constant migration rate. The distance of migration is inversely correlated with the molecular weight of the protein (small proteins move faster through the gel than large proteins do and therefore migrate further down the gel). After migration, the gel is placed in a renaturing buffer to allow proteins to regain their tertiary structure, necessary for enzymatic activity. The gel is then placed in a developing buffer designed to allow the protease to digest its substrate. The developing buffer also contains p-aminophenylmercuric acetate (APMA) to activate the non-proteolytic pro-MMPs into active MMPs. The next step consists of staining the substrate (gelatin in our example). After washing the excess dye off the gel, areas of protease digestion appear as clear bands. The clearer the band, the more concentrated the protease it contains. Band staining intensity can then be determined by densitometry, using a software such as ImageJ, allowing for sample comparison.

Detection of Functional Matrix Metalloproteinases by Zymography

Matrix metalloproteinases (MMPs) are zinc-containing endopeptidases. They degrade proteins by cleavage of peptide bonds. More than twenty MMPs have been identified and are separated into six groups based on their structure and substrate specificity (collagenases, gelatinases, membrane type [MT-MMP], stromelysins, matrilysins, and others). MMPs play a critical role in cell invasion, cartilage degradation, tissue remodeling, wound healing, and embryogenesis. They therefore participate in both normal processes and in the pathogenesis of many diseases, such as rheumatoid arthritis, cancer, or chronic obstructive pulmonary disease1-6. Here, we will focus on MMP-2 (gelatinase A, type IV collagenase), a widely expressed MMP. We will demonstrate how to detect MMP-2 in cell culture supernatants by zymography, a commonly used, simple, and yet very sensitive technique first described in 1980 by C. Heussen and E.B. Dowdle7-10. This technique is semi-quantitative, it can therefore be used to determine MMP levels in test samples when known concentrations of recombinant MMP are loaded on the same gel11.Solutions containing MMPs (e.g. cell culture supernatants, urine, or serum) are loaded onto a polyacrylamide gel containing sodium dodecyl sulfate (SDS; to linearize the proteins) and gelatin (substrate for MMP-2). The sample buffer is designed to increase sample viscosity (to facilitate gel loading), provide a tracking dye (bromophenol blue; to monitor sample migration), provide denaturing molecules (to linearize proteins), and control the pH of the sample. Proteins are then allowed to migrate under an electric current in a running buffer designed to provide a constant migration rate. The distance of migration is inversely correlated with the molecular weight of the protein (small proteins move faster through the gel than large proteins do and therefore migrate further down the gel). After migration, the gel is placed in a renaturing buffer to allow proteins to regain their tertiary structure, necessary for enzymatic activity. The gel is then placed in a developing buffer designed to allow the protease to digest its substrate. The developing buffer also contains p-aminophenylmercuric acetate (APMA) to activate the non-proteolytic pro-MMPs into active MMPs. The next step consists of staining the substrate (gelatin in our example). After washing the excess dye off the gel, areas of protease digestion appear as clear bands. The clearer the band, the more concentrated the protease it contains. Band staining intensity can then be determined by densitometry, using a software such as ImageJ, allowing for sample comparison.

Competition and species coexistence in a metapopulation model: Can fast asymmetric migration reverse the outcome of competition in a homogeneous environment?

We investigate whether asymmetric fast migration can modify the predictions of classical competition theory and, in particular revert species dominance. We consider a model of two species competing for an implicit resource on a habitat divided into two patches. Both patches are connected through constant migration rates and in each patch local dynamics are driven by a Lotka–Volterra competition system. Local competition is asymmetric with the same superior competitor in both patches. Migration is asymmetric, species dependent and fast in comparison to local competitive interactions. The species and patches are taken to be otherwise similar: in both patches we assume the same carrying capacities for both species, and the same growth rates and pair-wise competition coefficients for each species. We show that global dynamics can be described by a classical Lotka–Volterra competition model. We found that by modifying the ratio of intraspecific migration rates for both species all possible combinations of global species relative dominance can be achieved. We find specific conditions for which the local superior competitor is globally excluded. This is to our knowledge the first study showing that fast asymmetric migration can lead to inferior competitor dominance in a homogeneous environment. We conclude that disparity of temporal scales between migration and local dynamics may have important consequences for the maintenance of biodiversity in spatially structured populations.

Migration in a Solow Growth Model

In this work we deal with the Solow-Swan economic growth model, when the labor force is ruled by the Malthusian law added by a constant migration rate I. Considering a Cobb-Douglas production function, we prove some stability issues and find a closed-form solution for the emigration case, involving Gauss’ Hypergeometric functions. In addition, we prove that, depending on the value of the emigration rate, the economy could collapse, stabilize at a constant level, or grow more slowly than the Solow-Swan model. Immigration also can be analyzed by the model if the Malthusian manpower is declining.

Closed-Form Solutions to an Economic Growth Logistic Model with Migration

This paper presents a Solow Growth Model with the labor force ruled by the logistic equation added by a constant migration rate, I. We prove the global asymptotic stability of the capital and production per capita. Considering a Cobb-Douglas production function, we show this model to have a closed-form solution. This transient behavior is expressed in terms of the Beta and Appell F1 functions. We also show that if I > 0, it implies in a higher (minor) output of the economy, and in a minor (greater) capital and production per capita in the short term (middle and long term); furthermore, these ratios converge to the same steady-state value of the no-migration model; if I

Cationic balance and current efficiency of a three-compartment bipolar membrane electrodialysis system during the preparation of chitosan oligomers

Chitosan oligomers, known for their specific biological properties, were produced by an alternate method using a three-compartment bipolar membrane electrodialysis (BMED) system. The three main products (i.e. an acidified chitosan solution, a basified chitosanase solution and a demineralized chito-oligomer solution) were analyzed by inductively coupled plasma (ICP) for their cationic content as a function of BMED duration. It was found that sodium and potassium were the main cations present in the solutions. Using a current density of 10 mA/cm 2 for BMED, these cations were removed from the diluate compartment with constant migration rates of 0.30 and 0.37 mequiv. L −1 min −1, respectively for sodium and potassium. The cationic balance showed that all cations were preserved during the electrodialysis treatment, and that 80% of the cations were distributed between the basified and the diluate compartments. In addition, a current efficiency of 80%, constant during all the process, was calculated from the total cations migrated in the basified compartment, confirming the energetical performance of the system.

On the observability of resonant structures in planetesimal disks due to planetary migration

Context. The observed clumpy structures in debris disks are commonly interpreted as particles trapped in mean-motion resonances with an unseen exo-planet. Populating the resonances requires a migrating process of either the particles (spiraling i nward due to drag forces) or the planet (moving outward). Because the drag time-scale in resolved debris disks is generally long compared to the collisional time-scale, the planet migration scenario mig ht be more likely, but this model has so far only been investigated for planets on circular orbits. Aims. We present a thorough study of the impact of a migrating planet on a planetesimal disk, by exploring a broad range of masses and eccentricities for the planet. We discuss the sensitivi ty of the structures generated in debris disks to the basic pl anet parameters. Methods. We perform many N-body numerical simulations, using the symplectic integrator SWIFT, taking into account the gravitational influence of the star and the planet on massless test pa rticles. A constant migration rate is assumed for the planet . Results. The effect of planetary migration on the trapping of particles in mean motion resonances is found to be very sensitive to the initial eccentricity of the planet and of the planetesim als. A planetary eccentricity as low as 0.05 is enough to smear out all the resonant structures, except for the most massive planets. The planetesimals also initially have to be on orbits with a mean eccentricity of less than than 0.1 in order to keep the resonant clumps visible. Conclusions. This numerical work extends previous analytical studies and provides a collection of disk images that may help in interpreting the observations of structures in debris disk s. Overall, it shows that stringent conditions must be fulfil led to obtain observable resonant structures in debris disks. Theoretical models of the origin of planetary migration will therefore have to explain how planetary systems remain in a suitable configuration to repr oduce the observed structures.

Experimental investigations on different modes of headcut migration/ Investigations expérimentales sur différents modes de migration de headcut

Flume experiments were conducted to characterize the headcut erosion process on low bed slope landforms such as floodplain. Two different series of experiments were performed to investigate the headcut erosion and migration phenomenon both in homogeneous and heterogeneous non-cohesive soil. The flume bed was prepared with homogeneous coarse sand of uniform diameter for the first series and a composite fill of coarse sand and fine particles of polyvinyl chloride for the second series. Adhesive spray was applied on the top surface, which resisted the surface erosion and ensured the development of headcut. The effects of hydraulic and geometric conditions on headcut migration rate were analyzed. When all the detached sediments resulting from the erosion process were transported easily far downstream as wash load, then the overland flow rate and the headcut height governed the plunge-pool erosion process and the headcut migration rate as well (second series of experiments). In contrast, when the detached sediment resulting from the erosion process was transported as bed-material load, then the migration rate was governed not only by the upstream parameters but also by the downstream bed morphology (first series of experiments). The experimental results of both series showed that the shape of the plunge-pool remained unchanged with time for a given flow discharge. For a given flow rate and initial headcut-height, variable migration rate was observed in the first series of experiments, whereas the second series of experiments showed a constant migration rate. Conceptual models were proposed to explain the details of headcut migration process for both cases. In addition to overland flow rate and headcut height, the sediment transport capacity as well as the bed slope downstream of headcut was found to be a significant parameter that controlled the migration rate when the detached sediment was transported as bed-material load. The plunge-pool scour-rate that is governed by the overland flow rate, headcut-height and the properties of bed material controlled the migration rate when the detached sediment was transported as wash load. The migration rates calculated using conceptual models reasonably agreed with the experimental data for both cases.

Effect of predator density dependent dispersal of prey on stability of a predator–prey system

This work presents a predator–prey Lotka–Volterra model in a two patch environment. The model is a set of four ordinary differential equations that govern the prey and predator population densities on each patch. Predators disperse with constant migration rates, while prey dispersal is predator density-dependent. When the predator density is large, the dispersal of prey is more likely to occur. We assume that prey and predator dispersal is faster than the local predator–prey interaction on each patch. Thus, we take advantage of two time scales in order to reduce the complete model to a system of two equations governing the total prey and predator densities. The stability analysis of the aggregated model shows that a unique strictly positive equilibrium exists. This equilibrium may be stable or unstable. A Hopf bifurcation may occur, leading the equilibrium to be a centre. If the two patches are similar, the predator density dependent dispersal of prey has a stabilizing effect on the predator–prey system.

Effects of Density Dependent Migrations on the Dynamics of a Predator Prey Model

We study the effects of density dependent migrations on the stability of a predator-prey model in a patchy environment which is composed with two sites connected by migration. The two patches are different. On the first patch, preys can find resource but can be captured by predators. The second patch is a refuge for the prey and thus predators do not have access to this patch. We assume a repulsive effect of predator on prey on the resource patch. Therefore, when the predator density is large on that patch, preys are more likely to leave it to return to the refuge. We consider two models. In the first model, preys leave the refuge to go to the resource patch at constant migration rates. In the second model, preys are assumed to be in competition for the resource and leave the refuge to the resource patch according to the prey density. We assume two different time scales, a fast time scale for migration and a slow time scale for population growth, mortality and predation. We take advantage of the two time scales to apply aggregation of variables methods and to obtain a reduced model governing the total prey and predator densities. In the case of the first model, we show that the repulsive effect of predator on prey has a stabilizing effect on the predator-prey community. In the case of the second model, we show that there exists a window for the prey proportion on the resource patch to ensure stability.

Island models and the coalescent process

Using a coalescent approach, we derive several classical results and extend them to more general models. We find that the classic result for constant population size and constant migration rates holds in models with varying population size and varying migration rates with the obvious substitution of effective population size and mean migration fraction. In addition, the relationship of a ‘local’FST to local gene flow is derived. This result may be useful for analysing gene flow in a regional subset of a large global population, using only data from the regional subset.

In vitro evaluation of human muscle satellite cell migration prior to fusion into myotubes.

We developed a short-time assay to evaluate muscle satellite cell migration, based on the fact that during myogenic differentiation, myoblasts migrate preferentially towards high cellular density areas where myotubes would form. This assay consists of a computer-assisted count of cells within a randomly chosen field, performed every hour for eight hours, and compared with the cell number at the start time of the experiment. Nine primary myoblast cultures were tested in triplicate. The method relies on several requisites. (1) Negligible cell proliferation: cell division was nearly absent in 8 h experiments. (2) Directional cell movement: a major flow of cells, either entering or exiting the fields, was constantly observed. 'Counter-flows', detected by visual counting, involved minor percentages of cells. (3) Constant migration rate: a linear increase in cell count variations over 8 h and a very high degree of intra-assay homogeneity were observed. Individual primary cell culture characteristics (depending on characteristics of the different donors) were the sole factor with a significant impact on migration rate. Automatic cell counting conveniently assessed the inhibitory effect of GRGDTP, an inhibitor of integrin-mediated cell adhesion. The method described here is rapid, does not require heavy equipment, and allows studies under serum-free conditions required to test molecules interfering with cell migration, in the course of the in vitro myogenic process.