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. (shrink)

Matrix models are widely used in biology to predict the temporal evolution of stage-structured populations. One issue related to matrix models that is often disregarded is the sampling variability. As the sample used to estimate the vital rates of the models are of finite size, a sampling error is attached to parameter estimation, which has in turn repercussions on all the predictions of the model. In this study, we address the question of building confidence bounds around the predictions of matrix (...) models due to sampling variability. We focus on a density-dependent Usher model, the maximum likelihood estimator of parameters, and the predicted stationary stage vector. The asymptotic distribution of the stationary stage vector is specified, assuming that the parameters of the model remain in a set of the parameter space where the model admits one unique equilibrium point. Tests for density-dependence are also incidentally provided. The model is applied to a tropical rain forest in French Guiana. (shrink)

A model is proposed for the population dynamics of an annual plant (Sesbania vesicaria) with a seed bank (i.e. in which a proportion of seeds remain dormant for at least one year). A simple linear matrix model is deduced from the life cycle graph. The dominant eigenvalue of the projection matrix is estimated from demographic parameters derived from field studies. The estimated values for population growth rate () indicates that the study population should be experiencing a rapid exponential increase, but (...) this was not the case in our population.The addition of density dependent effects on seedling survivorship and adult fecundity, effects for which field studies provide evidence, considerably improves our model. Depending on the demographic parameters, the model leads to stable equilibrium, oscillations, or chaos. Study of the behaviour of this model in the parameter space shows that the existence of a seed bank allows higher among-year variation of adult fecundity, without leaving the region of demographic stability. Field data obtained over 3 years confirm this prediction. (shrink)

A simple numerical procedure is presented for the problem of estimating the parameters of models for the distribution of eggs oviposited in a host. The modelling is extended to incorporate both host density and time dependence to produce a remarkably parsimonious structure with only seven parameters to describe a data set of over 3,000 observations. This is further refined using a mixed model to accommodate several large outliers. Both models show that the level of superparasitism declines with increasing (...) host density, and the rate declines over time. It is proposed that the differing behaviours represented by the mixed model may reflect a balance between behavioural strategies of different selective benefit. (shrink)

A simple numerical procedure is presented for the problem of estimating the parameters of models for the distribution of eggs oviposited in a host. The modelling is extended to incorporate both host density and time dependence to produce a remarkably parsimonious structure with only seven parameters to describe a data set of over 3,000 observations. This is further refined using a mixed model to accommodate several large outliers. Both models show that the level of superparasitism declines with increasing (...) host density, and the rate declines over time. It is proposed that the differing behaviours represented by the mixed model may reflect a balance between behavioural strategies of different selective benefit. (shrink)

A simple numerical procedure is presented for the problem of estimating the parameters of models for the distribution of eggs oviposited in a host. The modelling is extended to incorporate both host density and time dependence to produce a remarkably parsimonious structure with only seven parameters to describe a data set of over 3,000 observations. This is further refined using a mixed model to accommodate several large outliers. Both models show that the level of superparasitism declines with increasing (...) host density, and the rate declines over time. It is proposed that the differing behaviours represented by the mixed model may reflect a balance between behavioural strategies of different selective benefit. (shrink)

A simple numerical procedure is presented for the problem of estimating the parameters of models for the distribution of eggs oviposited in a host. The modelling is extended to incorporate both host density and time dependence to produce a remarkably parsimonious structure with only seven parameters to describe a data set of over 3,000 observations. This is further refined using a mixed model to accommodate several large outliers. Both models show that the level of superparasitism declines with increasing (...) host density, and the rate declines over time. It is proposed that the differing behaviours represented by the mixed model may reflect a balance between behavioural strategies of different selective benefit. (shrink)

The susceptible-transmissible-removed (STR) model is a deterministic compartment model, based on the susceptible-infected-removed (SIR) prototype. The STR replaces 2 SIR assumptions. SIR assumes that the emigration rate (due to death or recovery) is directly proportional to the infected compartment’s size. The STR replaces this assumption with the biologically appropriate assumption that the emigration rate is the same as the immigration rate one infected period ago. This results in a unique delay differential equation epidemic model with the delay equal to the (...) infected period. Hamer’s mass action law for epidemiology is modified to resemble its chemistry precursor—the law of mass action. Constructing the model for an isolated population that exists on a surface bounded by the extent of the population’s movements permits compartment density to replace compartment size. The STR reduces to a SIR model in a timescale that negates the delay—the transmissible timescale. This establishes that the SIR model applies to an isolated population in the disease’s transmissible timescale. Cyclical social interactions will define a rhythmic timescale. It is demonstrated that the geometric mean maps transmissible timescale properties to their rhythmic timescale equivalents. This mapping defines the hybrid incidence (HI). The model validation demonstrates that the HI-STR can be constructed directly from the disease’s transmission dynamics. The basic reproduction number (R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{R}}_0$$\end{document}) is an epidemic impact property. The HI-STR model predicts that R0∝ρnB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{R}}_0 \propto \root \mathfrak{B} \of {\rho_n}$$\end{document} where ρn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho_n$$\end{document} is the population density, and B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{B}}$$\end{document} is the ratio of time increments in the transmissible- and rhythmic timescales. The model is validated by experimentally verifying the relationship. R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{R}}_0$$\end{document}’s dependence on ρn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho_n$$\end{document} is demonstrated for droplet-spread SARS in Asian cities, aerosol-spread measles in Europe and non-airborne Ebola in Africa. (shrink)

This paper proposes a formalization of the class of sentences quantified by most, which is also interpreted as proportion of or majority of depending on the domain of discourse. We consider sentences of the form “Most A are B”, where A and B are plural nouns and the interpretations of A and B are infinite subsets of \. There are two widely used semantics for Most A are B: \ > C \) and \ > \dfrac{C}{2} \), where C denotes (...) the cardinality of a given finite set X. Although is more descriptive than, it also produces a considerable amount of insensitivity for certain sets. Since the quantifier most has a solid cardinal behaviour under the interpretation majority and has a slightly more statistical behaviour under the interpretation proportional of, we consider an alternative approach in deciding quantity-related statements regarding infinite sets. For this we introduce a new semantics using natural density for sentences in which interpretations of their nouns are infinite subsets of \, along with a list of the axiomatization of the concept of natural density. In other words, we take the standard definition of the semantics of most but define it as applying to finite approximations of infinite sets computed to the limit. (shrink)

We present a population density and moment-based description of the stochastic dynamics of domain $${\text{Ca}}^{2+}$$ -mediated inactivation of L-type $${\text{Ca}}^{2+}$$ channels. Our approach accounts for the effect of heterogeneity of local $${\text{Ca}}^{2+}$$ signals on whole cell $${\text{Ca}}^{2+}$$ currents; however, in contrast with prior work, e.g., Sherman et al. :985–995, 1990), we do not assume that $${\text{Ca}}^{2+}$$ domain formation and collapse are fast compared to channel gating. We demonstrate the population density and moment-based modeling approaches using a 12-state Markov (...) chain model of an L-type $${\text{Ca}}^{2+}$$ channel introduced by Greenstein and Winslow :2918–2945, 2002). Simulated whole cell voltage clamp responses yield an inactivation function for the whole cell $${\text{Ca}}^{2+}$$ current that agrees with the traditional approach when domain dynamics are fast. We analyze the voltage-dependence of $${\text{Ca}}^{2+}$$ inactivation that may occur via slow heterogeneous domain [ $${\text{Ca}}^{2+}$$ ]. Next, we find that when channel permeability is held constant, $${\text{Ca}}^{2+}$$ -mediated inactivation of L-type channels increases as the domain time constant increases, because a slow domain collapse rate leads to increased mean domain [ $${\text{Ca}}^{2+}$$ ] near open channels; conversely, when the maximum domain [ $${\text{Ca}}^{2+}$$ ] is held constant, inactivation decreases as the domain time constant increases. Comparison of simulation results using population densities and moment equations confirms the computational efficiency of the moment-based approach, and enables the validation of two distinct methods of truncating and closing the open system of moment equations. In general, a slow domain time constant requires higher order moment truncation for agreement between moment-based and population density simulations. (shrink)

This paper presents some finite combinatorics of set systems with applications to model theory, particularly the study of dependent theories. There are two main results. First, we give a way of producing lower bounds on $\mathrm {VC}_{\mathrm {ind}}$-density and use it to compute the exact $\mathrm {VC}_{\mathrm {ind}}$-density of polynomial inequalities and a variety of geometric set families. The main technical tool used is the notion of a maximum set system, which we juxtapose to indiscernibles. In the second (...) part of the paper we give a maximum set system analogue to Shelah’s characterization of stability using indiscernible sequences. (shrink)

The concept of time-coarsened density matrix for open systems has frequently featured in equilibrium and non-equilibrium statistical mechanics, without being probed as to the detailed consequences of the time averaging procedure. In this work we introduce and prove the need for a selective and non-uniform time-sampling, whose form depends on the properties of the bath. It is also applicable when an open microscopic sub-system is coupled to another finite system. By use of a time-periodic minimal coupling model between these (...) two systems, we present detailed quantitative consequences of time coarsening, which include initial state independence of equilibration, deviations from long term averages, their environment size dependence and the approach to classicality, as measured by a Leggett–Garg type inequality. An interacting multiple qubit model affords comparison between the time integrating procedure and the more conventional environment tracing method. (shrink)

Alcohol use disorder is one of the most common substance use disorders contributing to both behavioral and cognitive impairments in patients with AUD. Recent neuroimaging studies point out that AUD is a typical disorder featured by altered functional connectivity. However, the details about how voxel-wise functional coordination remain unknown. Here, we adopted a newly proposed method named functional connectivity density to depict altered voxel-wise functional coordination in AUD. The novel functional imaging technique, FCD, provides a comprehensive analytical method for (...) brain's “scale-free” networks. We applied resting-state functional MRI toward subjects to obtain their FCD, including global FCD, local FCD, and long-range FCD. Sixty-one patients with AUD and 29 healthy controls were recruited, and patients with AUD were further divided into alcohol-related cognitive impairment group and non-cognitive impairment group. All subjects were asked to stay stationary during the scan in order to calculate the resting-state gFCD, lFCD, and lrFCD values, and further investigate the abnormal connectivity alterations among AUD-NCI, ARCI, and HC. Compared to HC, both AUD groups exhibited significantly altered gFCD in the left inferior occipital lobe, left calcarine, altered lFCD in right lingual, and altered lrFCD in ventromedial frontal gyrus. It is notable that gFCD of the ARCI group was found to be significantly deviated from AUD-NCI and HC in left medial frontal gyrus, which changes probably contributed by the impairment in cognition. In addition, no significant differences in gFCD were found between ARCI and HC in left parahippocampal, while ARCI and HC were profoundly deviated from AUD-NCI, possibly reflecting a compensation of cognition impairment. Further analysis showed that within patients with AUD, gFCD values in left medial frontal gyrus are negatively correlated with MMSE scores, while lFCD values in left inferior occipital lobe are positively related to ADS scores. In conclusion, patients with AUD exhibited significantly altered functional connectivity patterns mainly in several left hemisphere brain regions, while patients with AUD with or without cognitive impairment also demonstrated intergroup FCD differences which correlated with symptom severity, and patients with AUD cognitive impairment would suffer less severe alcohol dependence. This difference in symptom severity probably served as a compensation for cognitive impairment, suggesting a difference in pathological pathways. These findings assisted future AUD studies by providing insight into possible pathological mechanisms. (shrink)

In the energy–momentum density expressions for a relativistic perfect fluid with a bulk motion, one comes across a couple of pressure-dependent terms, which though well known, are to an extent, lacking in their conceptual basis and the ensuing physical interpretation. In the expression for the energy density, the rest mass density along with the kinetic energy density of the fluid constituents due to their random motion, which contributes to the pressure as well, are already included. However, (...) in a fluid with a bulk motion, there are, in addition, a couple of explicit, pressure-dependent terms in the energy–momentum density, whose presence to an extent, is shrouded in mystery, especially from a physical perspective. We show here that one such pressure-dependent term appearing in the energy density, represents the work done by the fluid pressure against the Lorentz contraction during transition from the rest frame of the fluid to another frame in which the fluid has a bulk motion. This applies equally to the electromagnetic energy density of electrically charged systems in motion and explains in a natural manner an apparently paradoxical result that the field energy of a charged capacitor system decreases with an increase in the system velocity. The momentum density includes another pressure-dependent term, that represents an energy flow across the system, due to the opposite signs of work being done by pressure on two opposite sides of the moving fluid. From Maxwell’s stress tensor we demonstrate that in the expression for electromagnetic momentum of an electric charged particle, it is the presence of a similar pressure term, arising from electrical self-repulsion forces in the charged sphere, that yields a natural solution for the notorious, more than a century old but thought by many as still unresolved, 4/3 problem in the electromagnetic mass. (shrink)

The estimation of causal effects is fundamental in situations where the underlying system will be subject to active interventions. Part of building a causal inference engine is defining how variables relate to each other, that is, defining the functional relationship between variables entailed by the graph conditional dependencies. In this article, we deviate from the common assumption of linear relationships in causal models by making use of neural autoregressive density estimators and use them to estimate causal effects within Pearl’s (...) do-calculus framework. Using synthetic data, we show that the approach can retrieve causal effects from non-linear systems without explicitly modeling the interactions between the variables and include confidence bands using the non-parametric bootstrap. We also explore scenarios that deviate from the ideal causal effect estimation setting such as poor data support or unobserved confounders. (shrink)

Based on the Lotka–Volterra system, a pest-natural enemy model with nonlinear feedback control as well as nonlinear action threshold is introduced. The model characterizes the implementation of comprehensive prevention and control measures when the pest density reaches the nonlinear action threshold level depending on the pest density and its change rate. The mortality rate of the pest is a saturation function that strictly depends on their density while the release of natural enemies is also a nonlinear pulse (...) term depending on the density of real-time natural enemies. The exact impulsive and phase sets are given. The definition and properties of the Poincaré map corresponding to the pulse points on the phase set are provided. We investigate the existence and stability of boundary and interior order-1 periodic solution. The theoretical analysis developed in the present paper combined with nonlinear controlling measures as well as nonlinear action threshold methods and techniques laid the foundation for the establishment and analysis of other state-dependent feedback control models. (shrink)

AimRapid eye movement (REM) sleep, non-rapid eye movement (NREM) sleep, and sleep spindles are all implicated in the consolidation of procedural memories. Relative contributions of sleep stages and sleep spindles were previously shown to depend on individual differences in task processing. However, no studies to our knowledge have focused on individual differences in experience with Vipassana meditation as related to sleep. Vipassana meditation is a form of mental training that enhances proprioceptive and somatic awareness and alters attentional style. The goal (...) of this study was to examine a potential role for Vipassana meditation experience in sleep-dependent procedural memory consolidation.MethodsGroups of Vipassana meditation practitioners (N = 22) and matched meditation-naïve controls (N = 20) slept for a daytime nap in the laboratory. Before and after the nap they completed a procedural task on the Wii Fit balance platform.ResultsMeditators performed slightly better on the task before the nap, but the two groups improved similarly after sleep. The groups showed different patterns of sleep-dependent procedural memory consolidation: in meditators, task learning was positively correlated with density of slow occipital spindles, while in controls task improvement was positively associated with time in REM sleep. Sleep efficiency and sleep architecture did not differ between groups. Meditation practitioners, however, had a lower density of occipital slow sleep spindles tha... (shrink)

Quantal penetration through a (stationary) one-dimensional potential barrier is considered as a time evolution of an initially prepared wave packet. The large-time asymptotics of the process is concerned. Locality of the potential imposes certain analytical properties of the interaction amplitudes in the energy representation. The results are presented in terms of development of the phase-space (Wigner's) quasi-distribution. The phase-space evolution kernel is constructed, and it is shown that in the presence of a positive potential no part of the distribution is (...) transported faster than the free particle. For the case of a small initial momentum uncertainty, the deformation of the coordinate density is considered, including a possible advance of its maximum, which would not mean any noncausal signal transport. (shrink)

One of the most efficient predator-prey models with spatial effects is the one with ratio-dependent functional response. However, there is a need to further explore the effects of spatial motion on the dynamic behavior of population. In this work, we study a ratio-dependent predator-prey model with diffusion terms. The aim of this work is to investigate the changes in predator’s distribution in space as the prey populations change their mobility. We observe that the frequency diffusion of the prey gives rise (...) to the sparse density of the predator. Moreover, we also observe that the increasing rate of the conversion into predator biomass induces pattern transitions of the predator. Specifically speaking, Turing pattern of the predator populations goes gradually from a spotted pattern to a black-eye pattern, with the intermediate state being the mixture of spot and stripe pattern. The simulation results and analysis of this work illustrate that the diffusion rate and the real intrinsic factor influence the persistence of the predator-prey system mutually. (shrink)

Using linear invariant operators in a constructive way we find the most general thermal density operator and Wigner function for time-dependent generalized oscillators. The general Wigner function has five free parameters and describes the thermal Wigner function about a classical trajectory in phase space. The contour of the Wigner function depicts an elliptical orbit with a constant area moving about the classical trajectory, whose eccentricity determines the squeezing of the initial vacuum.

Limited distribution phenomena related to negation and negative polarity are usually thought of in terms of affectivity where affective is understood as negative or downward entailing. In this paper I propose an analysis of affective contexts as nonveridical and treat negative polarity as a manifestation of the more general phenomenon of sensitivity to (non)veridicality (which is, I argue, what affective dependencies boil down to). Empirical support for this analysis will be provided by a detailed examination of affective dependencies in Greek, (...) but the distribution of any will also be shown to follow from (non)veridicality. (shrink)

This unique volume explores what ethics has to offer the practicing physician, nurse, and allied health care worker. The authors introduce the basic vocabulary of ethics and present and discuss the most commonly used ethical theories, using case studies to illustrate how ethics work within the context of health care. Newcomers to the field will learn what ethics is all about and how it relates to the pragmatic concerns of the health care professional. Those who already have a working knowledge (...) of the field will find a new approach to ethical theory--personalism--which the authors believe can make the practical use of ethics more effective and reliable. (shrink)

The balance of nature concept is an old idea that manifests itself in anumber of forms in population and community ecology. This paper focuseson population ecology, where controversy surrounding the balance ofnature takes the form of perennial debates over the significance ofdensity dependence, population regulation, and species interactions suchas competition. One of the most striking features of these debates, overthe course of the previous century in ecology, is the tendency to arguethe case on largely conceptual grounds. This paper explores (...) twoquestions. Why this tendency to settle on conceptual grounds what is soobviously an empirical issue? Are there any good conceptual arguments tobe had in this area? (shrink)

Alternative ways to ensure mate compatibility, such as hermaphroditism and the breakdown of self‐incompatibility, evolved repeatedly when finding a mating partner is difficult. In a variety of microorganisms where compatibility is determined by mating‐types, a highly regulated form of universal compatibility system called mating‐type switching has evolved several times. This sophisticated system allows for the genetic adjustment of the mating type during asexual growth, and it most likely evolved for reproductive assurance of immotile species under low densities. In this review, (...) we compare the switching strategy to other universal compatibility systems such as “unisexual mating” and homothallism. We identify the costs of switching, including genome instability, and mechanistic costs, as well as the benefits, mainly the maintenance of important mating‐type functions. Given the potential benefits of mating‐type switching, we speculate that switching is likely to have evolved many times independently, and may be more common in groups where genetic mating types regulate mate compatibility than assumed so far. (shrink)

I criticize some arguments against the causal interpretability of population genetics put forward by Denis Walsh ([2007], [2010]). In particular, I seek to undermine the contention that population genetics exhibits frame of reference relativity or subjectivity with respect to its formal representations. I also show that classical population genetics does not fall foul of some criteria for causal representation put forward by James Woodward ([2003]), although those criteria do undermine some causalist stances. 1 Introduction2 Modularity3 The Crucially Important Point4 The (...) Gillespie Case: Density-Dependent Selection5 Conclusion. (shrink)

If all origins of life or of any new grade, level, or major transition as such begin with “competitive development”—with juveniles rather than adults, and multiple individuals rather than a single one—then the evolution of progeneration and of replication always requires an explanation. This article proposes that principles of evolutionary ecology such as density-dependence can be used to explain three kinds of developmental repetitions, viz., sequences of inductive and niche-constructing interactions between the ecological environment and population members, which (...) take place in such a way that the sequence is repeated: individual or somatic repetitions, discussed in Section 1, demographic or progenerative repetitions , discussed in Section 2, and replicative repetitions , discussed in Section 3. This results in a statement of the evolutionary process that includes rather than excludes development and ecology, but one which requires some additions to Van Valen’s aphorism that evolution is the control of development by ecology. (shrink)

Wildlife populations in the northern reaches of the globe have long been observed to fluctuate or cycle periodically, with dramatic increases followed by catastrophic crashes. Focusing on the early work of Charles S. Elton, this article analyzes how investigations into population cycles shaped the development of Anglo-American animal ecology during the 1920s–1930s. Population cycling revealed patterns that challenged ideas about the “balance” of nature; stimulated efforts to quantify population data; and brought animal ecology into conversation with intellectual debates about natural (...) selection. Elton used the problem of understanding wildlife population cycles to explore a central tension in ecological thought: the relative influences of local conditions (food supply, predation) and universal forces (such as climate change and natural selection) in regulating wild animal populations. He also sought patronage and built research practices and the influential Bureau of Animal Population around questions of population regulation during the 1930s. Focusing on disease as a local population regulator that could interact with global climatic influences, Elton facilitated an interdisciplinary and population-based approach in early animal ecology. Elton created a network of epidemiologists, conservationists, pathologists and mathematicians, who contributed to population cycle research. I argue that, although these people often remained peripheral to ecology, their ideas shaped the young discipline. Particularly important were the concepts of abundance, density, and disease; and the interactions between these factors and natural selection. However, Elton’s reliance on density dependence unwittingly helped set up conditions conducive to the development of controversies in animal ecology in later years. While ecologists did not come to consensus on the ultimate causes of population cycles, this phenomenon was an important early catalyst for the development of theory and practice in animal ecology. (shrink)

Explaining the persistence of populations is an important quest in ecology, and is a modern manifestation of the balance of nature metaphor. Increasingly, however, ecologists see populations (and ecological systems generally) as not being in equilibrium or balance. The portrayal of ecological systems as “non-equilibrium” is seen as a strong alternative to deterministic or equilibrium ecology, but this approach fails to provide much theoretical or practical guidance, and warrants formalisation at a more fundamental level. This is available in adaptation theory, (...) which allows population persistence to be explained as an epiphenomenon stemming from the maintenance, survival, movement and reproduction of individual organisms. These processes take place within a physicochemical and biotic environment that persists through structured annual cycles, but which is also spatiotemporally dynamic and subject to stochastic variation. The focus is thus shifted from the overproduction of offspring and the consequent density dependent population pressure thought to follow, to the adaptations and ecological circumstances that support those relatively few individuals that do survive. (shrink)

The aim of this work is to present aggregation methods of hierarchically organized systems allowing one to replace the initial micro-system by a macro-system described by a few global variables. We also study the relations between the fast micro-dynamics and the slow macro-dynamics which can produce global properties. Emergence corresponds to a bottom-up coupling that is the result effected by a micro-level at a macro-level. As an example, we present prey-predator models with different time scales in an heterogeneous environment. A (...) fast time scale is associated to the migration process on spatial patches and a slow time scale is associated to growth and interactions between the populations. Preys must go on spatial patches where resources are located and where predators can attack them. The efficiency of the predators to catch preys is patch dependent. Perturbation methods allow us to aggregate the initial system of differential equations for the patch sub-populations into a macro-system of two differential equations governing the total population densities. We study the case of density independent and density dependent migrations. In the latter case, we show that different functional responses can emerge in the macro prey-predator model as a result of the coupling between the slow and fast systems. (shrink)

This article utilizes three premises. There are commonly ecologically oriented, naturally selected specialized differences in frequency and/or quality as well as sexually selected differences between the sexes. Sex in the sense of coming together and going apart or going apart and coming together is trade in these naturally selected differences, i.e., there is a mating market in sexual species. While such trade is beneficial to the population as a whole, sexual competition and selection is conflict over the profits of that (...) trade and can be detrimental to the population as a whole. These premises yield a naturally selected sex allocation theory of the possible directions and forms of sexual selection, i.e., one that includes costs as well as frequencies. This can explain conventional sex roles, the sex-role reversed, inter- as well as intrasexual selection, and passive as well as active choice. Any of these alternatives may be over mates, over gametes, or both. A hypothetical example based on density dependence relative to resources is provided, one that suggests that centrioles may be a cytoplasmic resource in males in multicellular animals, and which are the target of active choice and the mechanism of manipulation in passive female choice. As a whole, the approach yields a truly general theory of sexual selection, provides an alternative to the mechanism for Fisher’s principle, and gives a theoretical explanation for Mayr’s biological species definition. (shrink)

A simple model, illustrating the transition from a population of free swimming, solitary cells to one consisting of small colonies serves as a basis to discuss the evolution of the cooperative group. The transition is the result of a mutation of the dynamics of cell division, delayed cell separation leads to colonies of four cells. With this mutation cooperative features appear, such as synchronised cell divisions within colonies and coordinated flagellar function which enables the colony to swim in definite directions. (...) The selective advantages under given, environmental conditions are defined and the periods necessary for complete allelic replacement in small populations are calculated for asexual and sexual reproduction. The assumption of a steady-state population during allelic substitution is critically considered, particularly under conditions of competition. It is shown that density-dependent population control must operate in the process of selection. Sexual reproduction slows down the rate of selection even though all cells dre haploid. This phenomenon can be explained in general terms of `organizational dominance', where individual units coordinate the function of their neighbours which may be of a different allelotype.Cooperativity is pointed out as an a priori systemic feature which resides in the sub-units of systems, group formation and coordination appears thus as an almost inevitable event. A particular type of system described as ‘closed cycle of positive fitness interaction’ is discussed in more detail. It has the remarkable feature that its members cannot compete with each other; selection takes place between whole cycles .Gonium has a wide spectrum of `somatic plasticity' which enables it to assume various colonial configurations depending on physiological and environmental conditions. This feature can be explained as the result of dynamic flexibilities on the macro-molecular level. The particular relationship between the vast, molecular complexity and the relative simple dynamics of the cell cycle must lead eventually to the genetic fixation of an environmentally induced phenotype. (shrink)

We present a mathematical model of two competing marine species that are harvested. We consider three models according to different levels of complexity, without and with species refuge and density-independent and density-dependent species movement between fishing area and refuge. We particularly study the effects of the fishing pressure on the outcome of the competition. We focus on conditions that allow an inferior competitor to invade as a result of fishing pressure. The model is discussed in relationship to the (...) case of the thiof and the octopus along the Atlantic West African coast. At the origin, the thiof was abundant and the octopus scarce in that region. Since, the fishing pressure has strongly increased in some fishing areas leading to the depletion of the thiof and the invasion of its competitor, the octopus. (shrink)

The exogenous cycles and population dynamics of the community at Penrith, Cumbria, England, have been studied (1557-1812) using aggregative analysis, family reconstitution and time series analysis. This community was living under marginal conditions for the first 200 years and the evidence presented is of a homeostatic regime where famine, malnutrition and epidemic disease acted to regulate the balance between resources and population size. This provides an ideal historic population for an investigation of the direct and indirect effects of malnutrition. Throughout (...) the period studied, a short wavelength oscillation in grain prices was apparently the major external factor that drove exogenous cycles in mortality, birth rate, and migration. In particular, the different responses of children to variations in food supply are emphasised; fluctuations in poor nutrition correlated significantly with the variations in mortality rates for infants (probably indirectly during pregnancy and directly during the first year of life) and for young children (via susceptibility to lethal infectious diseases). Migratory movements contributed to the maintenance of homeostasis in the population dynamics. A medium wavelength cycle in low winter temperatures was associated with a rise in adult mortality which, in turn, promoted an influx of migrants into this saturated habitat. A model incorporating these interacting associations between vital events and exogenous cycles is presented: grain prices were an important density-dependent factor and constituted the major component of the negative feedback of this population and drove the exogenous, short wavelength mortality cycles. Cycles of births and immigration provide a positive feedback for the build-up of susceptibles and the initiation of smallpox epidemics and increased population size. (shrink)