Stability of a diverse immunological memory is determined by T cell population dynamics

The correlation between properties of the T cell memory pool and the two regulatory mechanisms of cell death (apoptosis) and memory entry (differentiation) is investigated mathematically. Apoptosis of T cells occurs at the end of an immune response, removing unwanted activated T cells. T cells escaping apoptosis enter the memory pool composed of T cells specific for previously encountered antigens. We find that the relative efficiencies of these two pathways determine the clonal distribution and the long-term stability of the memory pool by regulating the number of new entries. The main result presented in this paper is that immunological memory of previously encountered pathogens cannot be erased by either severe or repeat infections with a particular pathogen (the diversity of the memory pool is ensured) only if apoptosis and/or memory differentiation are regulated by population dependent processes. Furthermore, vaccination properties are improved significantly by population dependent mechanisms and our mathematical analysis reveals that the T cell population must communicate with other parts of the immune system to ensure optimal performance of immunological memory.     

The radish gene reveals a memory component with variable temporal properties

Memory phases, dependent on different neural and molecular mechanisms, strongly influence memory performance. Our understanding, however, of how memory phases interact is far from complete. In Drosophila, aversive olfactory learning is thought to progress from short-term through long-term memory phases. Another memory phase termed anesthesia resistant memory, dependent on the radish gene, influences memory hours after aversive olfactory learning. How does the radish-dependent phase influence memory performance in different tasks? It is found that the radish memory component does not scale with the stability of several memory traces, indicating a specific recruitment of this component to influence different memories, even within minutes of learning.     

Stability and function of secondary Th1 memory cells are dependent on the nature of the secondary stimulus

Following acute infection in some mouse models, CD4(+) memory T cells steadily decline over time. Conversely, in humans, CD4(+) memory T cells can be maintained for many years at levels similar to CD8(+) T cells. Because we previously observed that the longevity of Th1 memory cell survival corresponded to their functional avidity, we hypothesized that secondary challenge, which enriches for high functional avidity Th1 responders, would result in more stable Th1 memory populations. We found that following a heterologous secondary challenge, Th1 memory cells were maintained at stable levels compared with primary Th1 memory cells, showing little to no decline after day 75 postinfection. The improved stability of secondary Th1 memory T cells corresponded to enhanced homeostatic turnover; enhanced trafficking of effector memory Th1 cells to tissue sites of infection, such as the liver; and acquisition or maintenance of high functional avidity following secondary challenge. Conversely, a weaker homologous rechallenge failed to induce a stable secondary Th1 memory population. Additionally, homologous secondary challenge resulted in a transient loss of functional avidity by Th1 memory cells recruited into the secondary response. Our findings suggest that the longevity of Th1 memory T cells is dependent, at least in part, on the combined effects of primary and secondary Ag-driven differentiation. Furthermore, they demonstrate that the quality of the secondary challenge can have profound effects on the longevity and function of the ensuing secondary Th1 memory population.     

Experimental duration and predator satiation levels systematically affect functional response parameters

Empirical feeding studies where density‐dependent consumption rates are fitted to functional response models are often used to parameterize the interaction strengths in models of population or food‐web dynamics. However, the relationship between functional response parameter estimates from short‐term feeding studies and real‐world, long‐term, trophic interaction strengths remains largely unexamined. In a critical first step to address this void, we tested for systematic effects of experimental duration and predator satiation on the estimate of functional response parameters, namely attack rate and handling time. Analyzing a large data set covering a wide range of predator taxa and body masses, we show that attack rates decrease with increasing experimental duration, and that handling times of starved predators are consistently shorter than those of satiated predators. Therefore, both the experimental duration and the predator satiation level have a strong and systematic impact on the predictions of population dynamics and food‐web stability. Our study highlights potential pitfalls at the intersection of empirical and theoretical applications of functional responses. We conclude our study with some practical suggestions for how these implications should be addressed in the future to improve predictive abilities and realism in models of predator–prey interactions.     

Disentangling demographic co‐effects of predation and pollution on population dynamics

In nature species react to a variety of endogenous and exogenous ecological factors. Understanding the mechanisms by which these factors interact and drive population dynamics is a need for understanding and managing ecosystems. In this study we assess, using laboratory experiments, the effects that the combinations of two exogenous factors exert on the endogenous structure of the population dynamics of a size‐structured population of Daphnia. One exogenous factor was size‐selective predation, which was applied on experimental populations through simulating: 1) selective predation on small prey, 2) selective predation on large prey and 3) non‐selective predation. The second exogenous factor was pesticide exposure, applied experimentally in a quasi‐continuous regime. Our analysis combined theoretical models and statistical testing of experimental data for analyzing how the density dependence structure of the population dynamics was shifted by the different exogenous factors. Our results showed that pesticide exposure interacted with the mode of predation in determining the endogenous dynamics. Populations exposed to the pesticide and to either selective predation on newborns or selective predation on adults exhibited marked nonlinear effects of pesticide exposure. However, the specific mechanisms behind such nonlinear effects were dependent on the mode of size‐selectivity. In populations under non‐selective predation the pesticide exposure exerted a weak lateral effect. The ways in which endogenous process and exogenous factors may interact determine population dynamics. Increases in equilibrium density results in higher variance of population fluctuations but do not modify the stability properties of the system, while changes in the maximum growth rate induce changes in the dynamic regimes and stability properties of the population. Future consideration for research includes the consequences of the seasonal variation in the composition and activity of the predator assembly in interaction with the seasonal variation in exposure to agrochemicals on freshwater population dynamics.     

THE WELL-POSEDNESS OF SIZE STRUCTURED POPULATION MODELS WITH DENSITY DEPENDENT PARAMETERS

Thewell-posednessofnonlinearsizestructuredpopulationmodelsisstudied.Thenonlinearitiesareintroducedbyassumingthevitalparameters(thebirthrate,thedeathrate,andthegrowthrate)tobedensitydependent.TheidealadoptedhereisbasedonthemethodofGurtinandMacCamy[4]usedfornonlinearage-dependentpopulationmodels.Thenetreproductivenumberisintroducedandusedtodeterminethelocalandglobalstabilityoftrivialequilibrium.Thestabilityconditionsoftrivialequilibriumareobtained.     

Interspecific population regulation and the stability of mutualism: fruit abortion and density-dependent mortality of pollinating seed-eating insects

Two questions central to the population ecology of mutualism include: (1) what mechanisms prevent the inherent positive feedback of mutualism from leading to unbounded population growth; and (2) what mechanisms prevent instability from arising due to overexploitation. Theory and empiricism suggest that preventing such instability requires density‐dependent processes. A recent theory proposes that if benefits and costs to a mutualist vary with the density of its partner, then instability can be prevented if the former species can control demographic rates and regulate (or limit) the population density of its partner. The ecological and evolutionary feasibility of this theory of interspecific population regulation has been demonstrated using quantitative models of mutualism between plants and pollinating seed‐consuming insects. In these models, resource‐limited fruit set and ensuing fruit abortion are mechanisms that can lead to density‐dependent recruitment and population regulation of the insects. Yet, there has been little interplay between these theoretical results and empirical research. A recent study empirically examined the density‐dependent effects of resource‐limited fruit set and fruit abortion in the Yucca/moth mutualism. An analysis of the study led to the conclusion that, even though fruit abortion can account for >95% of moth mortality, it is largely a density‐independent source of mortality that cannot regulate moth population density. Here, we re‐analyze those empirical data and conduct further theoretical analyses to examine the nature of fruit abortion on moth recruitment. We conclude that resource‐limited fruit set and fruit abortion can effectively regulate and limit moth populations, due to its density‐dependent feedback on moth recruitment. Nonetheless, in any given interaction, multiple sources of mortality may contribute to the regulation and limitation of populations, and hence the stability of mutualism, including, larval competition and mortality due to locule damage in the Yucca/moth mutualism.     

Stability of an age specific population with density dependent fertility

A nonlinear version of the Lotka-Sharpe model of population growth is considered in which the age specific fertility is a function of the population size. The stability of an equilibrium population distribution is investigated with respect to both global and local perturbations. Sufficient conditions for such stability are presented, as are estimates for the rate of return of the population to the equilibrium configuration. Particular attention is paid to those situations in which the age dependent stability criteria coincide with those of age independent models.     

Effects of delay,truncations and density dependence in reproduction schedules on stability of nonlinear Leslie matrix models

Understanding effects of hypotheses about reproductive influences, reproductive schedules and the model mechanisms that lead to a loss of stability in a structured model population might provide information about the dynamics of natural population. To demonstrate characteristics of a discrete time, nonlinear, age structured population model, the transition from stability to instability is investigated. Questions about the stability, oscillations and delay processes within the model framework are posed. The relevant processes include delay of reproduction and truncation of lifetime, reproductive classes, and density dependent effects. We find that the effects of delaying reproduction is not stabilizing, but that the reproductive delay is a mechanism that acts to simplify the system dynamics. Density dependence in the reproduction schedule tends to lead to oscillations of large period and towards more unstable dynamics. The methods allow us to establish a conjecture of Levin and Goodyear about the form of the stability in discrete Leslie matrix models.This research was supported in part by the US Environmental Protection Agency under cooperation agreement CR-816081     

Regulation of TB Vaccine-Induced Airway Luminal T Cells by Respiratory Exposure to Endotoxin

Tuberculosis (TB) vaccine-induced airway luminal T cells (ALT) have recently been shown to be critical to host defense against pulmonary TB. However, the mechanisms that maintain memory ALT remain poorly understood. In particular, whether respiratory mucosal exposure to environmental agents such as endotoxin may regulate the size of vaccine-induced ALT population is still unclear. Using a murine model of respiratory genetic TB vaccination and respiratory LPS exposure, we have addressed this issue in the current study. We have found that single or repeated LPS exposure increases the number of antigen-specific ALT which are capable of robust secondary responses to pulmonary mycobacterial challenge. To investigate the potential mechanisms by which LPS exposure modulates the ALT population, we have examined the role of ALT proliferation and peripheral T cell recruitment. We have found that LPS exposure-increased ALT is not dependent on increased ALT proliferation as respiratory LPS exposure does not significantly increase the rate of proliferation of ALT. But rather, we find it to be dependent upon the recruitment of peripheral T cells into the airway lumen as blockade of peripheral T cell supplies markedly reduces the initially increased ALT. Thus, our data suggest that environmental exposure to airborne agents such as endotoxin has a profound modulatory effect on TB vaccine-elicited T cells within the respiratory tract. Our study provides a new, M.tb antigen-independent mechanism by which the respiratory mucosal anti-TB memory T cells may be maintained.     

Mechanisms underpinning community stability along a latitudinal gradient: Insights from a niche-based approach

At large scales, the mechanisms underpinning stability in natural communities may vary in importance due to changes in species composition, mean abundance, and species richness. Here we link species characteristics (niche positions) and community characteristics (richness and abundance) to evaluate the importance of stability mechanisms in 156 butterfly communities monitored across three European countries and spanning five bioclimatic regions. We construct niche-based hierarchical structural Bayesian models to explain first differences in abundance, population stability, and species richness between the countries, and then explore how these factors impact community stability both directly and indirectly (via synchrony and population stability). Species richness was partially explained by the position of a site relative to the niches of the species pool, and species near the centre of their niche had higher average population stability. The differences in mean abundance, population stability, and species richness then influenced how much variation in community stability they explained across the countries. We found, using variance partitioning, that community stability in Finnish communities was most influenced by community abundance, whereas this aspect was unimportant in Spain with species synchrony explaining most variation; the UK was somewhat intermediate with both factors explaining variation. Across all countries, the diversity–stability relationship was indirect with species richness reducing synchrony which increased community stability, with no direct effects of species richness. Our results suggest that in natural communities, biogeographical variation observed in key drivers of stability, such as population abundance and species richness, leads to community stability being limited by different factors and that this can partially be explained due to the niche characteristics of the European butterfly assemblage.     

Network bursting using experimentally constrained single compartment CA3 hippocampal neuron models with adaptation

The hippocampus is a brain structure critical for memory functioning. Its network dynamics include several patterns such as sharp waves that are generated in the CA3 region. To understand how population outputs are generated, models need to consider aspects of network size, cellular and synaptic characteristics and context, which are necessarily 'balanced' in appropriate ways to produce particular outputs. Thick slice hippocampal preparations spontaneously produce sharp waves that are initiated in CA3 regions and depend on the right balance of glutamatergic activities. As a step toward developing network models that can explain important balances in the generation of hippocampal output, we develop models of CA3 pyramidal cells. Our models are single compartment in nature, use an Izhikevich-type structure and involve parameter values that are specifically designed to encompass CA3 intrinsic properties. Importantly, they incorporate spike frequency adaptation characteristics that are directly comparable to those measured experimentally. Excitatory networks using these model cells are able to produce bursting suggesting that the amount of spike frequency adaptation expressed in the biological cells is an essential contributor to network bursting, and as such, may be important for sharp wave generation. The network bursting mechanism is numerically dissected showing the critical balance between adaptation and excitatory drive. The compact nature of our models allows large network simulations to be efficiently computed. This, together with the linkage of our models to cellular characteristics, will allow us to develop an understanding of population output of CA3 hippocampus with direct biological comparisons.     

Age or Stage Structure?

Discrete stage-structured density-dependent and discrete age-structured density-dependent population models are considered. Regarding the former, we prove that the model at hand is permanent (i.e., that the population will neither go extinct nor exhibit explosive oscillations) and given density dependent fecundity terms we also show that species with delayed semelparous life histories tend to be more stable than species which possess precocious semelparous life histories. Moreover, our findings together with results obtained from other stage-structured models seem to illustrate a fairly general ecological principle, namely that iteroparous species are more stable than semelparous species. Our analysis of various age-structured models does not necessarily support the conclusions above. In fact, species with precocious life histories now appear to possess better stability properties than species with delayed life histories, especially in the iteroparous case. We also show that there are dynamical outcomes from semelparous age-structured models which we are not able to capture in corresponding stage-structured cases. Finally, both age- and stage-structured population models may generate periodic dynamics of low period (either exact or approximate). The important prerequisite is to assume density-dependent survival probabilities.     

Mathematically modeling dynamics of T cell responses: predictions concerning the generation of memory cells

Mathematical models of T cell population dynamics after infection typically assume that T cells differentiate according to a linear process in which they first become effector cells, and then after some time, differentiate further into memory cells. In this paper, we offer a different mathematical model which can equally well capture T cell dynamics, using data from lymphocytic choriomeningitis (LCMV) infection. Our model assumes that memory cells are intermediates that further differentiate into effector cells only from additional or stronger antigenic stimulation. Our assumption naturally leads to a testable prediction about the generation of T cell memory-that the memory phenotype of T cells should be present in detectable numbers during the expansion phase of the response. We use our model to estimate a rate of differentiation from memory type cells to effectors. We argue that this differentiation assumption, where memory cells are intermediates, captures recent experimental work on T cell differentiation, and hence this new mathematical model could be helpful in doing further studies of T cell population dynamics. We also propose a method of distinguishing the models by examining the ratio of memory T cells detectable long after an infection to the peak numbers of T cells at the end of the expansion phase.     

Long-Term Recency in Anterograde Amnesia

Amnesia is usually described as an impairment of a long-term memory (LTM) despite an intact short-term memory (STM). The intact recency effect in amnesia had supported this view. Although dual-store models of memory have been challenged by single-store models based on interference theory, this had relatively little influence on our understanding and treatment of amnesia, perhaps because the debate has centred on experiments in the neurologically intact population. Here we tested a key prediction of single-store models for free recall in amnesia: that people with amnesia will exhibit a memory advantage for the most recent items even when all items are stored in and retrieved from LTM, an effect called long-term recency. People with amnesia and matched controls studied, and then free-recalled, word lists with a distractor task following each word, including the last (continual distractor task, CDFR). This condition was compared to an Immediate Free Recall (IFR, no distractors) and a Delayed Free Recall (DFR, end-of-list distractor only) condition. People with amnesia demonstrated the full long-term recency pattern: the recency effect was attenuated in DFR and returned in CDFR. The advantage of recency over midlist items in CDFR was comparable to that of controls, confirming a key prediction of single-store models. Memory deficits appeared only after the first word recalled in each list, suggesting the impairment in amnesia may emerge only as the participant’s recall sequence develops, perhaps due to increased susceptibility to output interference. Our findings suggest that interference mechanisms are preserved in amnesia despite the overall impairment to LTM, and challenge strict dual-store models of memory and their dominance in explaining amnesia. We discuss the implication of our findings for rehabilitation.     

Dynamics of termite populations-some theoretical considerations

Summary Various mathematical models are examined to fit the growth of termite populations. Termite populations show marked periodic fluctuations and these have their own biological significance. In the long run, notwith-standing the periodic fluctuations, the population continues to grow, if not infinitely.The intrinsic rate of population growth is dependent primarily on the fecundity of the queen. The population levels of different castes and population fluctuations are brought about by the selective development of the eggs into the adults of different castes and alates. Most of the models fail to account for the physiological and biological factors involved in termite population growth. A tentative model is suggested to express the population growth against time.Several hypotheses concerning the population regulation mechanisms of insects are examined and evaluated in relation to the termite populations. It is suggested that population growth of termites is probably regulated by homeostatic mechanisms.     

Individual Energetics and the Equilibrium Demography of Structured Populations

This paper considers the relationship between the demographic mechanisms of population control and the energetics of the individuals who comprise the population. We examine the equilibrium properties of a class of structured population models in which individuals compete for some environmental resource (such as food) and demonstrate that population demography is independent of the nature of the feedback loop which establishes the equilibrium state. We thus derive general insights into the influence exerted by individual energetic and allocation strategies on population average demographic characteristics. We show that models of individual energetics which produce apparently very similar predictions at the individual level can result in very different behaviour at the population level. In addition, we observe that different models of individual mortality can imply marked differences in population demography and that the common assumption of constant mortality can be responsible for potentially unrealistic model behaviour. Our results emphasise the substantial data requirements for parameterising and testing individual-based models.     

Modeling gynodioecy: novel scenarios for maintaining polymorphism

Nuclear-cytoplasmic gynodioecy is a breeding system of plants in which females and hermaphrodites co-occur in populations, and gender is jointly determined by cytoplasmic male sterility (CMS) genes and nuclear restorers of male fertility. Persistent polymorphism at both CMS and nuclear-restorer loci is necessary to maintain this breeding system. Theoretical models have explained how nuclear-cytoplasmic gynodioecy can be stable for certain assumptions. However, recent advances in our understanding of the genetics, population biology, and molecular mechanisms of sex determination in nuclear-cytoplasmic gynodioecious species suggest the utility of new models with different underlying assumptions. In this article, we examine different negative pleiotropic fitness effects of nuclear restorers (costs of restoration) using genetic and population assumptions based on recent literature. Specifically, we model populations with two CMS types and separate nuclear restorer loci for each CMS type. Under these assumptions, both overdominance for fitness and frequency-dependent selection at nuclear-restorer loci can support nuclear-cytoplasmic gynodioecy. Costs of restoration can be either dependent or independent of the cytoplasmic background. Seed fitness costs are more vulnerable to fixation of CMS types than pollen costs. Survivorship costs are effective at maintaining polymorphism even when total reproductive effects are low. Overall, our models display differences in the stability of nuclear-cytoplasmic gynodioecy and predicted population sex ratios that should be informative to researchers studying gynodioecy in the wild.     

Are the numbers adding up? Exploiting discrepancies among complementary population models

Large carnivores are difficult to monitor because they tend to be sparsely distributed, sensitive to human activity, and associated with complex life histories. Consequently, understanding population trend and viability requires conservationists to cope with uncertainty and bias in population data. Joint analysis of combined data sets using multiple models (i.e., integrated population model) can improve inference about mechanisms (e.g., habitat heterogeneity and food distribution) affecting population dynamics. However, unobserved or unobservable processes can also introduce bias and can be difficult to quantify. We developed a Bayesian hierarchical modeling approach for inference on an integrated population model that reconciles annual population counts with recruitment and survival data (i.e., demographic processes). Our modeling framework is flexible and enables a realistic form of population dynamics by fitting separate density-dependent responses for each demographic process. Discrepancies estimated from shared parameters among different model components represent unobserved additions (i.e., recruitment or immigration) or removals (i.e., death or emigration) when annual population counts are reliable. In a case study of gray wolves in Wisconsin (1980–2011), concordant with policy changes, we estimated that a discrepancy of 0% (1980–1995), −2% (1996–2002), and 4% (2003–2011) in the annual mortality rate was needed to explain annual growth rate. Additional mortality in 2003–2011 may reflect density-dependent mechanisms, changes in illegal killing with shifts in wolf management, and nonindependent censoring in survival data. Integrated population models provide insights into unobserved or unobservable processes by quantifying discrepancies among data sets. Our modeling approach is generalizable to many population analysis needs and allows for identifying dynamic differences due to external drivers, such as management or policy changes.     

Population dynamics of three songbird species in a nestbox population in Central Europe show effects of density,climate and competitive interactions

Unravelling the contributions of density‐dependent and density‐independent factors in determining species population dynamics is a challenge, especially if the two factors interact. One approach is to apply stochastic population models to long‐term data, yet few studies have included interactions between density‐dependent and density‐independent factors, or explored more than one type of stochastic population model. However, both are important because model choice critically affects inference on population dynamics and stability. Here, we used a multiple models approach and applied log‐linear and non‐linear stochastic population models to time series (spanning 29 years) on the population growth rates of Blue Tits Cyanistes caeruleus, Great Tits Parus major and Pied Flycatchers Ficedula hypoleuca breeding in two nestbox populations in southern Germany. We focused on the roles of climate conditions and intra‐ and interspecific competition in determining population growth rates. Density dependence was evident in all populations. For Blue Tits in one population and for Great Tits in both populations, addition of a density‐independent factor improved model fit. At one location, Blue Tit population growth rate increased following warmer winters, whereas Great Tit population growth rates decreased following warmer springs. Importantly, Great Tit population growth rate also decreased following years of high Blue Tit abundance, but not vice versa. This finding is consistent with asymmetric interspecific competition and implies that competition could carry over to influence population dynamics. At the other location, Great Tit population growth rate decreased following years of high Pied Flycatcher abundance but only when Great Tit population numbers were low, illustrating that the roles of density‐dependent and density‐independent factors are not necessarily mutually exclusive. The dynamics of this Great Tit population, in contrast to the other populations, were unstable and chaotic, raising the question of whether interactions between density‐dependent and density‐independent factors play a role in determining the (in) stability of the dynamics of species populations.