Constant Mortality Research Articles

Age-dependent stochastic models for understanding population fluctuations in continuously cultured cells

For symmetrically dividing cells, large variations in the cell cycle time are typical, even among clonal cells. The consequence of this variation is important in stem cell differentiation, tissue and organ size control, and cancer development, where cell division rates ultimately determine the cell population. We explore the connection between cell cycle time variation and population-level fluctuations using simple stochastic models. We find that standard population models with constant division and death rates fail to predict the level of population fluctuation. Instead, variations in the cell division time contribute to population fluctuations. An age-dependent birth and death model allows us to compute the mean squared fluctuation or the population dispersion as a function of time. This dispersion grows exponentially with time, but scales with the population. We also find a relationship between the dispersion and the cell cycle time distribution for synchronized cell populations. The model can easily be generalized to study populations involving cell differentiation and competitive growth situations.

Stand dynamics and tree coexistence in an analytical structured model: The role of recruitment

Understanding the mechanisms of coexistence and niche partitioning in plant communities is a central question in ecology. Current theories of forest dynamics range between the so-called neutral theories which assume functional equivalence among coexisting species to forest simulators that explain species assemblages as the result of tradeoffs in species individual strategies at several ontogenetic stages. Progress in these questions has been hindered by the inherent difficulties of developing analytical size-structured models of stand dynamics. This precludes examination of the relative importance of each mechanism on tree coexistence. In previous simulation and analytical studies emphasis has been given to interspecific differences at the sapling stage, and less so to interspecific variation in seedling recruitment. In this study we develop a partial differential equation model of stand dynamics in which competition takes place at the recruitment stage. Species differ in their size-dependent growth rates and constant mortality rates. Recruitment is described as proportional to the basal area of conspecifics, to account for fecundity and seed supply per unit of basal area, and is corrected with a decreasing function of species specific basal area to account for competition. We first analyze conditions for population persistence in monospecific stands and second we investigate conditions of coexistence for two species. In the monospecific case we found a stationary stand structure based on an inequality between mortality rate and seed supply. In turn, intra-specific competition does not play any role on the asymptotic extinction or population persistence. In the two-species case we found that coexistence can be attained when the reciprocal negative effect on recruitment follows a given relation with respect to intraspecific competition. Specifically a tradeoff between recruitment potential (i.e. shade tolerance or predation avoidance) and fecundity or growth rate. This is to our knowledge the first study that describes coexistence mechanisms in an analytical size-structured model in terms of competitive differences at the regeneration state.

Modeling the spring blooms of ciliates in a deep lake

In contrast to the macro/mesozooplankton, microzooplankton has received much less attention in ecosystem models. In many modeling studies, microzooplankton has been either entirely neglected, or else, data were often not available for validation, or agreement between the observed and the simulated abundances was rather poor. In this study, we compare the simulation results from several alternative models considering different formulations of ciliate growth in a hydrodynamically driven 1D nutrient-phytoplankton–multiple zooplankton model, with long-term datasets from the deep, monomictic Lake Constance. We show that the parameterization of the limitation of ciliate growth with a constant specific mortality rate and/or predation by copepods leads to uncontrolled ciliate blooms. In contrast, implementation of a density-dependent mortality rate enables reproduction of algae–ciliate dynamics over a variety of environmental settings encompassed by the 14-year dataset spanning 21 years in a lake undergoing oligotrophication. Considering the numerous processes that can be responsible for the dampening of ciliate blooms, our findings suggest that employing a simple density-dependent mortality term offers a pragmatic solution for the challenge of including the microzooplankton, characterized by an overwhelming complexity of trophic interactions, in ecosystem models.

Qualitative analysis of an age-structured SEIR epidemic model with treatment

A new age-structured model, which incorporates the use of treatment, is designed and qualitatively analysed. The model is, first of all, shown to be properly-posed mathematically by formulating it as an abstract Cauchy problem. For the case where the contact rate is separable (i.e., β(a,b)=β1(a)β2(b)), it is shown that the disease-free equilibrium of the model is locally- and globally-asymptotically stable whenever a certain epidemiological threshold, denoted by R0s, is less than unity. Furthermore, the model has a unique endemic equilibrium when the threshold exceeds unity (this equilibrium is shown to be locally-asymptotically stable if another condition holds). For the case where the natural death and contact rates are constant (i.e., independent of age), the unique endemic equilibrium of the resulting model is shown, using Lyapunov function theory and LaSalle’s Invariance Principle, to be globally-asymptotically stable when it exists. Furthermore, for this reduced version of the model (with constant natural death and contact rates), it is shown that the use of treatment could offer positive or negative population-level impact, depending on the size of the parameter associated with the reduction of infectiousness of treated individuals.

Growth and Population Size of Grass Carp Incrementally Stocked for Hydrilla Control

AbstractIn weed control plans that use Grass Carp Ctenopharyngodon idella for intermediate control of hydrilla Hydrilla verticillata, the knowledge of population dynamics improves efficacy of management. Our objective was to characterize growth, mortality, and associated population metrics of long‐lived (up to 16 years) triploid Grass Carp that were incrementally stocked into Lake Gaston, Virginia–North Carolina, starting in 1995. Grass Carp (ages 1–16) were collected by bowfishers during 2006–2010. Growth of Grass Carp was described by the von Bertalanffy growth model as Lt = 1,297[1 − e −0.1352(t +1.52)], where Lt is TL at age t. We used three methods to estimate Grass Carp mortality, and annual abundance and biomass of Grass Carp were estimated from each mortality estimate. Estimated annual mortality ranged from 0.20 to 0.25 depending on the method used. The use of constant mortality rates versus age‐specific mortality rates produced divergent models of Grass Carp biomass and represented a different approach for tracking the progress of weed control. Grass Carp biomass (but not abundance) was related to hydrilla coverage in Lake Gaston based on several scenarios that described time lags between Grass Carp stocking in year i and decreases in hydrilla coverage (in years i, i + 1, …, i + 5). Regardless of the mortality estimate used to derive Grass Carp biomass, the strongest biomass–hydrilla coverage relationship was observed for a time lag of 4 years. Fish older than age 10 constituted nearly 50% of the total Grass Carp biomass in Lake Gaston during some years, and the relationship between Grass Carp biomass and hydrilla coverage was strongest when fish up to age 16 were included in models. These results indicate that Grass Carp up to at least age 16 are important for weed control, thus highlighting the need for stocking models and bioenergetics models that include contributions of older fish when assessing long‐lived Grass Carp populations.Received January 23, 2012; accepted October 3, 2012

Hot-Water Phytosanitary Treatment Against <I>Ceratitis capitata</I> (Diptera: Tephritidae) in ‘Ataulfo’ Mangoes

We determined the thermal death rate constants and mortality curves for the eggs and different instars of Ceratitis capitata (Mediterranean fruit fly) (Wiedemann) submerged in isolation in water at 44, 46, and 48 degrees C and submerged within fruits of Mangifera indica (mango) (L.) in water at 43.1, 44.1, 45.1, and 46.1 degrees C. The first instar was the most tolerant to this treatment, with estimated times for achieving 99.9968% mortality of 103.28, 92.73, and 92.49 min at temperatures of 43.1, 44.1, and 45.1 degrees C, respectively. The results of the study indicate that 'Ataulfo' mangoes weighing < 329 +/- 2.11 g and at risk immature Mediterranean fruit fly infestation should be immersed for 95 min at 46.1-47 degrees C to ensure that the fruit pulp remains at this temperature for 10 min. An efficacy test was conducted that involved treating 730 mangoes, with an average weight of 326 +/- 2.11 g (mean +/- SE) and infested with 84 +/- 1.15 first instars. In this test, none of the 61,720 larvae treated survived. The confirmatory test was performed using commercial equipment in which 1,112 infested mango fruit weighing an average of 329 +/- 2.11 g were treated. Each fruit was previously infested with an average of 59 +/- 0.61 first instars (= 65,825 total larvae) of which none survived. The data collected on mango quality indicate that hot water immersion for 95 min at 46.1-47 degrees C can produce a more uniform fruit-color and positively modify the pH (producing more palatable fruits), but can also produce a loss of firmness and weight (5%). Taking all factors into consideration, we conclude that this treatment is sufficient to meet quarantine restrictions against C. capitata while maintaining market quality at least for 15 d.

Systems Pharmacological Analysis of Paclitaxel-Mediated Tumor Priming That Enhances Nanocarrier Deposition and Efficacy

Paclitaxel (PAC)-mediated apoptosis decompresses and primes tumors for enhanced deposition of nanoparticulate agents such as pegylated liposomal doxorubicin (DXR). A quantitative pharmacokinetic/pharmacodynamic (PK/PD) approach was developed to analyze efficacy and identify optima for PAC combined with sterically stabilized liposome (SSL)-DXR. Using data extracted from diverse literature sources, Cremophor-paclitaxel (Taxol(®)) PK was described by a carrier-mediated dispositional model and SSL-DXR PK was described by a two-compartment model with first-order drug release. A hybrid-physiologic, well-stirred model with partition coefficients (Kp) captured intratumor concentrations. Apoptotic responses driving tumor priming were modeled using nonlinear, time-dependent transduction functions. The tumor growth model used net first-order growth and death rate constants, and two transit compartments that captured the temporal displacement of tumor exposure versus effect, and apoptotic signals from each agent were used to drive cytotoxic effects of the combination. The final model captured plasma and intratumor PK data, apoptosis induction profiles, and tumor growth for all treatments/sequences. A feedback loop representing PAC-induced apoptosis effects on Kp(_DXR) enabled the model to capture tumor-priming effects. Simulations to explore time- and sequence-dependent effects of priming indicated that PAC priming increased K(p_DXR) 3-fold. The intratumor concentrations producing maximal and half-maximal effects were 18 and 7.2 μg/ml for PAC, and 17.6 and 14.3 μg/ml for SSL-DXR. The duration of drug-induced apoptosis was 27.4 h for PAC and 15.8 h for SSL-DXR. Simulations suggested that PAC administered 24 h before peak priming could increase efficacy 2.5-fold over experimentally reported results. The quantitative approach developed in this article is applicable for evaluating tumor-priming strategies using diverse agents.

How emergence and death assumptions affect count‐based estimates of butterfly abundance and lifespan

AbstractTransect count data form the basis of many butterfly and other insect monitoring programs worldwide. A clear understanding of the limitations of such datasets, including the potential for biases in the statistical methods used to analyze them, is therefore crucial. The classical Zonneveld model (CZ) can extract estimates of a suite of demographic parameters from transect count datasets, and has also been used in theoretical analyses of protandry and reproductive asynchrony. The CZ relies on strong assumptions about the emergence and death processes underlying observed transect count datasets. Though reasonable as a starting place, a growing body of empirical evidence suggests these assumptions will, in many cases, not hold. Here, I explore how violations of these assumptions bias CZ‐based estimates of two key population parameters: total population size and mean individual lifespan. To do this, I generalize the Zonneveld model by relaxing the symmetrical emergence distribution and constant death rate assumptions such that the generalized models contain the CZ as a special case. Using the generalized models as data generating processes, I then show that the CZ is able to closely mimic the shape of the abundance time course produced by either variant of the generalized model under a wide range of conditions, but produces highly biased estimates of population size and mean lifespan in doing so. My analysis therefore demonstrates both that the CZ is not robust to violations of its emergence and death assumptions, and that a good observed fit to transect count data does not mean these assumptions are satisfied.

A Bayesian model for gene family evolution

BackgroundA birth and death process is frequently used for modeling the size of a gene family that may vary along the branches of a phylogenetic tree. Under the birth and death model, maximum likelihood methods have been developed to estimate the birth and death rate and the sizes of ancient gene families (numbers of gene copies at the internodes of the phylogenetic tree). This paper aims to provide a Bayesian approach for estimating parameters in the birth and death model.ResultsWe develop a Bayesian approach for estimating the birth and death rate and other parameters in the birth and death model. In addition, a Bayesian hypothesis test is developed to identify the gene families that are unlikely under the birth and death process. Simulation results suggest that the Bayesian estimate is more accurate than the maximum likelihood estimate of the birth and death rate. The Bayesian approach was applied to a real dataset of 3517 gene families across genomes of five yeast species. The results indicate that the Bayesian model assuming a constant birth and death rate among branches of the phylogenetic tree cannot adequately explain the observed pattern of the sizes of gene families across species. The yeast dataset was thus analyzed with a Bayesian heterogeneous rate model that allows the birth and death rate to vary among the branches of the tree. The unlikely gene families identified by the Bayesian heterogeneous rate model are different from those given by the maximum likelihood method.ConclusionsCompared to the maximum likelihood method, the Bayesian approach can produce more accurate estimates of the parameters in the birth and death model. In addition, the Bayesian hypothesis test is able to identify unlikely gene families based on Bayesian posterior p-values. As a powerful statistical technique, the Bayesian approach can effectively extract information from gene family data and thereby provide useful information regarding the evolutionary process of gene families across genomes.

Steep Increase in Best‐Practice Cohort Life Expectancy

We analyze trends in best-practice life expectancy among female cohorts born from 1870 to 1950. Cohorts experience declining rather than constant death rates, and cohort life expectancy usually exceeds period life expectancy. Unobserved mortality rates in non-extinct cohorts are estimated using the Lee-Carter model for mortality in 1960–2008. Best-practice cohort and period life expectancies increased nearly linearly. Across cohorts born from 1870 to 1920 the annual increase in cohort length of life was 0.43 years. Across calendar years from 1870 to 2008, the annual increase was 0.28 years. Cohort life expectancy increased from 53.7 years in the 1870 cohort to 83.8 years in the 1950 cohort. The corresponding cohort/period longevity gap increased from 1.2 to 10.3 years. Among younger cohorts, survival to advanced ages is substantially higher than could have been anticipated by period mortality regimes when these cohorts were young or middle-aged. A large proportion of the additional expected years of life are being lived at ages 65 and older. This substantially changes the balance between the stages of the life cycle.

An Individual Based Model of Arctic cod ( Boreogadus saida) early life in Arctic polynyas: II. Length-dependent and growth-dependent mortality

A bioenergetics individual based model (IBM) of early growth is used to investigate the relative importance of length-dependent and growth-dependent mortality during the early life (0–45 d) of Arctic cod in the Northeast Water (NEW) in 1993 and the North Water (NOW) in 1998. In the model, individual growth is forced by the observed temperature and prey concentration histories as prescribed by the hatch date of a larva. The IBM reproduced well the observed length-at-age and revealed large ontogenetic and interregional fluctuations in instantaneous growth. Four mortality scenarios were compared for each population: (1) constant mortality (estimated from catch-at-age data); (2) length-dependent mortality; (3) growth-dependent mortality; and (4) combined length- and growth-dependent mortality. Scenarios 2, 3, and 4 were parameterized to achieve the final survival produced by the constant mortality rates estimated from observations (scenario 1). Scenario 2 accounted well for declining mortality with size but not for the large variations in growth-dependent mortality. Scenario 3 failed to capture the decreasing vulnerability of surviving larvae to predation. Only scenario 4 accounted for both the large fluctuations in growth-dependent mortality and the progressive shift in dominance from length-dependent to growth-dependent mortality as the survivors increased in size. Sub-sampling the model output to reproduce the limited temporal resolution of sampling at sea improved the fit between observed and modeled frequencies-at-age, and pointed to the under-sampling of the smallest larvae as a major sampling bias.

Modal analysis of the deep-water solitary scleractinian, Desmophyllum dianthus, on SW Pacific seamounts: inferred recruitment periodicity, growth, and mortality rates

Little is known about the demography of corals inhabiting deep-sea features due to the logistical difficulties of working at the extreme depths they inhabit. To obtain basic information about growth, mortality, and recruitment dynamics for such a coral, we applied modal analysis to the size frequency distributions of live-caught and sub-fossil specimens of the widely distributed solitary cup coral, Desmophyllum dianthus, collected on SW Pacific seamounts. Comparison of live-caught material collected in 1997 and 2007–2009 indicated modal progression over time and an implied maximum age of approximately 190 years, which is similar to ages determined previously for D. dianthus using radiometric techniques. A log-linear decline in the number of individuals with increasing size further implies a constant adult mortality rate, of 15.1% per annum in 1997 and 9.2% per annum in 2007–2009. The spacing of size modes in the 2007–2009 samples suggests regularly episodic recruitment events, at 22- to 32-year intervals, which may relate to periodic variability in large-scale Southern Ocean circulation. Preliminary analyses of size frequency distributions of the sub-fossil material suggest that the trophodynamics, growth, and adult mortality schedules of D. dianthus in the SW Pacific have remained basically similar throughout the Holocene.

Modelling the effects of recent changes in climate, host density and acaricide treatments on population dynamics of Ixodes ricinus in the UK

Summary 1. A population model for the tick Ixodes ricinus, the most significant vector of pathogens in Europe, is used to explore the relative impact of changes in climate, host density and acaricide-treated hosts on tick abundance and seasonality. 2. A rise in temperature of the sort witnessed since 1989 speeds up the inter-stadial development of ticks, thereby reducing the cumulative effect of constant daily mortality rates and potentially raising population levels. The predicted earlier onset of tick-questing activity in the spring, due to stage-specific temperature thresholds, could increase contact between ticks and humans during recreational visits to the countryside in spring holidays. These tick population effects vary geographically with background climate. 3. The significant increase in deer abundance across Europe, including the UK, in recent decades is predicted to drive tick population increases, the effect varying with the initial density of hosts. In areas only recently colonized by deer, tick numbers are predicted to rise dramatically (given suitable climatic conditions). Where host densities are already high, however, further increases may reduce numbers of questing ticks; unfed ticks leave the questing population more rapidly, even though the overall tick population (and therefore pathogen transmission potential) increases. 4. Culling high-density deer populations as a control measure could, therefore, initially cause an apparent increase in questing ticks, with the predicted long-term population trajectory depending on the severity of the cull. 5. Conversely, the further addition of large hosts (e.g. sheep) would effectively reduce the number of questing ticks and therefore the risk to humans. If such sheep were treated with acaricide, tick populations are predicted to decrease rapidly, to an extent that depends on the relative abundance of wild (untreated) and treated hosts. Tick control in designated areas may be achieved by using sheep in this way as ‘lethal mops’, as used to occur in the past when sheep were regularly dipped. 6. Synthesis and applications. Both abiotic and biotic environmental changes witnessed recently could have contributed to apparent increases in tick populations, especially where these environmental factors were limiting in the past. The release of additional hosts treated with long-lasting acaricide is potentially an effective control strategy.

Better Catch Curves: Incorporating Age‐Specific Natural Mortality and Logistic Selectivity

AbstractCatch‐curve analysis is one of the simplest methods for stock assessment and is widely applied in data‐poor fisheries. Conventional catch‐curve methods rely on the strong assumptions of constant fishing and natural mortality rates above some fully selected age that is usually estimated by visually inspecting a plot of catch at age. Here, we evaluate the performance of three catch‐curve methods that relax or modify these assumptions by (1) estimating logistic selectivity parameters, (2) assuming Lorenzen‐form natural mortality (natural mortality that decreases with weight), and (3) using both methods simultaneously. We used simulation modeling and decision tables to compare estimates of fishing mortality from four catch‐curve methods, including the conventional method, across a variety of observable and unobservable data characteristics. We then applied the methods to catch‐at‐age data for Atlantic menhadenBrevoortia tyrannusfrom the U.S. South Atlantic fishery management region and compared the resulting estimates with published estimates of fishing mortality (F). In our simulation modeling, catch curves that estimated logistic selectivity parameters performed better than those derived by the conventional method when logistic selectivity was present. There was generally little difference in performance between estimates assuming constant natural mortality and those assuming Lorenzen natural mortality. The improvements from estimating selectivity parameters were particularly pronounced when the sample sizes for catch‐at‐age data were large: in those instances, estimating selectivity improved the estimation accuracy forFby nearly 20%. In our example involving Atlantic menhaden, estimates ofFassuming logistic selectivity were most similar to those of published stock assessments, which had previously estimated logistic selectivity at age. We recommend our logistic‐selectivity catch curve when selectivity is likely to be logistic because it improves accuracy at only a very small cost in terms of computational complexity.

Prey-Dependent Mortality Rate: A Critical Parameter in Microbial Models

Protozoa are key components of a wide range of ecosystems, but ecological models that incorporate these microbes often suffer from poor parameterisation, specifically of top-level predator loss rates. We (1) suggest that top-level predator mortality is prey-dependent, (2) provide a novel approach to assess this response, and (3) illustrate the ecological relevance of these findings. Ciliates, Paramecium caudatum (prey) and Didinium nasutum (predator), were used to evaluate predator mortality at varying prey levels. To assess mortality, multiple (>100) predators were individually examined (in 2-ml wells), daily (for 3 days), between 0 and 120 preys ml(-1). Data were used to determine non-linear mortality and growth responses over a range of prey abundances. The responses, plus literature data were then used to parameterise a predator-prey model, based on the Rosenzweig-MacArthur structure. The model assessed the impact of variable and three levels of constant (high, average and low) mortality rates on P. caudatum-D. nasutum population dynamics. Our method to determine variable mortality rate revealed a strong concave decline in mortality with increasing prey abundance. The model indicated: (1) high- and low-constant mortality rates yielded dynamics that deviate substantially from those obtained from a variable rate; (2) average mortality rate superficially produced dynamics similar to the variable rate, but there were differences in the period of predator-prey cycles, and the lowest abundance of prey and predators (by ~2 orders of magnitude). The differences between incorporating variable and constant mortality rate indicate that including a variable rate could substantially improve microbial-based ecological models.

Can Life Expectancy and QALYs Be Improved by a Framework for Deciding Whether to Apply Clinical Guidelines to Patients With Severe Comorbid Disease?

Guidelines with short-term harms and long-term benefits are often applied to chronically ill patients who may not benefit. The payoff time framework has been proposed (i.e., do not apply a guideline if a patient's life expectancy (LE) is shorter than when a guideline's cumulative incremental benefits first exceed its cumulative incremental harms), but its health impact is unclear. To investigate whether the payoff time framework improves LE and/or quality-adjusted life-years (QALY) for chronically ill patients. I evaluate impact of the payoff time framework on LE and QALYs, assuming (1) high and constant background mortality rate from chronic illness (≥ 10% per year), (2) immediate guideline-related harm with probability < 1, and (3) constant guideline-related benefit that occurs over an extended time. I apply the framework to questions of whether to screen chronically ill 50-year-old women for colorectal cancer using colonoscopy, and whether to advocate intensive glucose control for chronically ill diabetics. If a guideline's payoff time is greater than a patient's LE, then withholding that guideline will increase LE and QALYs for that patient. For a 50-year-old chronically ill woman with background mortality > 0.15 per year (corresponding to LE < 6.5 years), withholding CR screening will increase LE. For a diabetic with background mortality > 0.11 per year (corresponding to LE < 9.4 years), withholding CR screening will increase QALYs. The payoff time framework may indicate when withholding a guideline with short-term harms and long-term benefits may increase LE and/or QALY.

Malignes Melanom der Haut: beeinflusst die Krebsfrüherkennung Inzidenz und Mortalität?

The increase in incidence of malignant melanoma, early diagnosis activities increasingly reaching ever larger population groups and mortality remaining at a constant level in trend comprise the background of the study. We aimed at answering the question whether the early diagnosis can have an influence on the increase in incidence and how one can one judge the effect on the reduction of the mortality. The study is based on data from official tumour registries of the regions Saarland, Schleswig-Holstein, the administrative district Münster, the former GDR and the New Dfederal states (Berlin, Brandenburg, Mecklenburg-Vorpommern, Sachsen, Sachsen-Anhalt, Thüringen), as well as that of Queensland (Australia). Parallel to the increasing incidence, there is also an increase in the number of melanomas detected at early stages. Hence, it is obvious to assume that this increase in incidence is due to a large extent to screening programmes. In a non-determinable number of cases, overdiagnostics could have contributed to the increase in incidence. In the period of observation mortality remained constant in the regions described in this study. It can be assumed the mortality risk is influenced by tumours with a high degree of malignancy whose share in the number of melanomas remains roughly constant. The early diagnosis of cancer, the inclusion of increasingly larger groups of the populations in the regions described, and constant mortality rates for men and women during the period of observation all relate the use of early diagnosis. If the efficiency of population screening is measured against the outcome reduction of the mortality rate, it appears to be sufficient to continue cancer early detection according to SGB V § 25. A preventive check-up is indicated for risk groups, e. g., those with a positive familiar history or if potentially malignant skin alterations have been diagnosed.

Land-use legacies in the forest structure of silvopastoral oak woodlands in the Eastern Mediterranean

Eastern Mediterranean silvopastoral oak woodlands have been greatly damaged through forest conversion, illegal lumbering, overgrazing, and forest fires. The aim of this study was to assess land-use changes and the legacies that they have imprinted on the forest structure of Quercus macrolepis and accompanying Quercus pubescens and Quercus cerris woodlands on Lesvos Island, Greece. The size structures of adult oak populations were analyzed as indicators of long-term oak regeneration, while short-term recruitment was determined by counting oak seedlings and saplings. The size structure of the adult Q. macrolepis population was similar to the inverse J-shaped distribution typical for natural Mediterranean oak forests, indicating continuous recruitment with a constant mortality rate of mature individuals. Seedling and sapling densities were highly variable, but generally low in relation to adult oak densities. Recruitment of oak seedlings and saplings was positively related to determinants such as forest cover, adult oak density and basal area, woody plant richness, and litter cover. Both seedling and sapling occurrence were negatively associated with dung frequency, which suggests that sheep grazing imposes a barrier to oak recruitment. The study outlines a comprehensive land-use transition from the 1950 to 1970s, during which a complex and multifunctional agrosilvopastoral land-use system was simplified to an intensive grazing system. The discrepancy between the successful long-term regeneration and the less successful short-term recruitment of oaks illustrates that intensified livestock grazing has been a major driver of vegetation change. Grazing impact is likely to interact with increasing drought conditions, which may trigger a negative feedback cycle that undermines the capacity of woodlands to sustain ecosystem services.

Modelling annual individual-tree growth and mortality of Scots pine with data obtained at irregular measurement intervals and containing missing observations

An individual-tree growth model was developed with data from 54 permanent plots of Scots pine ( Pinus sylvestris L.) located in Galicia (northwestern Spain). The study involved two model fitting approaches, one considering constant growth and mortality rates in the period between two consecutive inventories, and another considering variable growth and mortality rates in the same period. The individual-tree growth model was based on annual basal area growth, height growth and survival probability. The model included variables from groups pertaining to tree size, competition and age. Weighted regression was used as a tool for dealing with missing height observations in model fitting. Evaluation of the model via simulation of growth and mortality in the period between inventories showed that the variable growth rate approach provided slightly better results than the constant growth rate approach. The final model was consistent with expected diameter growth, height growth, dominant height growth, stand basal area growth and reduction in number of stems per hectare.

Quasi-stationary distributions for structured birth and death processes with mutations

We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric space. Each individual can die or generate a new individual. The birth and death rates may depend on the environment through the action of the whole population. The offspring can have the same trait or can mutate to a randomly distributed trait. We assume that the population will be extinct almost surely. Our goal is the study, in this infinite dimensional framework, of quasi-stationary distributions when the process is conditioned on non-extinction. We firstly show in this general setting, the existence of quasi-stationary distributions. This result is based on an abstract theorem proving the existence of finite eigenmeasures for some positive operators. We then consider a population with constant birth and death rates per individual and prove that there exists a unique quasi-stationary distribution with maximal exponential decay rate. The proof of uniqueness is based on an absolute continuity property with respect to a reference measure.