Continuous-discrete models of the dynamics of an isolated population and of 2 competing species

The paper presents the analysis of various mathematical models for dynamics of isolated population and for competition between two species. It is assumed that mortality is continuous and birth of individuals of new generations takes place in certain fixed moments. Influence of winter upon the population dynamics and conditions of classic discrete model "deduction" of population dynamics (in particular, Moran-Ricker and Hassel's models) are investigated. Dynamic regimes of models under various assumptions about the birth and death rates upon the population states are also examined. Analysis of models of isolated population dynamics with nonoverlapping generations showed the density changes regularly if the birth rate is constant. Moreover, there exists a unique global stable level and population size stabilizes asymptotically at this equilibrium, i.e. cycle and chaotic regimes in various discrete models depend on correlation between individual productivity and population state in previous time. When the correlation is exponential upon mean population size the discrete Hassel model is realized. Modification of basis model, based on the assumption that during winter survival/death changes are constant, showed that population size at global level is stable. Generally, the dependence of population rate upon "winter parameters" has nonlinear character. Nonparametric models of competition between two species does not vary if the individual productivity is constant. In a phase space there are several stable stationary states and population stabilizes at one or other level asymptotically. So, in discrete models of competition between two species oscillation can be explained by dependence of population growth rate on the population size at previous times.     

Neurotrophins and cell death

The neurotrophins - NGF, BDNF, NT-3 - are secreted proteins that play a major role in neuron survival, differentiation and axon wiring toward target territories. They do so by interacting with their main tyrosine kinase receptors TrkA, TrkB, TrkC and p75(NTR). Even though there is a general consensus on the view that neurotrophins are survival factors, there are two fundamentally different views on how they achieve this survival activity. One prevailing view is that all neurons and more generally all normal cells are naturally committed to die unless a survival factor blocks this death. This death results from the engagement of a "default" apoptotic cell program. The minority report supports, on the opposite, that neurotrophin withdrawal is associated with an active signal of cell death induced by unbound dependence receptors. We will discuss here how neurotrophins regulate cell death and survival and how this has implications not only during nervous system development but also during cancer progression.     

On maximum likelihood solutions for exponential survival models

"Stochastic survival models which adjust for covariate information have been developed by Beck (1979). These models can include one or two living states and several competing death states. The transitions between stages are assumed irreversible and the transition intensity functions are assumed to be independent of time but dependent upon the covariates." Explicit solutions of the maximum likelihood equations for such models when there are one or two dichotomous covariates are presented. Applications of these models to the case of heart transplants and lung cancer are discussed, and survival in two or four groups is compared. (summary in FRE)     

A spatial open-population capture-recapture model

A spatial open-population capture-recapture model is described that extends both the non-spatial open-population model of Schwarz and Arnason and the spatially explicit closed-population model of Borchers and Efford. The superpopulation of animals available for detection at some time during a study is conceived as a two-dimensional Poisson point process. Individual probabilities of birth and death follow the conventional open-population model. Movement between sampling times may be modeled with a dispersal kernel using a recursive Markovian algorithm. Observations arise from distance-dependent sampling at an array of detectors. As in the closed-population spatial model, the observed data likelihood relies on integration over the unknown animal locations; maximization of this likelihood yields estimates of the birth, death, movement, and detection parameters. The models were fitted to data from a live-trapping study of brushtail possums (Trichosurus vulpecula) in New Zealand. Simulations confirmed that spatial modeling can greatly reduce the bias of capture-recapture survival estimates and that there is a degree of robustness to misspecification of the dispersal kernel. An R package is available that includes various extensions.     

Nonhomogeneous birth and death models for epidemic outbreak data

In this paper, generalized nonlinear models are proposed in order to incorporate the following considerations in modeling an epidemic disease outbreak statistically. (1) The dependence of the data is handled with a nonhomogeneous death or a nonhomogeneous birth process. (2) The first stage of the outbreak is described with an epidemic susceptibles-infectives-removed (SIR) model. Soon the control measures taken will dominate the process. These measures are in addition to the natural epidemic removal process. The prevalence is related to the censored infection times in such a way that the distribution function and thus the survival function satisfy approximately the first equation of the SIR model. This leads in a natural way to the Burr family of distributions. (3) The nonhomogeneous birth process handles the fact that in practice, with some delay, infecteds are registered, but not susceptibles. (4) Finally, the ending of the epidemic caused by the measures taken is incorporated through a modification of the survival function with a final-size parameter, in the same way as is done in long-term survival models. These models are applied to three outbreaks: The Dutch classical swine fever outbreak from 1997 to 1998, the foot- and-mouth disease outbreak in Great Britain from 2001, and the Dutch avian influenza (H7N7) outbreak from 2003.     

Relevance of motoneuron specification and programmed cell death in embryos to therapy of ALS

The molecular cues that generate spinal motoneurons in early embryonic development are well defined. Motoneurons are generated in excess and consequently undergo a natural period of programmed cell death. Although it is not known exactly how motoneurons compete for survival in embryonic development, it is hypothesized that they rely on the ability to access limited amounts of trophic factors from peripheral tissues, a process that is tightly regulated by skeletal muscle activity. Attempts to elucidate the molecular mechanisms that underlie motoneuron generation and programmed cell death in embryos have led to various effective strategies for treating injury and disease in animal models. Such studies provide great hope for the amelioration of human amyotrophic lateral sclerosis (ALS), a devastating progressive motoneuron degenerative disease. Here we review the clinical relevance of studying motoneuron specification and death during embryonic development.     

A note on life tables and nonlinear death processes

This note is viewing survival data of a natural cohort as being generated by a possibly nonlinear, nonhomogeneous death process. It proves that the usual conditional distributions of the number of survivors at a certain age are binomial if and only if the death process is linear. Thus the customary statistical methods for the analysis of life table data are, strictly speaking, invalid whenever the underlying death process is nonlinear. For example, if a contagious disease is the cause of some or all of the deaths, the deaths will not be independent and the death process, not linear. One should then base the statistical analysis on a model for the spread of the disease rather than the routine binomial model.     

Cell death by autophagy: facts and apparent artefacts

Autophagy (the process of self-digestion by a cell through the action of enzymes originating within the lysosome of the same cell) is a catabolic process that is generally used by the cell as a mechanism for quality control and survival under nutrient stress conditions. As autophagy is often induced under conditions of stress that could also lead to cell death, there has been a propagation of the idea that autophagy can act as a cell death mechanism. Although there is growing evidence of cell death by autophagy, this type of cell death, often called autophagic cell death, remains poorly defined and somewhat controversial. Merely the presence of autophagic markers in a cell undergoing death does not necessarily equate to autophagic cell death. Nevertheless, studies involving genetic manipulation of autophagy in physiological settings provide evidence for a direct role of autophagy in specific scenarios. This article endeavours to summarise these physiological studies where autophagy has a clear role in mediating the death process and discusses the potential significance of cell death by autophagy.     

Apoptosis meets autophagy-like cell death in the ischemic penumbra: Two sides of the same coin?

Autophagy is a homeostatic cellular process required for the recycling of proteins and damaged organelles, and in most scenarios is believed to promote cell survival. However, there is accumulating evidence that under certain pathological situations, autophagy can also trigger and mediate programmed cell death (type II death). Despite the well-established pathophysiological role of apoptosis (type I cell death) in post-ischemic neuron death, there is now increasing interest whether alternative types of programmed cell death might be involved in regulation of neuronal death after both global and focal cerebral ischemia. Initial studies demonstrating the involvement of lysosomal proteases of the cathepsin family in neuron death after global ischemia already had suggested that this type of cell death may occur in an autophagy-dependent manner. Recently it was also shown that focal ischemia is associated with potently enhanced expression of the autophagy regulator Beclin 1 and subcellular redistribution of the autophagic marker LC3 to vacuolic structures in ischemic neurons. Increasing evidence suggests that the effects of autophagy are highly contextual. An insufficient autophagic response might render cells more susceptible to stress conditions whereas on the other hand prolonged overactivation of autophagy can lead to a complete self digestion of the cell. The extent of autophagy may represent a master switch between cell survival and cell death, and it will be of fundamental importance to dissect whether autophagy is primarily a strategy for survival or whether autophagy can also be a part of a cell death program and thus contribute to cell death after cerebral ischemia. A profound understanding of the biological effects and the mechanisms underlying ischemia-induced autophagy in neurons might be helpful in seeking effective new treatments for cerebral ischemia.     

Apoptosis meets autophagy-like cell death in the ischemic penumbra: Two sides of the same coin?

Autophagy is a homeostatic cellular process required for the recycling of proteins and damaged organelles, and in most scenarios is believed to promote cell survival. However, there is accumulating evidence that under certain pathological situations, autophagy can also trigger and mediate programmed cell death (type II death). Despite the well-established pathophysiological role of apoptosis (type I cell death) in post-ischemic neuron death, there is now increasing interest whether alternative types of programmed cell death might be involved in regulation of neuronal death after both global and focal cerebral ischemia. Initial studies demonstrating the involvement of lysosomal proteases of the cathepsin family in neuron death after global ischemia already had suggested that this type of cell death may occur in an autophagy-dependent manner. Recently it was also shown that focal ischemia is associated with potently enhanced expression of the autophagy regulator Beclin 1 and subcellular redistribution of the autophagic marker LC3 to vacuolic structures in ischemic neurons. Increasing evidence suggests that the effects of autophagy are highly contextual. An insufficient autophagic response might render cells more susceptible to stress conditions whereas on the other hand prolonged overactivation of autophagy can lead to a complete self digestion of the cell. The extent of autophagy may represent a master switch between cell survival and cell death, and it will be of fundamental importance to dissect whether autophagy is primarily a strategy for survival or whether autophagy can also be a part of a cell death program and thus contribute to cell death after cerebral ischemia. A profound understanding of the biological effects and the mechanisms underlying ischemia-induced autophagy in neurons might be helpful in seeking effective new treatments for cerebral ischemia.     

The effect of maternal care on child survival: a demographic, genetic, and evolutionary perspective

Models of population dynamics generally assume that child survival is independent of maternal survival. However, in humans, the death of a mother compromises her immature children's survival because children require postnatal care. A child's survival therefore depends on her mother's survival in years following her birth. Here, we provide a model incorporating this relationship and providing the number of children surviving until maturity achieved by females at each age. Using estimates of the effect that a mother's death has on her child's survival until maturity, we explore the effect of the model on population dynamics. Compared to a model that includes a uniform child survival probability, our model slightly raises the finite rate of increase lambda and modifies generation time and the stable age structure. We also provide estimates of selection on alleles that change the survival of females. Selection is higher at all adult ages in our model and remains significant after menopause (at ages for which the usual models predict neutrality of such alleles). Finally, the effect of secondary caregivers who compensate maternal care after the death of a mother is also emphasized. We show that allocare (as an alternative to maternal care) can have a major effect on population dynamics and is likely to have played an important role during human evolution.     

Autoregressive models for capture-recapture data: a Bayesian approach

In this article, we incorporate an autoregressive time-series framework into models for animal survival using capture-recapture data. Researchers modeling animal survival probabilities as the realization of a random process have typically considered survival to be independent from one time period to the next. This may not be realistic for some populations. Using a Gibbs sampling approach, we can estimate covariate coefficients and autoregressive parameters for survival models. The procedure is illustrated with a waterfowl band recovery dataset for northern pintails (Anas acuta). The analysis shows that the second lag autoregressive coefficient is significantly less than 0, suggesting that there is a triennial relationship between survival probabilities and emphasizing that modeling survival rates as independent random variables may be unrealistic in some cases. Software to implement the methodology is available at no charge on the Internet.     

Improving the reporting of cancer-specific mortality and survival in research using cancer registry data

Population-based registries are increasingly used in cancer research. In such studies, cancer-specific mortality or survival is frequently used as the primary outcome. To determine whether a putative cancer was part of the causal chain of events leading to death, cancer registries primarily rely on death certificates. Hence, they depend on the subjective interpretation of information available to medical examiners at the time of death. Misclassification may occur: studies report misclassification of cancer as a cause of death in 15%–35% of death certificates based on evaluation by expert panels and/or autopsy reports. Further misclassification may occur when coding death causes in the cancer registry. Researchers should be aware of potential misclassification bias when using cancer registry data. Differential misclassification may bias the results towards or away from the null hypothesis, depending on whether there is relative over- or under-reporting of cancer-related deaths in one group. Strategies to improve reporting of cancer-specific survival/mortality include (1) describing the procedure used to identify cancer-specific deaths; (2) considering the use of multiple definitions of cancer-related deaths (strict/liberal definitions of cancer-specific deaths, and/or addition of relative survival as an outcome); and (3) reporting cancer-specific survival/mortality together with the objectively measured parameters overall survival or all-cause mortality.     

Multiple imputation for estimating the risk of developing dementia and its impact on survival

Dementia, Alzheimer's disease in particular, is one of the major causes of disability and decreased quality of life among the elderly and a leading obstacle to successful aging. Given the profound impact on public health, much research has focused on the age-specific risk of developing dementia and the impact on survival. Early work has discussed various methods of estimating age-specific incidence of dementia, among which the illness-death model is popular for modeling disease progression. In this article we use multiple imputation to fit multi-state models for survival data with interval censoring and left truncation. This approach allows semi-Markov models in which survival after dementia depends on onset age. Such models can be used to estimate the cumulative risk of developing dementia in the presence of the competing risk of dementia-free death. Simulations are carried out to examine the performance of the proposed method. Data from the Honolulu Asia Aging Study are analyzed to estimate the age-specific and cumulative risks of dementia and to examine the effect of major risk factors on dementia onset and death.     

Modelling the growth,survival and death of Listeria monocytogenes

In this paper, the predictive microbiology approach has been generalized to the study of growth, survival and death of Listeria monocytogenes. As this micro-organism is involved in food poisoning, its growth, survival and death were studied as functions of low temperatures, NaCl and phenol compounds, in a synthetic medium, by a factorially designed experiment. A significant inactivation of L. monocytogenes was obtained with 20 ppm of phenol and 4% (w/v) NaCl at temperatures from 4 to 12 degrees C. An empirical model is proposed to describe, in a single step, the biomass profile vs studied factors. Thereby, the influence of temperature, NaCl and phenol concentration on L. monocytogenes biomass quantity (0.5-8 log cfu ml(-1)) are presented as a function of storage duration. The comparisons of the proposed model with existing models (Gompertz for growth, vitalistic for survival and death) were performed. The use of a single equation allows the prediction of contamination levels in all experimental conditions without knowledge a priori. The model offers considerable prospects for its use in food microbiology.     

Involvement of capacitive calcium entry and calcium store refilling in osteoclastic survival and bone resorption process

Bone resorption is closely dependent on osteoclastic survival and osteoclast apoptotic cell death could represent a key step at the end of this process. In order to precise the possible role of calcium movement in osteoclastic cell death, we investigated whether intracellular calcium store replenishment and capacitive calcium entry (CCE) are involved in osteoclastic survival and bone resorption. We demonstrate that (i). thapsigargin, a sarco-endoplasmic reticulum calcium ATPase pump (SERCA) blocker, decreases both osteoclastic survival and bone resorption process, (ii). 2-aminoethoxydiphenyl borate (2-APB) and SKF-96365, two store-operated channel (SOC) blockers, dramatically decrease osteoclastic survival and bone resorption and (iii). culture in calcium-free medium and thapsigargin exposure synergically inhibit osteoclastic survival which falls dramatically to a value close to 0% (P<0.001). Inversely, osteoclastic survival increases significantly when thapsigargin-treated cells are cultured in the presence of 20mM calcium, suggesting that increasing extracellular calcium concentration stimulates osteoclasts survival when the filling of intracellular stores is prevented. Taken together, our data strongly suggest that in osteoclasts, calcium movements between cellular compartments involved in the regulation of calcium signalling, such as calcium stores refilling and CCE, are closely associated to the regulation of osteoclast survival and bone resorption.     

Lobe and Serrate are required for cell survival during early eye development in Drosophila

Organogenesis involves an initial surge of cell proliferation, leading to differentiation. This is followed by cell death in order to remove extra cells. During early development, there is little or no cell death. However, there is a lack of information concerning the genes required for survival during the early cell-proliferation phase. Here, we show that Lobe (L) and the Notch (N) ligand Serrate (Ser), which are both involved in ventral eye growth, are required for cell survival in the early eye disc. We observed that the loss-of-ventral-eye phenotype in L or Ser mutants is due to the induction of cell death and the upregulation of secreted Wingless (Wg). This loss-of-ventral-eye phenotype can be rescued by (i) increasing the levels of cell death inhibitors, (ii) reducing the levels of Hid-Reaper-Grim complex, or (iii) reducing canonical Wg signaling components. Blocking Jun-N-terminal kinase (JNK) signaling, which can induce caspase-independent cell death, significantly rescued ventral eye loss in L or Ser mutants. However, blocking both caspase-dependent cell death and JNK signaling together showed stronger rescues of the L- or Ser-mutant eye at a 1.5-fold higher frequency. This suggests that L or Ser loss-of-function triggers both caspase-dependent and -independent cell death. Our studies thus identify a mechanism responsible for cell survival in the early eye.     

Apoptosis: Programmed cell death in health and disease

Apoptosis is a normal physiological cell death process of eliminating unwanted cells from living organisms during embryonic and adult development. Apoptotic cells are characterised by fragmentation of nuclear DNA and formation of apoptotic bodies. Genetic analysis revealed the involvement of many death and survival genes in apoptosis which are regulated by extracellular factors. There are multiple inducers and inhibitors of apoptosis which interact with target cell specific surface receptors and transduce the signal by second messengers to programme cell death. The regulation of apoptosis is elusive, but defective regulation leads to aetiology of various ailments. Understanding the molecular mechanism of apoptosis including death genes, death signals, surface receptors and signal pathways will provide new insights in developing strategies to regulate the cell survival/death. The current knowledge on the molecular events of apoptotic cell death and their significance in health and disease is reviewed.     

Demographic estimation methods for plants with unobservable life-states

Demographic estimation of vital parameters in plants with an unobservable dormant state is complicated, because time of death is not known. Conventional methods assume that death occurs at a particular time after a plant has last been seen aboveground but the consequences of assuming a particular duration of dormancy have never been tested. Capture–recapture methods do not make assumptions about time of death; however, problems with parameter estimability have not yet been resolved. To date, a critical comparative assessment of these methods is lacking. We analysed data from a 10 year study of Cleistes bifaria, a terrestrial orchid with frequent dormancy, and compared demographic estimates obtained by five varieties of the conventional methods, and two capture–recapture methods. All conventional methods produced spurious unity survival estimates for some years or for some states, and estimates of demographic rates sensitive to the time of death assumption. In contrast, capture–recapture methods are more parsimonious in terms of assumptions, are based on well founded theory and did not produce spurious estimates. In Cleistes, dormant episodes lasted for 1–4 years (mean 1.4, SD 0.74). The capture–recapture models estimated ramet survival rate at 0.86 (SE～0.01), ranging from 0.77–0.94 (SEs≤0.1) in any one year. The average fraction dormant was estimated at 30% (SE 1.5), ranging 16–47% (SEs≤5.1) in any one year. Multistate capture–recapture models showed that survival rates were positively related to precipitation in the current year, but transition rates were more strongly related to precipitation in the previous than in the current year, with more ramets going dormant following dry years. Not all capture–recapture models of interest have estimable parameters; for instance, without excavating plants in years when they do not appear aboveground, it is not possible to obtain independent time‐specific survival estimates for dormant plants. We introduce rigorous computer algebra methods to identify the parameters that are estimable in principle. As life‐states are a prominent feature in plant life cycles, multistate capture–recapture models are a natural framework for analysing population dynamics of plants with dormancy.