Gradient and likelihood ratio tests in cure rate models

In some survival studies part of the population may be no longer subject to the event of interest. The called cure rate models take this fact into account. They have been extensively studied for several authors who have proposed extensions and applications in real lifetime data. Classic large sample tests are usually considered in these applications, especially the likelihood ratio. Recently a new test called gradient test has been proposed. The gradient statistic shares the same asymptotic properties with the classic likelihood ratio and does not involve knowledge of the information matrix, which can be an advantage in survival models. Some simulation studies have been carried out to explore the behavior of the gradient test in finite samples and compare it with the classic tests in different models. However little is known about the properties of these large sample tests in finite sample for cure rate models. In this work we performed a simulation study based on the promotion time model with Weibull distribution, to assess the performance of likelihood ratio and gradient tests in finite samples. An application is presented to illustrate the results

The role of heterogeneity in the population ecology and resilience of marine predator species

The marine environment is intrinsically linked to the biotic and abiotic processes that regulate the life support systems of the planet, including nutrient and hydrological cycling, climate patterns, geological processes, oxygen production, and nutritional resourcing. Long-term natural cycles in climate variation have pronounced impacts on weather systems, sea surface temperature and marine food webs. Spatial and temporal heterogeneity in these systems and processes can influence communities directly via modulation of survival, reproductive success, and the distribution of resources, and anthropogenic pressures can contribute to heterogeneity in natural systems, influencing bottom-up and top-down processes. For ecological communities regulated by top-down processes, climate-linked shifts in the distribution, population and community dynamics of predators are likely to have pronounced effects on ecosystem composition and function. The influence of environmental variability upon predator ecology is therefore an area of particular research focus. In marine habitats, spatial and temporal heterogeneity in sea surface temperature has been associated with changes to reproductive phenology in predator and prey species, while spatial and temporal heterogeneity in resource availability may be associated with changes in the survival rates of animals across developmental stages. Likewise, heterogeneity in the approach to data collection, management and analysis may influence the interpretation of results and guide subsequent management decisions. To investigate the role of heterogeneity in marine predator ecology I focus on two apex predators in the Irish Sea: the grey seal (Halichoerus grypus) and the Manx shearwater (Puffinus puffinus). I explore how temporal heterogeneity of environmental conditions may affect reproductive phenology, how spatial and temporal heterogeneity of data collection and analysis methods affects estimates of population dynamics, and how heterogeneity in survival at different developmental stages can be reflected in population-level dynamics. After providing an overview of the focus of my thesis in Chapter one, using multi-decade time series from eight major grey seal and Manx shearwater breeding sites, I use logistic population growth models and generalised additive models in Chapter two to explore how changes in the timing and progression of the grey seal pupping season are dependent on climatic drivers. In Chapters three and four I use matrix population models (MPM) to quantify the effects of data aggregation and substitution of missing model parameters upon estimates of population dynamics over multiple spatial and temporal scales. In Chapter five I then continue the application of MPMs to calculate indices of resilience in scenarios of perturbation, to explore the population-level effects of reduced survival in specific demographic groups, namely fledgling, juvenile and adult Manx shearwater. My results suggest that contemporaneous heterogeneity in broad- and local-scale climate indices is less influential to reproductive phenology than intrinsic drivers, and that variation in survival rates of year-one animals is largely explained by fine-scale spatial heterogeneity. The substitution of demographic information when parameterising population models introduced biases and uncertainty into projections of population dynamics, and the simulated reduction of survival in juvenile animals appeared to have a potential latent effect on population stability – the consequences of reduced juvenile survival being realised as a reduction in recruitment to the breeding adult population. Finally, in Chapter six I summarise the main findings of this mosaic of studies and discuss them in the context of existing research, to identify avenues for future research. These investigations highlight the need for intrinsic and spatial processes to be incorporated into studies of climatic drivers of ecological change, and the importance of ensuring the accuracy and appropriate collection, management and analysis of data sources. They also illustrate the potential population-level effects of perturbations to survival in demographic groups which can be logistically difficult to monitor, and act as a reminder that the challenging option is often the one that is necessary

Variable Selection in Discrete Survival Models Including Heterogeneity

Several variable selection procedures are available for continuous time-to-event data. However, if time is measured in a discrete way and therefore many ties occur models for continuous time are inadequate. We propose penalized likelihood methods that perform efficient variable selection in discrete survival modeling with explicit modeling of the heterogeneity in the population. The method is based on a combination of ridge and lasso type penalties that are tailored to the case of discrete survival. The performance is studied in simulation studies and an application to the birth of the first child

Local Adaptation of Reproductive Performance During Thermal Stress

Considerable evidence exists for local adaptation of critical thermal limits in ectotherms following adult temperature stress, but fewer studies have tested for local adaptation of sub-lethal heat stress effects across life history stages. In organisms with complex life cycles, such as holometablous insects, heat stress during juvenile stages may severely impact gametogenesis, having downstream consequences on reproductive performance that may be mediated by local adaptation, although this is rarely studied. Here, we tested how exposure to either benign or heat stress temperature during juvenile and adult stages, either independently or combined, influences egg-to-adult viability, adult sperm motility and fertility in high and low latitude populations of Drosophila subobscura. We found both population- and temperature-specific effects on survival and sperm motility; juvenile heat stress decreased survival and subsequent sperm motility and each trait was lower in the northern population. We found an interaction between population and temperature on fertility following application of juvenile heat stress; while fertility was negatively impacted in both populations, the southern population was less affected. When the adult stage was also subject to heat stress, the southern population exhibited positive carry-over effects whereas the northern population’s fertility remained low. Thus, the northern population is more susceptible to sub-lethal reproductive consequences following exposure to juvenile heat stress. This may be common in other organisms with complex life cycles and current models predicting population responses to climate change, which do not take into account the impact of juvenile heat stress on reproductive performance, may be too conservativeThis study was funded by the Natural Environment Research Council (NE/I013962/1)

Developing population models with data from marked individuals

Population viability analysis (PVA) is a powerful tool for biodiversity assessments, but its use has been limited because of the requirements for fully specified population models such as demographic structure, densitydependence, environmental stochasticity, and specification of uncertainties. Developing a fully specified population model from commonly available data sources -notably, mark-recapture studies -remains complicated due to lack of practical methods for estimating fecundity, true survival (as opposed to apparent survival), natural temporal variability in both survival and fecundity, density-dependence in the demographic parameters, and uncertainty in model parameters. We present a general method that estimates all the key parameters required to specify a stochastic, matrix-based population model, constructed using a long-term mark-recapture dataset. Unlike standard mark-recapture analyses, our approach provides estimates of true survival rates and fecundities, their respective natural temporal variabilities, and density-dependence functions, making it possible to construct a population model for long-term projection of population dynamics. Furthermore, our method includes a formal quantification of parameter uncertainty for global (multivariate) sensitivity analysis. We apply this approach to 9 bird species and demonstrate the feasibility of using data from the Monitoring Avian Productivity and Survivorship (MAPS) program. Bias-correction factors for raw estimates of survival and fecundity derived from markrecapture data (apparent survival and juvenile:adult ratio, respectively) were non-negligible, and corrected parameters were generally more biologically reasonable than their uncorrected counterparts. Our method allows the development of fully specified stochastic population models using a single, widely available data source, substantially reducing the barriers that have until now limited the widespread application of PVA. This method is expected to greatly enhance our understanding of the processes underlying population dynamics and our ability to analyze viability and project trends for species of conservation concern

Demographic estimation methods for plants with dormancy

Demographic studies in plants appear simple because unlike animals, plants do not run away. Plant individuals can be marked with, e.g., plastic tags, but often the coordinates of an idividual may be sufficient to identify it. Vascular plants in temperate latitudes have a pronounced seasonal life–cycle, so most plant demographers survey their study plots once a year often during or shortly after flowering. Life–states are pervasive in plants, hence the results of a demographic study for an individual can be summarized in a familiar encounter history, such as 0VFVVF000. A zero means that an individual was not seen in a year and a letter denotes its state for years when it was seen aboveground. V and F here stand for vegetative and flowering states, respectively. Probabilities of survival and state transitions can then be obtained by mere counting. Problems arise when there is an unobservable dormant state, i.e., when plants may stay belowground for one or more growing seasons. Encounter histories such as 0VF00F000 may then occur where the meaning of zeroes becomes ambiguous. A zero can either mean a dead or a dormant plant. Various ad hoc methods in wide use among plant ecologists have made strong assumptions about when a zero should be equated to a dormant individual. These methods have never been compared among each other. In our talk and in Kéry et al. (submitted), we show that these ad hoc estimators provide spurious estimates of survival and should not be used. In contrast, if detection probabilities for aboveground plants are known or can be estimated, capturerecapture(CR) models can be used to estimate probabilities of survival and state–transitions and the fraction of the population that is dormant. We have used this approach in two studies of terrestrial orchids, Cleistes bifaria (Kéry et al., submitted) and Cypripedium reginae (Kéry & Gregg, submitted) in West Virginia, U.S.A. For Cleistes, our data comprised one population with a total of 620 marked ramets over 10 years, and for Cypripedium, two populations with 98 and 258 marked ramets over 11 years. We chose the ramet (= single stem or shoot) as the demographic unit of our study since there was no way distinguishing among genets (genet = genetical individual, i.e., the "individual" that animal ecologists are mostly concerned with). This will introduce some non–independence into the data, which can nevertheless be dealt with easily by correcting variances for overdispersion. Using ramets instead of genets has the further advantage that individuals can be assigned to a state such as flowering or vegetative in an unambiguous manner. This is not possible when genets are the demographic units. In all three populations, auxiliary data was available to show that detection probability of aboveground plants was > 0.995. We fitted multistate models in program MARK by specifying three states (D, V, F), even though the dormant state D does not occur in the encounter histories. Detection probability is fixed at 1 for the vegetative (V) and the flowering state (F) and at zero for the dormant state (D). Rates of survival and of state transitions as well as slopes of covariate relationships can be estimated and LRT or the AIC machinery be used to select among models. To estimate the fraction of the population in the unobservable dormant state, the encounter histories are collapsed to 0 (plant not observed aboveground) and 1 (plant observed aboveground). The Cormack–Jolly–Seber model without constraints on detection probability is used to estimate detection probability, the complement of which is the estimated fraction of the population in the dormant state. Parameter identifiability is an important issue in multi state models. We used the Catchpole–Morgan–Freeman approach to determine which parameters are estimable in principle in our multi state models. Most of 15 tested models were indeed estimable with the notable exception of the most general model, which has fully interactive state- and time-dependent survival and state transition rates. This model would become identifiable if at least some plants would be excavated in years when they do not show up aboveground. Our analyses for three analyzed populations of Cleistes and Cypripedium yielded annual ramet survival rates ranging from 0.86–0.96. Estimates of the average fraction dormant ranged from 0.02–0.30, but with up to half a population in the dormant state in some years. Ultrastructural modeling enables interesting hypotheses to be tested about the relationships of demographic rates with climatic covariates for instance. Such covariate modeling makes the CR approach particularly interesting for evolutionary–ecological questions about, e.g., the adaptive significance of the dormant state. Previous and foreseeable future applications of CR in plant ecology Since the paper by Alexander et al. (1997), it has become increasingly clear that CR models may be useful for demographic analysis of plant populations. In the future, we are likely to see increasing use of these methods that were originally developed for animal populations. Here is a summary about all previous applications that I have come across. I am grateful if readers point out to me any titles that I may have missed. If a reliable way to mark seeds can be devised, CR might indeed provide the analysis tool for tackling one of the ultimate frontiers in plant population ecology: the dynamics of the seed bank. Indeed, the first ever application of CR to plants that I have come across (Naylor, 1972) used a fluorescent dye to mark seeds and a Lincoln–Peterson–type estimator to estimate the seed bank size in an agricultural weed. The application of CR to plants with dormancy has been treated by hefferson et al. (2001, 2003), Kéry et al. (submitted) and Kéry & Gregg (submitted). Population size, and survival rates of plants whose aboveground states are easily overlooked have been estimated for an elusive prairie plant (Alexander et al., 1997; Slade et al., 2003) and for a tropical savannah tree (Lahoreau et al., 2003). For plot–based plant demographic studies, we have shown previously that (not surprisingly) different life–states may have different detection probabilities, and that this may seriously bias inference from population modelling (Kéry & Gregg, 2003). It is somewhat astonishing that there still appear to be no applications of CR to the analysis of plant populations and communities. For instance, species richness, patch occupancy, population extinction rates, and species turnover in communities are all still based on adding up the raw data, even though the animal literature has plenty of papers showing more adequate ways of estimating these quantities (e.g., Boulinier et al., 1998; Nichols et al., 1998). I have submitted a note (Kéry, submitted) describing the use of the Cormack–Jolly–Seber model to estimate extinction probabilities for plant populations in a manner exactly analogous to patch occupancy models (MacKenzie et al., 2002, 2003). It is perhaps in plant community ecology where we will see most future applications of CR

Investigating the Epidemiology of bovine Tuberculosis in the European Badger

Global health is becoming increasingly reliant on our understanding and management of wildlife disease. An estimated 60% of emerging infectious diseases in humans are zoonotic and with human-wildlife interactions set to increase as populations rise and we expand further into wild habitats there is pressure to seek modelling frameworks that enable a deeper understanding of natural systems. Survival and mortality are fundamental parameters of interest when investigating the impact of disease with far reaching implications for species conservation, management and control. Survival analysis has traditionally been dominated by non- and semi-parametric methods but these can sometimes miss subtle yet important dynamics. Survival and mortality trajectory analysis can alleviate some of these problems by fitting fully parametric functions that describe lifespan patterns of mortality and survival. In the first part of this thesis we investigate the use of survival and mortality trajectories in epidemiology and uncover novel patterns of age-, sex- and infection-specific mortality in a wild population of European badgers (Meles meles) naturally infected with Mycobacterium bovis, the causative agent of bovine tuberculosis (bTB). Limitations of dedicated software packages to conduct such analyses led us to investigate alternative methods to build models from first principles and we found the NIMBLE package to offer an attractive blend of flexibility and speed. We create a novel parameterisation of the Siler model to enable more flexible model specification but encounter the common problem of competing models having comparable fits to the data. Multi-model inference approaches can alleviate some of these issues but require efficient methods to carry out model comparisons; we present an approach based on the estimation of the marginal likelihood through importance sampling and demonstrate its application through a series of simulation- and case-studies. The approach works well for both census and capture-mark-recapture (CMR) data, both of which are common within ecological research, but we uncover challenges in recording and modelling early life mortality dynamics that occur as a result of the CMR sampling process. The final part of the thesis looks at another alternative approach for model comparison that doesn’t require direct estimation of the marginal likelihood, Reversible Jump Markov Chain Monte Carlo (RJMCMC), which is particularly efficient when models to be compared are nested and the problem can reduce to one of variable selection. In the final chapter we carry out an investigation of age-, sex-, infection- and inbreeding-specific variation in survival and mortality in a wild population of European badgers naturally infected with bovine Tuberculosis. Using the methods and knowledge presented through the earlier chapters of this thesis we uncover patterns of mortality consistent with both the mutation accumulation and antagonistic pleiotropy theories of senescence but most interestingly uncover antagonistic pleiotropic effects of inbreeding on age-specific mortality in a wild population for the first time. This thesis provides a number of straightforward approaches to Bayesian survival analysis that are widely applicable to ecological research and can offer greater insight and uncover subtle patterns of survival and mortality that traditional methods can overlook. Our investigation into the epidemiology of bovine Tuberculosis and in particular the effects of inbreeding have far-reaching implications for the control of this disease. This research can also inform future conservation efforts and management strategies as all species are likely to be at increasing risk of inbreeding in an age of dramatic global change, rapid habitat loss and isolation