Matrix models and sensitivity analysis of populations classified by age and stage : a vec-permutation matrix approach

© The Author(s), 2011. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Theoretical Ecology 5 (2012): 403-417, doi:10.1007/s12080-011-0132-2.Matrix population models in which individuals are classified by both age and stage can be constructed using the vec-permutation matrix. The resulting age-stage models can be used to derive the age-specific consequences of a stage-specific life history or to describe populations in which the vital rates respond to both age and stage. I derive a general formula for the sensitivity of any output (scalar, vector, or matrix-valued) of the model, to any vector of parameters, using matrix calculus. The matrices describing age-stage dynamics are almost always reducible; I present results giving conditions under which population growth is ergodic from any initial condition. As an example, I analyze a published stage-specific model of Scotch broom (Cytisus scoparius), an invasive perennial shrub. Sensitivity analysis of the population growth rate finds that the selection gradients on adult survival do not always decrease with age but may increase over a range of ages. This may have implications for the evolution of senescence in stage-classified populations. I also derive and analyze the joint distribution of age and stage at death and present a sensitivity analysis of this distribution and of the marginal distribution of age at death.This research was supported by National Science Foundation Grant DEB-0816514 and by a Research Award from the Alexander von Humboldt Foundation

Relative nutritional quality of C 3 and C 4 grasses for a graminivorous lepidopteran, Paratrytone melane (Hesperiidae)

We tested the hypothesis that C 4 grasses are inferior to C 3 grasses as host plants for herbivorous insects by measuring the relative performance of larvae of a graminivorous lepidopteran, Paratrytone melane (Hesperiidae), fed C 3 and C 4 grasses. Relative growth rates and final weights were higher in larvae fed a C 3 grass in Experiment I. However, in two additional experiments, relative growth rates and final weights were not significantly different in larvae fed C 3 and C 4 grasses. We examined two factors which are believed to cause C 4 grasses to be of lower nutritional value than C 3 grasses: foliar nutrient levels and nutrient digestibility. In general, foliar nutrient levels were higher in C 3 grasses. In Experiment I, protein and soluble carbohydrates were digested from a C 3 and a C 4 grass with equivalent efficiencies. Therefore, differences in larval performance are best explained by higher nutrient levels in the C 3 grass in this experiment. In Experiment II, soluble carbohydrates were digested with similar efficiencies from C 3 and C 4 grasses but protein was digested with greater efficiency from the C 3 grasses. We conclude (1) that the bundle sheath anatomy of C 4 grasses is not a barrier to soluble carbohydrate digestion and does not have a nutritionally significant effect on protein digestion and (2) that P. melane may consume C 4 grasses at compensatory rates.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47798/1/442_2004_Article_BF00317268.pd

Analysis of lethal and sublethal impacts of environmental disasters on sperm whales using stochastic modeling

Mathematical models are essential for combining data from multiple sources to quantify population endpoints. This is especially true for species, such as marine mammals, for which data on vital rates are difficult to obtain. Since the effects of an environmental disaster are not fixed, we develop time-varying (nonautonomous) matrix population models that account for the eventual recovery of the environment to the pre-disaster state. We use these models to investigate how lethal and sublethal impacts (in the form of reductions in the survival and fecundity, respectively) affect the population’s recovery process. We explore two scenarios of the environmental recovery process and include the effect of demographic stochasticity. Our results provide insights into the relationship between the magnitude of the disaster, the duration of the disaster, and the probability that the population recovers to pre-disaster levels or a biologically relevant threshold level. To illustrate this modeling methodology, we provide an application to a sperm whale population. This application was motivated by the 2010 Deepwater Horizon oil rig explosion in the Gulf of Mexico that has impacted a wide variety of species populations including oysters, fish, corals, and whales

Lung cancer diagnosed following emergency admission: a mixed methods study protocol to improve understanding of patients’ characteristics, needs, experiences and outcomes

Background Lung cancer is the leading cause of death from cancer in England. About 40% of patients with lung cancer are diagnosed following an emergency admission (DFEA) to hospital. DFEA is more common in women, and more likely with increasing age and deprivation. Most have advanced disease and survival is poor, but little else is known about this group. The aim of this study is to obtain a detailed understanding of the characteristics, needs, experiences and outcomes of this group. Methods/Design This is a single centre study with quantitative and qualitative work packages (WP). WP1 gathers basic details about all patients diagnosed with lung cancer during a 12 month period, focusing on demographics, diagnostic and treatment pathways and selected outcomes. WP2 obtains information from those patients DFEA or, when unable, their carers, about their holistic needs and experiences, using the Sheffield Profile for Assessment and Referral to Care questionnaire and selected questions from the National Cancer Patient Experience Survey. WP3 uses in-depth qualitative interviews with patients and carers to obtain detailed accounts of their symptoms, help-seeking behaviours prior to admission and subsequent experiences of care. Discussion Relatively little is known about the experiences of lung cancer patients DFEA and this study will provide detailed information about their needs, characteristics, experiences and outcomes. It should identify areas in the diagnostic and treatment pathway where there is scope to improve the care provided to this group of patients and their carers. The findings will also inform the need for further focused research

Age- and Sex-Specific Mortality Patterns in an Emerging Wildlife Epidemic: The Phocine Distemper in European Harbour Seals

Analyses of the dynamics of diseases in wild populations typically assume all individuals to be identical. However, profound effects on the long-term impact on the host population can be expected if the disease has age and sex dependent dynamics. The Phocine Distemper Virus (PDV) caused two mass mortalities in European harbour seals in 1988 and in 2002. We show the mortality patterns were highly age specific on both occasions, where young of the year and adult (>4 yrs) animals suffered extremely high mortality, and sub-adult seals (1–3 yrs) of both sexes experienced low mortality. Consequently, genetic differences cannot have played a main role explaining why some seals survived and some did not in the study region, since parents had higher mortality levels than their progeny. Furthermore, there was a conspicuous absence of animals older than 14 years among the victims in 2002, which strongly indicates that the survivors from the previous disease outbreak in 1988 had acquired and maintained immunity to PDV. These specific mortality patterns imply that contact rates and susceptibility to the disease are strongly age and sex dependent variables, underlining the need for structured epidemic models for wildlife diseases. Detailed data can thus provide crucial information about a number of vital parameters such as functional herd immunity. One of many future challenges in understanding the epidemiology of the PDV and other wildlife diseases is to reveal how immune system responses differ among animals in different stages during their life cycle. The influence of such underlying mechanisms may also explain the limited evidence for abrupt disease thresholds in wild populations

Demographic responses of Daphnia magna fed transgenic Bt-maize

The food/feed quality of a variety of genetically modified (GM) maize expressing Cry1Ab Bt-toxin was tested over the life-cycle of Daphnia magna, an arthropod commonly used as model organism in ecotoxicological studies. Demographic responses were compared between animals fed GM or unmodified (UM) near isogenic maize, with and without the addition of predator smell. Age-specific data on survival and birth rates were integrated and analysed using life tables and Leslie matrices. Survival, fecundity and population growth rate (PGR) data generally disfavoured transgenic Bt-maize as feed for D. magna compared to animals fed the unmodified (UM) near isogenic line of maize. Decomposition of age-specific effects revealed that the most important contributions to a reduced PGR in the GM-fed group came from both fecundity and survival differences early in life. We conclude that juvenile and young adult stages are the most sensitive experimental units and should be prioritized in future research. These stages are often omitted in toxicological/ecotoxicological studies and in feeding trials

Optimization of Control Strategies for Non-Domiciliated Triatoma dimidiata, Chagas Disease Vector in the Yucatán Peninsula, Mexico

Chagas disease is the most important vector-borne disease in Latin America. Residual insecticide spraying has been used successfully for the elimination of domestic vectors in many regions. However, some vectors of non-domestic origin are able to invade houses, and they are now a key challenge for further disease control. We developed a mathematical model to predict the temporal variations in abundance of non-domiciliated vectors inside houses, based on triatomine demographic parameters. The reliability of the predictions was demonstrated by comparing these with different sets of insect collection data from the Yucatan peninsula, Mexico. We then simulated vector control strategies based on insecticide spraying, insect, screens and bednets to evaluate their efficacy at reducing triatomine abundance in the houses. An optimum reduction in bug abundance by at least 80% could be obtained by insecticide application only when doses of at least 50 mg/m2 were applied every year within a two-month period matching the house invasion season by bugs. Alternatively, the use of insect screens consistently reduced bug abundance in the houses and offers a sustainable alternative. Such screens may be part of novel interventions for the integrated control of various vector-borne diseases

Does Sex-Selective Predation Stabilize or Destabilize Predator-Prey Dynamics?

Background: Little is known about the impact of prey sexual dimorphism on predator-prey dynamics and the impact of sexselective harvesting and trophy hunting on long-term stability of exploited populations. Methodology and Principal Findings: We review the quantitative evidence for sex-selective predation and study its longterm consequences using several simple predator-prey models. These models can be also interpreted in terms of feedback between harvesting effort and population size of the harvested species under open-access exploitation. Among the 81 predator-prey pairs found in the literature, male bias in predation is 2.3 times as common as female bias. We show that long-term effects of sex-selective predation depend on the interplay of predation bias and prey mating system. Predation on the ‘less limiting’ prey sex can yield a stable predator-prey equilibrium, while predation on the other sex usually destabilizes the dynamics and promotes population collapses. For prey mating systems that we consider, males are less limiting except for polyandry and polyandrogyny, and male-biased predation alone on such prey can stabilize otherwise unstable dynamics. On the contrary, our results suggest that female-biased predation on polygynous, polygynandrous or monogamous prey requires other stabilizing mechanisms to persist. Conclusions and Significance: Our modelling results suggest that the observed skew towards male-biased predation might reflect, in addition to sexual selection, the evolutionary history of predator-prey interactions. More focus on these phenomena can yield additional and interesting insights as to which mechanisms maintain the persistence of predator-prey pairs over ecological and evolutionary timescales. Our results can also have implications for long-term sustainability of harvesting and trophy hunting of sexually dimorphic species

Empirical Models of Transitions between Coral Reef States: Effects of Region, Protection, and Environmental Change

There has been substantial recent change in coral reef communities. To date, most analyses have focussed on static patterns or changes in single variables such as coral cover. However, little is known about how community-level changes occur at large spatial scales. Here, we develop Markov models of annual changes in coral and macroalgal cover in the Caribbean and Great Barrier Reef (GBR) regions

A hierarchical kinetic theory of birth, death, and fission in age-structured interacting populations

We study mathematical models describing the evolution of stochastic age-structured populations. After reviewing existing approaches, we develop a complete kinetic framework for age-structured interacting populations undergoing birth, death and fission processes in spatially dependent environments. We define the full probability density for the population-size age chart and find results under specific conditions. Connections with more classical models are also explicitly derived. In particular, we show that factorial moments for non-interacting processes are described by a natural generalization of the McKendrick-von Foerster equation, which describes mean-field deterministic behavior. Our approach utilizes mixed-type, multidimensional probability distributions similar to those employed in the study of gas kinetics and with terms that satisfy BBGKY-like equation hierarchies