Verhulst Model of Interval Grey Number Based on Information Decomposing and Model Combination

Grey Verhulst models are often employed to simulate the development tendency with the characteristic of saturated process of S curve. However, the uncertainty of interval grey numbers will be increased since the boundaries of interval grey number are extended by the Axiom of nondecreasing grey degree in the existing Verhulst modeling method. In this paper, the interval grey number is divided into two real number parts, that is, “white” and “grey” parts. Then the “white” and “grey” parts are simulated and forecasted by building the grey Verhulst model and DGM (1, 1) model, respectively. To some degree, this method resolves the issue of amplifying the range of interval grey number. Finally, an example is used to compare the simulation performance between the new model and the traditional model, and the results show that the new model is superior to the other model

Explaining patterns of age-specific performance

Individual life histories are frequently studied to gain insight into the mechanisms of ageing. However, various challenges complicate the accurate quantification of age-specific variation in fitness. In this thesis I develop and apply methods to accurately characterise patterns of ageing, and to explain why such patterns arise. All mammals and birds have an upper bound on litter size, and for many species this limit is quite low. In addition, in many species, not all individuals breed at every possible opportunity. Reproduction should consequently be considered as two processes: whether an individual breeds or not and the number of offspring produced. These processes mean that reproduction in many species does not follow a Poisson process as is often assumed in analyses of breeding performance. A more appropriate model for a repeated ordinal response like annual reproductive success is a proportional odds model with a random intercept for individuals. Such a model has not previously been used in ecology or evolutionary biology. I apply this model to analyse age and temporal variation in the number of fledglings produced annually by male and female common terns (Sterna hirundo). I use data collected from this intensively studied, long-lived species, repeatedly throughout the thesis. The proportional odds analysis reveal that reproductive performance in females initially increased with age, before declining as individuals began to senesce. But why does this pattern arise? Is it purely an effect of getting physiologically older or are other processes involved? I estimate the effect of the length of time spent with the current partner using the common tern data. Despite the quality of the data, it is not always obvious if unmarked partners are new or not. I use a hierarchical Bayesian model of the steps that lead to the number of fledglings. Modelling this complicated process requires a complex model, but results show that no substantial amount of observed age-related patterns in reproductive performance can be attributed to length of pair bond. While the proportional odds and Bayesian analyses account for repeated measures on individuals they do not account for compositional change. Such a change in the composition of the population caused by heterogeneity between individuals can mask true rates of individual change. I develop a novel retrospective decomposition method related to the Price equation to address this issue. The equation gives the exact contributions of selective disappearance and average change in individual performance among survivors to the aggregate change at the level of the population. This equation can be extended by including a term for the compositional change due to selective appearance of individuals in the study population. I apply this decomposition to the common tern dataset to disentangle whether apparent increases and decreases in reproductive performance with age reflect genuine changes within individuals or are an artefact of compositional change in a heterogeneous population. I show an improvement in average reproductive performance of individuals over most of adult life and give support for reproductive senescence at old ages. I show that the contribution of compositional change is of minor importance, suggesting that population-level averages accurately capture the individual-level ageing process well. Can the decomposition method I develop be applied to other systems? Does it lead to similar conclusions? I apply it to two different datasets dealing with functioning at old age in humans: the ability to live independently in the Danish 1905-cohort, and cognitive functioning for people aged 80 and older participating in the Chinese Longitudinal Health and Longevity Survey. In both studies I reveal that average individual functioning declines at old ages. Although the decline is also apparent at the population level it is less strong due to the tendency of individuals with lower functioning to drop out earlier. Finally, I illustrate the general use of the decomposition by applying it to epidemiological and economic studies in the appendix. Overall, I find that reproductive performance improves over many age classes before senescence begins. Numerous processes can influence rates of age-related change, with results apparently specific to the trait and population under study

Delayed timing of breeding as a cost of reproduction

Timing of breeding is a trait with considerable individual variation, often closely linked to fitness because of seasonal declines in reproduction. The drivers of this variation have received much attention, but how reproductive costs may influence the timing of subsequent breeding has been largely unexplored. We examined a population of northern wheatears Oenanthe oenanthe to compare three groups of individuals that differed in their timing of breeding termination and reproductive effort to investigate how these factors may carry over to influence reproductive timing and reproductive output in the following season. Compared to females that bred successfully, females that put in less effort and terminated breeding early due to nest failure tended to arrive and breed earlier in year 2 (mean advancement = 2.2 and 3.3 d respectively). Females that spent potentially more effort and terminated breeding later due to production of a replacement clutch after nest failure, arrived later than other females in year 2. Reproductive output (number of fledglings) in year 2 differed between the three groups as a result of group-level differences in the timing of breeding in combination with the general seasonal decline in reproductive output. Our study shows that the main cost of reproduction was apparent in the timing of arrival and breeding in this migratory species. Hence, reproductive costs can arise through altered timing of breeding since future reproductive success (including adult survival) is often dependent on the timing of breeding in seasonal systems

Altitudinal Effects on Innate Immune Response of a Subterranean Rodent.

Solak HM, Yanchukov A, Colak F, et al. Altitudinal Effects on Innate Immune Response of a Subterranean Rodent. Zoological science. 2020;37(1):31-41.Immune defense is costly to maintain and deploy, and the optimal investment into immune defense depends on risk of infection. Altitude is a natural environmental factor that is predicted to affect parasite abundance, with lower parasite abundance predicted at higher altitudes due to stronger environmental stressors, which reduce parasite transmission. Using high and low altitude populations of the Turkish blind mole-rat (TBMR) Nannospalax xanthodon, we tested for effects of altitude on constitutive innate immune defense. Field studies were performed with 32 wild animals in 2017 and 2018 from two low- and one high-altitude localities in the Central Taurus Mountains, at respective altitudes of 1010 m, 1115 m, and 2900 m above sea level. We first compared innate standing immune defense as measured by the bacteria-killing ability of blood serum. We then measured corticosterone stress hormone levels, as stressful conditions may affect immune response. Finally, we compared prevalence and intensity of gastrointestinal parasites of field-captured TBMR. We found that the bacteria-killing ability of serum is greater in the mole-rat samples from high altitude. There was no significant difference in stress (corticosterone) levels between altitude categories. Coccidian prevalence and abundance were significantly higher in 2017 than 2018 samples, but there was no significant difference in prevalence, abundance, or intensity between altitudes, or between sexes. Small sample sizes may have reduced power to detect true differences; nevertheless, this study provides support that greater standing innate immunity in high altitude animals may reflect greater investment into constitutive defense

Stock index prediction based on Grey theory, ARIMA model and Wavelet method

In this thesis, we develop a new forecasting method by merging traditional statistical methods with innovational non-statistical theories for the purpose of improving prediction accuracy of stock time series. The method is based on a novel hybrid model which combines the grey model, the ARIMA model and wavelet methods. First of all, we improve the traditional GM(1, 1) model to the GM(1, 1, o, y) model by introducing two parameters: the grey coefficient and the grey dimension degree y. Then we revise the normal G-ARMA model by merging the ARMA model with the GM(1, 1, o, y) model. In order to overcome the drawback of directly modeling original stock time series, we introduce wavelet methods into the revised G-ARMA model and name this new hybrid model WG-ARMA model. Finally, we obtain the WPG-ARMA model by replacing the wavelet transform with the wavelet packet decomposition. To keep consistency, all the proposed models are merged into a single model by estimating-parameters simultaneously based on the total absolute error (TAE) criterion. To verify prediction performance of the models, we present case studies for the models based on the leading Canadian stock index: S&P/TSX Composite Index on the daily bases. The experimental results give the rank of predictive ability in terms of the TAE, MPAE and DIR metrics as following: WPG-ARMA, WG-ARMA, G-ARMA, GM(1, 1, o, y), ARIMA

Evolutionary Fitness in Variable Environments

One essential ingredient of evolutionary theory is the concept of fitness as a measure for a species' success in its living conditions. Here, we quantify the effect of environmental fluctuations onto fitness by analytical calculations on a general evolutionary model and by studying corresponding individual-based microscopic models. We demonstrate that not only larger growth rates and viabilities, but also reduced sensitivity to environmental variability substantially increases the fitness. Even for neutral evolution, variability in the growth rates plays the crucial role of strongly reducing the expected fixation times. Thereby, environmental fluctuations constitute a mechanism to account for the effective population sizes inferred from genetic data that often are much smaller than the census population size.Comment: main: 5 pages, 4 figures; supplement: 7 pages, 7 figue

Declining home range area predicts reduced late-life survival in two wild ungulate populations

Demographic senescence is increasingly recognised as an important force shaping the dynamics of wild vertebrate populations. However, our understanding of the processes that underpin these declines in survival and fertility in old age remains limited. Evidence for age‐related changes in foraging behaviour and habitat use is emerging from wild vertebrate studies, but the extent to which these are driven by within‐individual changes, and the consequences for fitness, remain unclear. Using longitudinal census observations collected over four decades from two long‐term individual‐based studies of unmanaged ungulates, we demonstrate consistent within‐individual declines in home range area with age in adult females. In both systems, we found that within‐individual decreases in home range area were associated with increased risk of mortality the following year. Our results provide the first evidence from the wild that age‐related changes in space use are predictive of adult mortality

Two drivers of acute phase response variation in free-living passerines

The acute phase response (APR) is an important first-line defense against microparasites (e.g., bacteria, viruses) that is broadly conserved across vertebrates. However, the magnitude and duration of the APR, which includes fever, sickness behaviors (e.g., lethargy, anorexia), production of pro-inflammatory cytokines, and upregulation of anti-microbial peptides are highly variable across individuals, populations, and species. Laboratory studies have identified many drivers of variability in the APR, including organisms’ social surroundings, type of infectious agent, whether animals are co-infected with multiple parasites, and even the order in which animals became co-infected. However, studies of the APR that can replicate the natural contexts experienced by animals in the wild are rare. Such studies are particularly important, however, as they may offer insights not possible in lab settings. This thesis builds upon prior lab results by incorporating more natural experimental context to uncover the importance of two potential drivers of variation in the APR, one external and one internal: social context (external) and co-infection with gut helminths (internal). To test an external driver of APR variation, I manipulated social context in flocks of house sparrows (Passer domesticus) kept in outdoor aviaries (chapter 2). Specifically, I varied the proportion of an animal’s social group that experienced a simulated infection (injection with lipopolysaccharide (LPS), a reliable inducer of the APR). Injected birds in flocks where all members were undergoing an APR expressed higher fevers than did birds in flocks where only half the group was experiencing a simulated infection. Despite these social context-associated differences in thermoregulation, I detected no differences in activity levels (sickness behaviors) between LPS-injected birds in different social contexts. I also investigated an internal driver of APR variation, helminth co-infection (chapters 3-4). Helminth-driven immunomodulation is frequently reported in studies on lab mice, but this phenomenon has not been studied in songbirds. In chapter 3, I report negative correlations between helminth infection burden and the severity of the APR within and between populations of song sparrows (Melospiza melodia). In chapter 4, I tested these association using experimental anthelminthic drug treatments paired with simulated bacterial infection (LPS injection in the higher-latitude population of birds (which had higher helminth burdens). Birds given both anthelminthic drugs and simulated bacterial infections expressed higher temperatures during the first night after LPS-injections were administered, but their activity levels did not differ from LPS-injected birds with intact helminth infections. Collectively, these experiments improve the existing knowledge of external and internal drivers on the APR in wild birds. Most notably, the two components of the APR investigated here (fever and lethargy) were decoupled under different social contexts and states of co-infection. Because physiological and behavioral responses to infection (e.g., fever and lethargy) could have very different impacts on disease outcomes and pathogen transmission, further exploration of the mechanisms underlying this decoupling is needed

The evolution of labile traits in sex- and age-structured populations

1. Many quantitative traits are labile (e.g. somatic growth rate, reproductive timing and investment), varying over the life cycle as a result of behavioural adaptation, developmental processes and plastic responses to the environment. At the population level, selection can alter the distribution of such traits across age classes and among generations. Despite a growing body of theoretical research exploring the evolutionary dynamics of labile traits, a data-driven framework for incorporating such traits into demographic models has not yet been developed. 2. Integral projection models (IPMs) are increasingly being used to understand the interplay between changes in labile characters, life histories and population dynamics. One limitation of the IPM approach is that it relies on phenotypic associations between parents and offspring traits to capture inheritance. However, it is well-established that many different processes may drive these associations, and currently, no clear consensus has emerged on how to model micro-evolutionary dynamics in an IPM framework. 3. We show how to embed quantitative genetic models of inheritance of labile traits into age-structured, two-sex models that resemble standard IPMs. Commonly used statistical tools such as GLMs and their mixed model counterparts can then be used for model parameterization. We illustrate the methodology through development of a simple model of egg-laying date evolution, parameterized using data from a population of Great tits (Parus major). 4. We demonstrate how our framework can be used to project the joint dynamics of species' traits and population density. We then develop a simple extension of the age-structured Price equation (ASPE) for two-sex populations, and apply this to examine the age-specific contributions of different processes to change in the mean phenotype and breeding value. 5. The data-driven framework we outline here has the potential to facilitate greater insight into the nature of selection and its consequences in settings where focal traits vary over the lifetime through ontogeny, behavioural adaptation and phenotypic plasticity, as well as providing a potential bridge between theoretical and empirical studies of labile trait variation