Robust design and the use of auxiliary variables in estimating population size for an open population

We consider the problem of estimating the population size for an open population where the data are collected over secondary periods within primary periods according to a robust design suggested by Pollock (1982, Journal of Wildlife Management 46, 757-760). A conditional likelihood is used to estimate the parameters associated with a generalized linear model in which the capture probability is assumed to have a logistic form depending on individual covariates. A Horvitz-Thompson-type estimator is used to estimate the population size for each primary period and the survival probabilities between primary periods. The asymptotic properties of the proposed estimators are investigated through simulation and are found to perform well. A data set for such a robust design of a small-mammal capture-recapture study conducted at Dummy Bottom within Browns Park National Wildlife Refuge is analyzed.     

Evaluating cetacean body condition; a review of traditional approaches and new developments

The ability to accurately gauge the body condition of free‐swimming cetaceans is invaluable in population and conservation biology, due to the direct implications that this measure has on individual fitness, survival, and reproductive success. Furthermore, monitoring temporal change in body condition offers insight into foraging success over time, and therefore the health of the supporting ecosystem, as well as a species’ resilience. These parameters are particularly relevant in the context of widespread and accelerated, climate‐induced habitat change. There are, however, significant logistical challenges involved with research and monitoring of large cetaceans, which often preclude direct measure of body condition of live individuals. Consequently, a wide variety of indirect approaches, or proxies, for estimating energetic stores have been proposed over past decades. To date, no single, standardized, approach has been shown to serve as a robust estimation of body condition across species, age categories, and in both live and dead individuals. Nonetheless, it is clear that streamlining and advancing body condition measures would carry significant benefits for diverse areas of cetacean research and management. Here, we review traditional approaches and new applications for the evaluation of cetacean energetic reserves. Specific attention is given to the criteria of measure performance (sensitivity and accuracy), level of invasiveness, cost and effort required for implementation, as well as versatility e.g. applicability across different species, age groups, as well as living versus deceased animals. Measures have been benchmarked against these criteria in an effort to identify key candidates for further development, and key research priorities in the field.     

Modeling the dynamics of natural rotifer populations: Phase-parametric analysis

A model of the dynamics of natural rotifer populations is described as a discrete non-linear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of these parameters were investigated by methods of bifurcation theory. A phase-parametric portrait of the model was constructed and domains of population persistence (stable equilibrium, periodic and a-periodic oscillations of population size) as well as population extinction were identified and investigated. The criteria for population persistence and approaches to determining critical parameter values are described. The results identify parameter values that lead to population extinction under various environmental conditions. They further illustrate that the likelihood of extinction can be substantially increased by small changes in environmental quality, which shifts populations into new dynamical regimes.     

Robust Rare-Variant Association Tests for Quantitative Traits in General Pedigrees

Next-generation sequencing technology has propelled the development of statistical methods to identify rare polygenetic variation associated with complex traits. The majority of these statistical methods are designed for case–control or population-based studies, with few methods that are applicable to family-based studies. Moreover, existing methods for family-based studies mainly focus on trios or nuclear families; there are far fewer existing methods available for analyzing larger pedigrees of arbitrary size and structure. To fill this gap, we propose a method for rare-variant analysis in large pedigree studies that can utilize information from all available relatives. Our approach is based on a kernel machine regression (KMR) framework, which has the advantages of high power, as well as fast and easy calculation of p-values using the asymptotic distribution. Our method is also robust to population stratification due to integration of a QTDT framework (Abecasis et al., Eur J Hum Genet 8(7):545–551, 2000b) with the KMR framework. In our method, we first calculate the expected genotype (between-family component) of a non-founder using all founders’ information and then calculate the deviates (within-family component) of observed genotype from the expectation, where the deviates are robust to population stratification by design. The test statistic, which is constructed using within-family component, is thus robust to population stratification. We illustrate and evaluate our method using simulated data and sequence data from Genetic Analysis Workshop 18.     

Stochastic models for the Trojan Y-Chromosome eradication strategy of an invasive species

The Trojan Y-Chromosome (TYC) strategy, an autocidal genetic biocontrol method, has been proposed to eliminate invasive alien species. In this work, we develop a Markov jump process model for this strategy, and we verify that there is a positive probability for wild-type females going extinct within a finite time. Moreover, when sex-reversed Trojan females are introduced at a constant population size, we formulate a stochastic differential equation (SDE) model as an approximation to the proposed Markov jump process model. Using the SDE model, we investigate the probability distribution and expectation of the extinction time of wild-type females by solving Kolmogorov equations associated with these statistics. The results indicate how the probability distribution and expectation of the extinction time are shaped by the initial conditions and the model parameters.     

Multiple-breed reaction norm animal model accounting for robustness and heteroskedastic in a Nelore–Angus crossed population

Our objective was to genetically characterize post-weaning weight gain (PWG), over a 345-day period after weaning, of Brangus-Ibagé (Nelore×Angus) cattle. Records (n=4016) were from the foundation herd of the Embrapa South Livestock Center. A Bayesian approach was used to assess genotype by environment (G×E) interaction and to identify a suitable model for the estimation of genetic parameters and use in genetic evaluation. A robust and heteroscedastic reaction norm multiple-breed animal model was proposed. The model accounted for heterogeneity of residual variance associated with effects of breed, heterozygosity, sex and contemporary group; and was robust with respect to outliers. Additive genetic effects were modeled for the intercept and slope of a reaction norm to changes in the environmental gradient. Inference was based on Monte Carlo Markov Chain of 110 000 cycles, after 10 000 cycles of burn-in. Bayesian model choice criteria indicated the proposed model was superior to simpler sub-models that did not account for G×E interaction, multiple-breed structure, robustness and heteroscedasticity. We conclude that, for the Brangus-Ibagé population, these factors should be jointly accounted for in genetic evaluation of PWG. Heritability estimates increased proportionally with improvement in the environmental conditions gradient. Therefore, an increased proportion of differences in performance among animals were explained by genetic factors rather than environmental factors as rearing conditions improved. As a consequence response to selection may be increased in favorable environments.     

Can possible evolutionary outcomes be determined directly from the population dynamics?

Traditionally, to determine the possible evolutionary behaviour of an ecological system using adaptive dynamics, it is necessary to calculate the fitness and its derivatives at a singular point. We investigate the claim that the possible evolutionary behaviour can be predicted directly from the population dynamics, without the need for calculation, by applying three criteria — one based on the form of the density dependent rates and two on the role played by the evolving parameters. Taking a general continuous time model, with broad ecological range, we show that the claim is true. Initially, we assume that individuals enter in class 1 and move through population classes sequentially; later we relax these assumptions and find that the criteria still apply. However, when we consider models where the evolving parameters appear non-linearly in the dynamics, we find some aspects of the criteria fail; useful but weaker results on possible evolutionary behaviour now apply.     

Cross-species microsatellite markers for elucidating population genetic structure in Arabidopsis and Arabis (Brassicaeae)

Species closely related to model organisms present the opportunity to efficiently apply molecular and functional tools developed by a large research community to taxa with different ecological and evolutionary histories. We complied 42 microsatellite loci that amplify under common conditions in four closely related Arabidopsis: A. thaliana; A. halleri; A. lyrata ssp. lyrata; and A. lyrata ssp. petraea, as well as in one more distantly related crucifer; Arabis drummondii. Variation at these loci is amenable to a diversity of applications including population genetics, phylogeographical analyses, mapping of inter and intraspecific crosses, and recombination mapping. Our analysis of microsatellite variation illustrates significant differences in population genetic parameters among three Arabidopsis species. A population of A. thaliana, an inbreeding annual plant associated with disturbed habitats, was highly monomorphic (P = 8% percent polymorphic loci) and only 0.2% heterozygous for 648 locus-by-individual combinations. A population of the self-incompatible perennial herb, A. halleri, was more genetically variable (P = 71%) and had an excess of heterozygosity that may reflect a recent population bottleneck associated with human-mediated founder events. A population of the self-incompatible perennial herb, A. lyrata ssp. petraea, was even more genetically variable (P = 86%) and appeared to be at mutation-drift equilibrium. Population structure estimated from neutrally evolving loci provides an empirical expectation against which hypotheses of adaptive evolution at functional loci can be tested.     

Model-based analysis of two-color arrays (MA2C)

A novel normalization method based on the GC content of probes is developed for two-color tiling arrays. The proposed method, together with robust estimates of the model parameters, is shown to perform superbly on published data sets. A robust algorithm for detecting peak regions is also formulated and shown to perform well compared to other approaches. The tools have been implemented as a stand-alone Java program called MA2C, which can display various plots of statistical analysis for quality control.     

The responses of a perch, Perca fluviatilis L., population to eutrophication and associated changes in fish fauna in a small lake

A number of parameters were measured in a population of perch whose numbers had declined steeply in a habitat subjected to increasing eutrophication, and these measurements were compared with those taken before the population decline. Contrary to expectation, no adaptive responses were identified. The growth rate of perch up to the age of III had only declined slightly, and there was a marked preponderance of young fish. Relative growth rate was consistent despite the population decline. No dominant year class was apparent. Mean instantaneous mortality rate and annual survival rate were calculated, and the length-weight relationship was analysed. Feeding strategy had not altered since an earlier study. A decline was seen in the percentage of perch maturing at early age. Ripeness coefficients and fecundity estimates were calculated. A previously documented spawning migration was confirmed. The absence of the expected adaptive changes is discussed.     

Genetic mapping of sterile genes with epistasis in backcross designs

The mapping of sterile genes is an essential issue, which should be solved for the investigation of sterility mechanism in wide hybridization of plants. However, the methods formerly developed cannot address the problem of mapping sterile loci with epistasis. In this study, we developed a new method to map sterile genes with epistasis in wide hybridizations of plants using a backcross design. The maximum likelihood method was used to estimate the parameters of recombination fractions and effects of sterile genes, and the convergent results of these parameters were obtained using the expectation maximization (EM) algorithm. The application and efficiency of this method were tested and demonstrated by a set of simulated data and real data analysis. Results from the simulation experiments showed that the method works well for simultaneously estimating the positions and effects of sterile genes, as well as the epistasis between sterile genes. A real data set of a backcross (BC) population from an interspecific hybrid between cultivated rice, Oryza sativa, and its wild African relative, Oryza longistaminata, was analyzed using the new method. Five sterile genes were detected on the chromosomes of 1, 3, 6, 8 and 10, and significant epistatic effects were found among the four pairs of sterile genes.     

A continuous optimization approach for inferring parameters in mathematical models of regulatory networks

Background

The advances of systems biology have raised a large number of sophisticated mathematical models for describing the dynamic property of complex biological systems. One of the major steps in developing mathematical models is to estimate unknown parameters of the model based on experimentally measured quantities. However, experimental conditions limit the amount of data that is available for mathematical modelling. The number of unknown parameters in mathematical models may be larger than the number of observation data. The imbalance between the number of experimental data and number of unknown parameters makes reverse-engineering problems particularly challenging.

Results

To address the issue of inadequate experimental data, we propose a continuous optimization approach for making reliable inference of model parameters. This approach first uses a spline interpolation to generate continuous functions of system dynamics as well as the first and second order derivatives of continuous functions. The expanded dataset is the basis to infer unknown model parameters using various continuous optimization criteria, including the error of simulation only, error of both simulation and the first derivative, or error of simulation as well as the first and second derivatives. We use three case studies to demonstrate the accuracy and reliability of the proposed new approach. Compared with the corresponding discrete criteria using experimental data at the measurement time points only, numerical results of the ERK kinase activation module show that the continuous absolute-error criteria using both function and high order derivatives generate estimates with better accuracy. This result is also supported by the second and third case studies for the G1/S transition network and the MAP kinase pathway, respectively. This suggests that the continuous absolute-error criteria lead to more accurate estimates than the corresponding discrete criteria. We also study the robustness property of these three models to examine the reliability of estimates. Simulation results show that the models with estimated parameters using continuous fitness functions have better robustness properties than those using the corresponding discrete fitness functions.

Conclusions

The inference studies and robustness analysis suggest that the proposed continuous optimization criteria are effective and robust for estimating unknown parameters in mathematical models.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-256) contains supplementary material, which is available to authorized users.     

Mexican mestizo population sub-structure: effects on genetic and forensic statistical parameters

Since Mexican mestizos are an admixed population, it is necessary to determine the effects that the substructure of the population has on genetic and forensic parameters. With this aim, a study was performed with 15 STR loci (CODIS plus D2S1338 and D19S433) on 1,640 unrelated Mexican mestizos. We determine allele and genotypic frequencies observing departure from Hardy–Weinberg expectation (12 out of 15 loci, with an excess of homozygotes, Fis?>?0), as well as pairs of loci in an apparent linkage disequilibrium (13 of 92 loci). We conducted a test for genetic population stratification, the results show that the Mexican mestizo population is substructured into three subgroups, which are in HW and linkage equilibrium. The combination of the 15 loci in the whole population has high forensic efficiency with the capacity to genetically discriminate one individual in one quintillion (1/10¹⁸). Our data potentially validates the use of these 15 STR loci to establish forensic identity and parentage testing for legal purposes, and offers a powerful tool for genetic variation analysis. However, given that the population is stratified, we highly recommend applying a correction with the inbreeding coefficient in calculations of paternity and forensic studies to avoid erroneous assumptions.     

Do evolutionary constraints on thermal performance manifest at different organizational scales?

The two foremost hypotheses on the evolutionary constraints on an organism's thermal sensitivity – the hotter‐is‐better expectation, and the specialist–generalist trade‐off – have received mixed support from empirical studies testing for their existence. Could these conflicting results reflect confusion regarding the organizational level (i.e. species > population > individual) at which these constraints should manifest? We propose that these evolutionary constraints should manifest at different organizational levels because of differences in their underlying causes and requirements. The hotter‐is‐better expectation should only manifest across separate evolutionary units (e.g. species, populations), and not within populations. The specialist–generalist trade‐off, by contrast, should manifest within as well as between separate evolutionary units. We measured the thermal sensitivity of sprint performance for 440 rainforest sun skinks (Lampropholis coggeri) representing 10 populations, and used the resulting performance curves to test for evidence for the hypothesized constraints at two organizational levels: (i) across populations and (ii) within populations. As predicted, the hotter‐is‐better expectation was evident only at the across‐population level, whereas the specialist–generalist trade‐off was evident within, as well as across, populations. Our results suggest that, depending on the processes that drive them, evolutionary constraints can manifest at different organizational levels. Consideration of these underlying processes, and the organizational level at which a constraint should manifest, may help resolve conflicting empirical results.     

Aspiration cytodiagnosis of pancreatic endocrine tumours

We have reviewed fine needle aspirates from 11 patients with pancreatic endocrine tumours and evaluated the diagnostic criteria as well as those proposed in the literature in an attempt to formulate reliable criteria for the cytological diagnosis of these tumours. As expected, no single criterion was reliable for diagnosis: however, cells with rounded or polygonal rather than a columnar shape, cytoplasmic granularity, and eccentricity of round or oval nuclei with a finely stippled, evenly distributed chromatin pattern were features which taken together, usually enabled one to make a reliable diagnosis. A striking feature of the smears was the cellular monotony and absence of pleomorphism of the tumour cells. Immunocytochemistry and electron microscopy identified tumour products and confirmed the diagnosis.     

Temporal variability in the way local habitat affects duck population growth

Climate change is expected to lead to greater temporal climatic variability across broad spatial extents. A potential consequence is that shifts in climatic conditions might alter how local habitat affects the population growth of animals dependent on those habitats for at least part of their life cycle. We tested whether such a phenomenon occurred when the North American Prairie Pothole Region transitioned through periods of wet and dry conditions by modeling the population growth of seven duck species over 52 years (1961–2012). We found that the influence of local habitat quality—indexed by wetland availability—on duck population growth varied in magnitude and direction on an annual basis. While the effect of wetlands was relatively small in most years, there were some years in which wetlands strongly affected duck population growth in both positive and negative directions (e.g., negative in 2002 and positive in 2008). Contrary to our expectation, inter-annual variability in the effect of wetlands on duck population growth did not depend on regional precipitation. We also found that for two species—American Wigeon (Anas americana) and Green-winged Teal (A. carolinensis)—duck population growth in the presence of wetlands rarely differed from what would be expected solely under density dependence. Our study is the first to demonstrate that the effect of local habitat on population growth varies over time even if the cause of that variation remains unexplained. Consequently, any study that attempts to identify a species’ critical habitat using time series abundance data must consider that local relationships are non-stationary. More complicated measures of climate change may reveal how local drivers of population growth depend on broader temporal climatic patterns.     

Mitotic autoregulation, growth control and neoplasia

A model is proposed for the mitotic autoregulation of the haemopoietic stem cell population. Conditions are derived for the model population to exhibit spontaneous self-limitation; these consist of the satisfaction of algebraic inequality relationships between mathematical parameters referring to the global porperties of the model cell population. Violation of these conditions precludes the possibility of spontaneous self-limitation of the population, which therefore grows indefinitely, but is not synonymous with abolition of all responsiveness to homeostatic regulation. Non-limiting growth modes exist for which “cybernetic” responsiveness to perturbations occur.It is suggested that certain features of the model accord well with some observed characteristics of neoplasia, such as the non-localized “field phenomena” frequently seen in tumour growth and the continued responsiveness of some tumours to hormones and other physiological signals.     

INVITED REVIEW: What is a population? An empirical evaluation of some genetic methods for identifying the number of gene pools and their degree of connectivity

We review commonly used population definitions under both the ecological paradigm (which emphasizes demographic cohesion) and the evolutionary paradigm (which emphasizes reproductive cohesion) and find that none are truly operational. We suggest several quantitative criteria that might be used to determine when groups of individuals are different enough to be considered 'populations'. Units for these criteria are migration rate (m) for the ecological paradigm and migrants per generation (Nm) for the evolutionary paradigm. These criteria are then evaluated by applying analytical methods to simulated genetic data for a finite island model. Under the standard parameter set that includes L = 20 High mutation (microsatellite-like) loci and samples of S = 50 individuals from each of n = 4 subpopulations, power to detect departures from panmixia was very high ( approximately 100%; P < 0.001) even with high gene flow (Nm = 25). A new method, comparing the number of correct population assignments with the random expectation, performed as well as a multilocus contingency test and warrants further consideration. Use of Low mutation (allozyme-like) markers reduced power more than did halving S or L. Under the standard parameter set, power to detect restricted gene flow below a certain level X (H(0): Nm < X) can also be high, provided that true Nm < or = 0.5X. Developing the appropriate test criterion, however, requires assumptions about several key parameters that are difficult to estimate in most natural populations. Methods that cluster individuals without using a priori sampling information detected the true number of populations only under conditions of moderate or low gene flow (Nm < or = 5), and power dropped sharply with smaller samples of loci and individuals. A simple algorithm based on a multilocus contingency test of allele frequencies in pairs of samples has high power to detect the true number of populations even with Nm = 25 but requires more rigorous statistical evaluation. The ecological paradigm remains challenging for evaluations using genetic markers, because the transition from demographic dependence to independence occurs in a region of high migration where genetic methods have relatively little power. Some recent theoretical developments and continued advances in computational power provide hope that this situation may change in the future.     

Stochastic analogues of deterministic single-species population models

Although single-species deterministic difference equations have long been used in modeling the dynamics of animal populations, little attention has been paid to how stochasticity should be incorporated into these models. By deriving stochastic analogues to difference equations from first principles, we show that the form of these models depends on whether noise in the population process is demographic or environmental. When noise is demographic, we argue that variance around the expectation is proportional to the expectation. When noise is environmental the variance depends in a non-trivial way on how variation enters into model parameters, but we argue that if the environment affects the population multiplicatively then variance is proportional to the square of the expectation. We compare various stochastic analogues of the Ricker map model by fitting them, using maximum likelihood estimation, to data generated from an individual-based model and the weevil data of Utida. Our demographic models are significantly better than our environmental models at fitting noise generated by population processes where noise is mainly demographic. However, the traditionally chosen stochastic analogues to deterministic models--additive normally distributed noise and multiplicative lognormally distributed noise--generally fit all data sets well. Thus, the form of the variance does play a role in the fitting of models to ecological time series, but may not be important in practice as first supposed.     

Loglinear models for the robust design in mark-recapture experiments

The robust design is a method for implementing a mark-recapture experiment featuring a nested sampling structure. The first level consists of primary sampling sessions; the population experiences mortality and immigration between primary sessions so that open population models apply at this level. The second level of sampling has a short mark-recapture study within each primary session. Closed population models are used at this stage to estimate the animal abundance at each primary session. This article suggests a loglinear technique to fit the robust design. Loglinear models for the analysis of mark-recapture data from closed and open populations are first reviewed. These two types of models are then combined to analyze the data from a robust design. The proposed loglinear approach to the robust design allows incorporating parameters for a heterogeneity in the capture probabilities of the units within each primary session. Temporary emigration out of the study area can also be accounted for in the loglinear framework. The analysis is relatively simple; it relies on a large Poisson regression with the vector of frequencies of the capture histories as dependent variable. An example concerned with the estimation of abundance and survival of the red-back vole in an area of southeastern Québec is presented.