The importance of individual developmental variation in stage‐structured population models

Population stage structure is fundamental to ecology, and models of this structure have proven useful in many different systems. Many ecological variables other than stage, such as habitat type, site occupancy and metapopulation status are also modelled using transitions among discrete states. Transitions among life stages can be characterised by the distribution of time spent in each stage, including the mean and variance of each stage duration and within‐individual correlations among multiple stage durations. Three modelling traditions represent stage durations differently. Matrix models can be derived as a long‐run approximation from any distribution of stage durations, but they are often interpreted directly as a Markov model for stage transitions. Statistical stage‐duration distribution models accommodate the variation typical of cohort development data, but such realism has rarely been incorporated in population theory or statistical population models. Delay‐differential equation models include lags but no variation, except in limited cases. We synthesise these models in one framework and illustrate how individual variation and correlations in development can impact population growth. Furthermore, different development models can yield the same long‐term matrix transition rates but different sensitivities and elasticities. Finally, we discuss future directions for estimating realistic stage duration models from data.     

Incorporating the temporal autocorrelation of demographic rates into structured population models

Population dynamics are typically temporally autocorrelated: population sizes are positively or negatively correlated with past population sizes. Previous studies have found that positive temporal autocorrelation increases the risk of extinction due to ‘inertia’ that prolongs downward fluctuations in population size. However, temporal autocorrelation has not yet been analyzed at the level of life cycle transitions. We developed an R package, colorednoise, which creates stochastic matrix population projections with distinct temporal autocorrelation values for each matrix element. We used it to analyze long-term demographic data on 25 populations from the COMADRE and COMPADRE databases and simulate their stochastic dynamics. We found a broad range of temporal autocorrelation across species, populations and life cycle stages. The number of stage-classes in the matrix strongly affected the temporal autocorrelation of the growth rate. In the plant populations, reproduction transitions had more negative temporal autocorrelation than survival transitions, and matrices dominated by positive temporal autocorrelation had higher extinction risk, while in animal populations transition type was not associated with noise color. Our results indicate that temporal autocorrelation varies across life cycle transitions, even among populations of the same species. We present the colorednoise package for researchers to analyze the temporal autocorrelation of structured demographic rates.     

Incorporating spatial autocorrelation into species distribution models alters forecasts of climate‐mediated range shifts

Species distribution models (SDMs) are widely used to forecast changes in the spatial distributions of species and communities in response to climate change. However, spatial autocorrelation (SA) is rarely accounted for in these models, despite its ubiquity in broad‐scale ecological data. While spatial autocorrelation in model residuals is known to result in biased parameter estimates and the inflation of type I errors, the influence of unmodeled SA on species' range forecasts is poorly understood. Here we quantify how accounting for SA in SDMs influences the magnitude of range shift forecasts produced by SDMs for multiple climate change scenarios. SDMs were fitted to simulated data with a known autocorrelation structure, and to field observations of three mangrove communities from northern Australia displaying strong spatial autocorrelation. Three modeling approaches were implemented: environment‐only models (most frequently applied in species' range forecasts), and two approaches that incorporate SA; autologistic models and residuals autocovariate (RAC) models. Differences in forecasts among modeling approaches and climate scenarios were quantified. While all model predictions at the current time closely matched that of the actual current distribution of the mangrove communities, under the climate change scenarios environment‐only models forecast substantially greater range shifts than models incorporating SA. Furthermore, the magnitude of these differences intensified with increasing increments of climate change across the scenarios. When models do not account for SA, forecasts of species' range shifts indicate more extreme impacts of climate change, compared to models that explicitly account for SA. Therefore, where biological or population processes induce substantial autocorrelation in the distribution of organisms, and this is not modeled, model predictions will be inaccurate. These results have global importance for conservation efforts as inaccurate forecasts lead to ineffective prioritization of conservation activities and potentially to avoidable species extinctions.     

Hybridization selects for prime‐numbered life cycles in Magicicada: An individual‐based simulation model of a structured periodical cicada population

We investigate competition between separate periodical cicada populations each possessing different life‐cycle lengths. We build an individual‐based model to simulate the cicada life cycle and allow random migrations to occur between patches inhabited by the different populations. We show that if hybridization between different cycle lengths produces offspring that have an intermediate life‐cycle length, then predation acts disproportionately to select against the hybrid offspring. This happens because they emerge in low densities without the safety‐in‐numbers provided by either parent population. Thus, prime‐numbered life cycles that can better avoid hybridization are favored. However, we find that this advantage of prime‐numbered cycles occurs only if there is some mechanism that can occasionally synchronize emergence between local populations in sufficiently many patches.     

Micro‐structured Devices for Chemical Sensing of Flavor and Fragrance

The aim of this study was to design, develop and test an integrated micro‐analytical system. Of special interest are micro‐fluidic and micro‐sensor applications in the field of chemical analysis, such as the optical detection of parameter changes, optical recognition of component profiles and technological micro‐reaction applications. For this purpose, a modular system was developed, which enables the realization of various application cases in an uncomplicated manner, and to execute (via serial or parallel combination of components) usually not compatible tasks. Software components were developed to control the measuring procedure as well as to execute the data interpretation up to a chemometrical discriminant analysis. Application is directed to the production and product control in life sciences mainly for food, natural products, cosmetics and pharmaceutics.     

Estimation and identification issues in the promotion time cure model when the same covariates influence long‐ and short‐term survival

The promotion time cure model is a survival model acknowledging that an unidentified proportion of subjects will never experience the event of interest whatever the duration of the follow‐up. We focus our interest on the challenges raised by the strong posterior correlation between some of the regression parameters when the same covariates influence long‐ and short‐term survival. Then, the regression parameters of shared covariates are strongly correlated with, in addition, identification issues when the maximum follow‐up duration is insufficiently long to identify the cured fraction. We investigate how, despite this, plausible values for these parameters can be obtained in a computationally efficient way. The theoretical properties of our strategy will be investigated by simulation and illustrated on clinical data. Practical recommendations will also be made for the analysis of survival data known to include an unidentified cured fraction.     

Kinetic modeling of native Cassava starch thermo‐oxidative degradation using Weibull and Weibull‐derived models

A new approach in kinetic modeling of thermo‐oxidative degradation process of starch granules extracted from the Cassava roots was developed. Based on the thermoanalytical measurements, three reaction stages were detected. Using Weibull and Weibull‐derived (inverse) models, it was found that the first two reaction stages could be described with the change of apparent activation energy (E_a) on conversion fraction (α(T)) (using “Model‐free” analysis). It was found that first reaction stage, which involves dehydration and evaporation of lower molecular mass fractions, can be described with an inverse Weibull model. This model with its distribution of E_a values and derived distribution parameters includes the occurrence of three‐dimensional diffusion mechanism. The second reaction stage is very complex, and it was found to contain the system of simultaneous reactions (where depolymerization occurs), and can be described with standard Weibull model. Identified statistical model with its distribution of E_a values and derived distribution parameters includes the kinetic model that gives the variable reaction order values. Based on the established models, shelf‐life studies for first two stages were carried out. Shelf‐life testing has shown that optimal dehydration time is achieved by a programmed heating at medium heating rate, whereas optimal time of degradation is achieved at highest heating rate. © 2013 Wiley Periodicals, Inc. Biopolymers 101: 41–57, 2014.     

Logistic regression when covariates are random effects from a non‐linear mixed model

In many studies, the association of longitudinal measurements of a continuous response and a binary outcome are often of interest. A convenient framework for this type of problems is the joint model, which is formulated to investigate the association between a binary outcome and features of longitudinal measurements through a common set of latent random effects. The joint model, which is the focus of this article, is a logistic regression model with covariates defined as the individual‐specific random effects in a non‐linear mixed‐effects model (NLMEM) for the longitudinal measurements. We discuss different estimation procedures, which include two‐stage, best linear unbiased predictors, and various numerical integration techniques. The proposed methods are illustrated using a real data set where the objective is to study the association between longitudinal hormone levels and the pregnancy outcome in a group of young women. The numerical performance of the estimating methods is also evaluated by means of simulation.     

Analysis of Zero‐Inflated Poisson Data Incorporating Extent of Exposure

When analyzing Poisson count data sometimes a high frequency of extra zeros is observed. The Zero‐Inflated Poisson (ZIP) model is a popular approach to handle zero‐inflation. In this paper we generalize the ZIP model and its regression counterpart to accommodate the extent of individual exposure. Empirical evidence drawn from an occupational injury data set confirms that the incorporation of exposure information can exert a substantial impact on the model fit. Tests for zero‐inflation are also considered. Their finite sample properties are examined in a Monte Carlo study.     

Choosing the right sigmoid growth function using the unified‐models approach

Growth of the young is an important part of the life history in birds. However, modelling methods have paid little attention to the choice of regression model used to describe its pattern. The aim of this study was to evaluate whether a single sigmoid model with an upper asymptote could describe avian growth adequately. We compared unified versions of five growth models of the Richards family (the four‐parameter U‐Richards and the three‐parameter U‐logistic, U‐Gompertz, U‐Bertalanffy and U4‐models) for three traits (body mass, tarsus‐length and wing‐length) for 50 passerine species, including species with varied morphologies and life histories. The U‐family models exhibit a unified set of parameters for all models. The four‐parameter U‐Richards model proved a good choice for fitting growth curves to various traits – its extra d‐parameter allows for a flexible placement of the inflection point. Which of the three‐parameter U‐models was the best performing varied greatly between species and between traits, as each three‐parameter model had a different fixed relative inflection value (fraction of the upper asymptote), implying a different growth pattern. Fixing the asymptotes to averages for adult trait value generally shifted the model preference towards one with lower relative inflection values. Our results illustrate an overlooked difficulty in the analysis of organismal growth, namely, that a single traditional three‐parameter model does not suit all growth data. This is mostly due to differences in inflection placement. Moreover, some biometric traits require more attention when estimating growth rates and other growth‐curve characteristics. We recommend fitting either several three‐parameter models from the U‐family, where the parameters are comparable between models, or only the U‐Richards model.     

Continental‐scale tree‐ring‐based projection of Douglas‐fir growth: Testing the limits of space‐for‐time substitution

A central challenge in global change research is the projection of the future behavior of a system based upon past observations. Tree‐ring data have been used increasingly over the last decade to project tree growth and forest ecosystem vulnerability under future climate conditions. But how can the response of tree growth to past climate variation predict the future, when the future does not look like the past? Space‐for‐time substitution (SFTS) is one way to overcome the problem of extrapolation: the response at a given location in a warmer future is assumed to follow the response at a warmer location today. Here we evaluated an SFTS approach to projecting future growth of Douglas‐fir (Pseudotsuga menziesii), a species that occupies an exceptionally large environmental space in North America. We fit a hierarchical mixed‐effects model to capture ring‐width variability in response to spatial and temporal variation in climate. We found opposing gradients for productivity and climate sensitivity with highest growth rates and weakest response to interannual climate variation in the mesic coastal part of Douglas‐fir's range; narrower rings and stronger climate sensitivity occurred across the semi‐arid interior. Ring‐width response to spatial versus temporal temperature variation was opposite in sign, suggesting that spatial variation in productivity, caused by local adaptation and other slow processes, cannot be used to anticipate changes in productivity caused by rapid climate change. We thus substituted only climate sensitivities when projecting future tree growth. Growth declines were projected across much of Douglas‐fir's distribution, with largest relative decreases in the semiarid U.S. Interior West and smallest in the mesic Pacific Northwest. We further highlight the strengths of mixed‐effects modeling for reviving a conceptual cornerstone of dendroecology, Cook's 1987 aggregate growth model, and the great potential to use tree‐ring networks and results as a calibration target for next‐generation vegetation models.     

Disease‐structured N‐mixture models: A practical guide to model disease dynamics using count data

Obtaining inferences on disease dynamics (e.g., host population size, pathogen prevalence, transmission rate, host survival probability) typically requires marking and tracking individuals over time. While multistate mark–recapture models can produce high‐quality inference, these techniques are difficult to employ at large spatial and long temporal scales or in small remnant host populations decimated by virulent pathogens, where low recapture rates may preclude the use of mark–recapture techniques. Recently developed N‐mixture models offer a statistical framework for estimating wildlife disease dynamics from count data. N‐mixture models are a type of state‐space model in which observation error is attributed to failing to detect some individuals when they are present (i.e., false negatives). The analysis approach uses repeated surveys of sites over a period of population closure to estimate detection probability. We review the challenges of modeling disease dynamics and describe how N‐mixture models can be used to estimate common metrics, including pathogen prevalence, transmission, and recovery rates while accounting for imperfect host and pathogen detection. We also offer a perspective on future research directions at the intersection of quantitative and disease ecology, including the estimation of false positives in pathogen presence, spatially explicit disease‐structured N‐mixture models, and the integration of other data types with count data to inform disease dynamics. Managers rely on accurate and precise estimates of disease dynamics to develop strategies to mitigate pathogen impacts on host populations. At a time when pathogens pose one of the greatest threats to biodiversity, statistical methods that lead to robust inferences on host populations are critically needed for rapid, rather than incremental, assessments of the impacts of emerging infectious diseases.     

Non‐parametric habitat models with automatic interactions

Questions: Can a statistical model be designed to represent more directly the nature of organismal response to multiple interacting factors? Can multiplicative kernel smoothers be used for this purpose? What advantages does this approach have over more traditional habitat modelling methods? Methods: Non‐parametric multiplicative regression (NPMR) was developed from the premises that: the response variable has a minimum of zero and a physiologically‐determined maximum, species respond simultaneously to multiple ecological factors, the response to any one factor is conditioned by the values of other factors, and that if any of the factors is intolerable then the response is zero. Key features of NPMR are interactive effects of predictors, no need to specify an overall model form in advance, and built‐in controls on overfitting. The effectiveness of the method is demonstrated with simulated and real data sets. Results: Empirical and theoretical relationships of species response to multiple interacting predictors can be represented effectively by multiplicative kernel smoothers. NPMR allows us to abandon simplistic assumptions about overall model form, while embracing the ecological truism that habitat factors interact.     

Temporal effects of disturbance on community composition in simulated stage‐structured plant communities

In an era of global environmental change, understanding how disturbance affects the dynamics of ecological communities is crucial. However, few studies have theoretically explored the potential influence of disturbance including both intensity and frequency on compositional change over time in communities with stage structure. A spatially explicit, individual‐based model was constructed incorporating the various demographic responses to disturbance of plants at two different growth stages: seedlings and adults. In the model, we assumed that individuals within each stage were demographically equivalent (neutral) but differed between stages. We simulated a common phenomenon that seedlings suffered more from disturbance such as grazing and fire than adults. We showed how stage‐structured communities of seedlings and adults responded to disturbance with various levels of disturbance frequency and intensity. In “undisturbed” simulations, the relationship between average species abundance (defined here as the total number of individuals divided by species richness) and community composition turnover (measured by the Bray–Curtis similarity index) was asymptotic. However, in strongly “disturbed” simulations with the between‐disturbance intervals greater than one, this relationship became unimodal. Stage‐dependent response to disturbance underlay the above discrepancy between undisturbed and disturbed communities.