Wolves alter the trajectory of forests by shaping the central place foraging behaviour of an ecosystem engineer.

Predators can directly and indirectly alter the foraging behaviour of prey through direct predation and the risk of predation, and in doing so, initiate indirect effects that influence myriad species and ecological processes. We describe how wolves indirectly alter the trajectory of forests by constraining the distance that beavers, a central place forager and prolific ecosystem engineer, forage from water. Specifically, we demonstrate that wolves wait in ambush and kill beavers on longer feeding trails than would be expected based on the spatio-temporal availability of beavers. This pattern is driven by temporal dynamics of beaver foraging: beavers make more foraging trips and spend more time on land per trip on longer feeding trails that extend farther from water. As a result, beavers are more vulnerable on longer feeding trails than shorter ones. Wolf predation appears to be a selective evolutionary pressure propelled by consumptive and non-consumptive mechanisms that constrain the distance from water beavers forage, which in turn limits the area of forest around wetlands, lakes and rivers beavers alter through foraging. Thus, wolves appear intricately linked to boreal forest dynamics by shaping beaver foraging behaviour, a form of natural disturbance that alters the successional and ecological states of forests.

Implications of the scale of detection for inferring co-occurrence patterns from paired camera traps and acoustic recorders.

Multifunctional landscapes that support economic activities and conservation of biological diversity (e.g., cattle ranches with native forest) are becoming increasingly important because small remnants of native forest may comprise the only habitat left for some wildlife species. Understanding the co-occurrence between wildlife and disturbance factors, such as poaching activity and domesticated ungulates, is key to successful management of multifunctional landscapes. Tools to measure co-occurrence between wildlife and disturbance factors include camera traps and autonomous acoustic recording units. We paired 52 camera-trap stations with acoustic recorders to investigate the association between 2 measures of disturbance (poaching and cattle) and wild ungulates present in multifunctional landscapes of the Colombian Orinoquía. We used joint species distribution models to investigate species-habitat associations and species-disturbance correlations. One model was fitted using camera-trap data to detect wild ungulates and disturbance factors, and a second model was fitted after replacing camera-trap detections of disturbance factors with their corresponding acoustic detections. The direction, significance, and precision of the effect of covariates depended on the sampling method used for disturbance factors. Acoustic monitoring typically resulted in more precise estimates of the effects of covariates and of species-disturbance correlations. Association patterns between wildlife and disturbance factors were found only when disturbance was detected by acoustic recorders. Camera traps allowed us to detect nonvocalizing species, whereas audio recording devices increased detection of disturbance factors leading to more precise estimates of co-occurrence patterns. The collared peccary (Pecari tajacu), lowland tapir (Tapirus terrestris), and white-tailed deer (Odocoileus virginianus) co-occurred with disturbance factors and are conservation priorities due to the greater risk of poaching or disease transmission from cattle.

Implicaciones de la escala de detección para inferir los patrones de coocurrencia a partir de fototrampas y grabaciones emparejadas Resumen Los paisajes multifuncionales que sostienen actividades económicas y la conservación de la biodiversidad (p. ej., ganadería en bosques nativos) son cada vez más importantes porque los pequeños reductos de bosque nativo podrían comprender el único hábitat disponible para algunas especies de fauna. Es importante entender la coocurrencia entre la fauna y los factores de perturbación, como la actividad furtiva y los ungulados domésticos, para tener un manejo exitoso de los paisajes multifuncionales. Las herramientas que miden esta relación incluyen las fototrampas y las unidades autónomas de grabaciones acústicas. Emparejamos 52 estaciones de fototrampas con grabadoras acústicas para investigar la asociación entre dos medidas de perturbación (actividad furtiva y ganado) y los ungulados silvestres presentes en los paisajes multifuncionales de la Orinoquía colombiana. Usamos modelos conjuntos de distribución de especies para investigar las asociaciones especie-hábitat y las correlaciones especie-perturbación. Ajustamos un modelo con datos de fototrampeo para detectar ungulados silvestres y factores de perturbación; un segundo modelo fue ajustado después de reemplazar las detecciones por fototrampas de los factores de perturbación con las detecciones acústicas correspondientes. La dirección, importancia y precisión del efecto de las covarianzas dependió del método de muestreo usado para los factores de perturbación. El monitoreo acústico casi siempre resultó en estimaciones más precisas de los efectos de las covarianzas y de las correlaciones especie-perturbación. Los patrones de asociación entre la fauna y los factores de perturbación sólo se presentaron cuando las grabadoras acústicas detectaron la perturbación. Las fototrampas nos permitieron detectar especies que no vocalizan, mientras que las grabaciones de audio incrementaron la detección de factores de perturbación, lo que resultó en estimados más precisos de los patrones de coocurrencia. El pecarí de collar (Pecari tajacu), el tapir (Tapirus terrestris) y el venado cola blanca (Odocoileus virginianus) tuvieron coocurrencia con los factores de perturbación y tienen prioridad de conservación debido al mayor riesgo de caza furtiva o transmisión de enfermedades del ganado.

Conceptual and methodological advances in habitat-selection modeling: guidelines for ecology and evolution.

Habitat selection is a fundamental animal behavior that shapes a wide range of ecological processes, including animal movement, nutrient transfer, trophic dynamics and population distribution. Although habitat selection has been a focus of ecological studies for decades, technological, conceptual and methodological advances over the last 20 yr have led to a surge in studies addressing this process. Despite the substantial literature focused on quantifying the habitat-selection patterns of animals, there is a marked lack of guidance on best analytical practices. The conceptual foundations of the most commonly applied modeling frameworks can be confusing even to those well versed in their application. Furthermore, there has yet to be a synthesis of the advances made over the last 20 yr. Therefore, there is a need for both synthesis of the current state of knowledge on habitat selection, and guidance for those seeking to study this process. Here, we provide an approachable overview and synthesis of the literature on habitat-selection analyses (HSAs) conducted using selection functions, which are by far the most applied modeling framework for understanding the habitat-selection process. This review is purposefully non-technical and focused on understanding without heavy mathematical and statistical notation, which can confuse many practitioners. We offer an overview and history of HSAs, describing the tortuous conceptual path to our current understanding. Through this overview, we also aim to address the areas of greatest confusion in the literature. We synthesize the literature outlining the most exciting conceptual advances in the field of habitat-selection modeling, discussing the substantial ecological and evolutionary inference that can be made using contemporary techniques. We aim for this paper to provide clarity for those navigating the complex literature on HSAs while acting as a reference and best practices guide for practitioners.

Using piecewise regression to identify biological phenomena in biotelemetry datasets.

Technological advances in the field of animal tracking have greatly expanded the potential to remotely monitor animals, opening the door to exploring how animals shift their behaviour over time or respond to external stimuli. A wide variety of animal-borne sensors can provide information on an animal's location, movement characteristics, external environmental conditions and internal physiological status. Here, we demonstrate how piecewise regression can be used to identify the presence and timing of potential shifts in a variety of biological responses using multiple biotelemetry data streams. Different biological latent states can be inferred by partitioning a time-series into multiple segments based on changes in modelled responses (e.g. their mean, variance, trend, degree of autocorrelation) and specifying a unique model structure for each interval. We provide six example applications highlighting a variety of taxonomic species, data streams, timescales and biological phenomena. These examples include a short-term behavioural response (flee and return) by a trumpeter swan Cygnus buccinator following a GPS collar deployment; remote identification of parturition based on movements by a pregnant moose Alces alces; a physiological response (spike in heart-rate) in a black bear Ursus americanus to a stressful stimulus (presence of a drone); a mortality event of a trumpeter swan signalled by changes in collar temperature and overall dynamic body acceleration; an unsupervised method for identifying the onset, return, duration and staging use of sandhill crane Antigone canadensis migration; and estimation of the transition between incubation and brood-rearing (i.e. hatching) for a breeding trumpeter swan. We implement analyses using the mcp package in R, which provides functionality for specifying and fitting a wide variety of user-defined model structures in a Bayesian framework and methods for assessing and comparing models using information criteria and cross-validation measures. These simple modelling approaches are accessible to a wide audience and offer a straightforward means of assessing a variety of biologically relevant changes in animal behaviour.

Individual-Level Memory Is Sufficient to Create Spatial Segregation among Neighboring Colonies of Central Place Foragers.

AbstractCentral place foragers often segregate in space, even without signs of direct agonistic interactions. Using parsimonious individual-based simulations, we show that for species with spatial cognitive abilities, individual-level memory of resource availability can be sufficient to cause spatial segregation in the foraging ranges of colonial animals. The shapes of the foraging distributions are governed by commuting costs, the emerging distribution of depleted resources, and the fidelity of foragers to their colonies. When colony fidelity is weak and foragers can easily switch to colonies located closer to favorable foraging grounds, this leads to space partitioning with equidistant borders between neighboring colonies. In contrast, when colony fidelity is strong-for example, because larger colonies provide safety in numbers or individuals are unable to leave-it can create a regional imbalance between resource requirements and resource availability. This leads to nontrivial space-use patterns that propagate through the landscape. Interestingly, while better spatial memory creates more defined boundaries between neighboring colonies, it can lower the average intake rate of the population, suggesting a potential trade-off between an individual's attempt for increased intake and population growth rates.

A 'How to' guide for interpreting parameters in habitat-selection analyses.

Habitat-selection analyses allow researchers to link animals to their environment via habitat-selection or step-selection functions, and are commonly used to address questions related to wildlife management and conservation efforts. Habitat-selection analyses that incorporate movement characteristics, referred to as integrated step-selection analyses, are particularly appealing because they allow modelling of both movement and habitat-selection processes. Despite their popularity, many users struggle with interpreting parameters in habitat-selection and step-selection functions. Integrated step-selection analyses also require several additional steps to translate model parameters into a full-fledged movement model, and the mathematics supporting this approach can be challenging for many to understand. Using simple examples, we demonstrate how weighted distribution theory and the inhomogeneous Poisson point process can facilitate parameter interpretation in habitat-selection analyses. Furthermore, we provide a 'how to' guide illustrating the steps required to implement integrated step-selection analyses using the amt package By providing clear examples with open-source code, we hope to make habitat-selection analyses more understandable and accessible to end users.

Within Reach? Habitat Availability as a Function of Individual Mobility and Spatial Structuring.

Organisms need access to particular habitats for their survival and reproduction. However, even if all necessary habitats are available within the broader environment, they may not all be easily reachable from the position of a single individual. Many species distribution models consider populations in environmental (or niche) space, hence overlooking this fundamental aspect of geographical accessibility. Here, we develop a formal way of thinking about habitat availability in environmental spaces by describing how limitations in accessibility can cause animals to experience a more limited or simply different mixture of habitats than those more broadly available. We develop an analytical framework for characterizing constrained habitat availability based on the statistical properties of movement and environmental autocorrelation. Using simulation experiments, we show that our general statistical representation of constrained availability is a good approximation of habitat availability for particular realizations of landscape-organism interactions. We present two applications of our approach, one to the statistical analysis of habitat preference (using step-selection functions to analyze harbor seal telemetry data) and a second that derives theoretical insights about population viability from knowledge of the underlying environment. Analytical expressions for habitat availability, such as those we develop here, can yield gains in analytical speed, biological realism, and conceptual generality by allowing us to formulate models that are habitat sensitive without needing to be spatially explicit.

Accounting for individual-specific variation in habitat-selection studies: Efficient estimation of mixed-effects models using Bayesian or frequentist computation.

Popular frameworks for studying habitat selection include resource-selection functions (RSFs) and step-selection functions (SSFs), estimated using logistic and conditional logistic regression, respectively. Both frameworks compare environmental covariates associated with locations animals visit with environmental covariates at a set of locations assumed available to the animals. Conceptually, slopes that vary by individual, that is, random coefficient models, could be used to accommodate inter-individual heterogeneity with either approach. While fitting such models for RSFs is possible with standard software for generalized linear mixed-effects models (GLMMs), straightforward and efficient one-step procedures for fitting SSFs with random coefficients are currently lacking. To close this gap, we take advantage of the fact that the conditional logistic regression model (i.e. the SSF) is likelihood-equivalent to a Poisson model with stratum-specific fixed intercepts. By interpreting the intercepts as a random effect with a large (fixed) variance, inference for random-slope models becomes feasible with standard Bayesian techniques, or with frequentist methods that allow one to fix the variance of a random effect. We compare this approach to other commonly applied alternatives, including models without random slopes and mixed conditional regression models fit using a two-step algorithm. Using data from mountain goats (Oreamnos americanus) and Eurasian otters (Lutra lutra), we illustrate that our models lead to valid and feasible inference. In addition, we conduct a simulation study to compare different estimation approaches for SSFs and to demonstrate the importance of including individual-specific slopes when estimating individual- and population-level habitat-selection parameters. By providing coded examples using integrated nested Laplace approximations (INLA) and Template Model Builder (TMB) for Bayesian and frequentist analysis via the R packages R-INLA and glmmTMB, we hope to make efficient estimation of RSFs and SSFs with random effects accessible to anyone in the field. SSFs with individual-specific coefficients are particularly attractive since they can provide insights into movement and habitat-selection processes at fine-spatial and temporal scales, but these models had previously been very challenging to fit.

Uncovering state-dependent relationships in shallow lakes using Bayesian latent variable regression.

Ecosystems sometimes undergo dramatic shifts between contrasting regimes. Shallow lakes, for instance, can transition between two alternative stable states: a clear state dominated by submerged aquatic vegetation and a turbid state dominated by phytoplankton. Theoretical models suggest that critical nutrient thresholds differentiate three lake types: highly resilient clear lakes, lakes that may switch between clear and turbid states following perturbations, and highly resilient turbid lakes. For effective and efficient management of shallow lakes and other systems, managers need tools to identify critical thresholds and state-dependent relationships between driving variables and key system features. Using shallow lakes as a model system for which alternative stable states have been demonstrated, we developed an integrated framework using Bayesian latent variable regression (BLR) to classify lake states, identify critical total phosphorus (TP) thresholds, and estimate steady state relationships between TP and chlorophyll a (chl a) using cross-sectional data. We evaluated the method using data simulated from a stochastic differential equation model and compared its performance to k-means clustering with regression (KMR). We also applied the framework to data comprising 130 shallow lakes. For simulated data sets, BLR had high state classification rates (median/mean accuracy >97%) and accurately estimated TP thresholds and state-dependent TP-chl a relationships. Classification and estimation improved with increasing sample size and decreasing noise levels. Compared to KMR, BLR had higher classification rates and better approximated the TP-chl a steady state relationships and TP thresholds. We fit the BLR model to three different years of empirical shallow lake data, and managers can use the estimated bifurcation diagrams to prioritize lakes for management according to their proximity to thresholds and chance of successful rehabilitation. Our model improves upon previous methods for shallow lakes because it allows classification and regression to occur simultaneously and inform one another, directly estimates TP thresholds and the uncertainty associated with thresholds and state classifications, and enables meaningful constraints to be built into models. The BLR framework is broadly applicable to other ecosystems known to exhibit alternative stable states in which regression can be used to establish relationships between driving variables and state variables.

Methods for implementing integrated step-selection functions with incomplete data.

Integrated step-selection analyses (iSSAs) are versatile and powerful frameworks for studying habitat and movement preferences of tracked animals. iSSAs utilize integrated step-selection functions (iSSFs) to model movements in discrete time, and thus, require animal location data that are regularly spaced in time. However, many real-world datasets are incomplete due to tracking devices failing to locate an individual at one or more scheduled times, leading to slight irregularities in the duration between consecutive animal locations. To address this issue, researchers typically only consider bursts of regular data (i.e., sequences of locations that are equally spaced in time), thereby reducing the number of observations used to model movement and habitat selection. We reassess this practice and explore four alternative approaches that account for temporal irregularity resulting from missing data. Using a simulation study, we compare these alternatives to a baseline approach where temporal irregularity is ignored and demonstrate the potential improvements in model performance that can be gained by leveraging these additional data. We also showcase these benefits using a case study on a spotted hyena (Crocuta crocuta).

A within-lake occupancy model for starry stonewort, Nitellopsis obtusa, to support early detection and monitoring.

To efficiently detect aquatic invasive species early in an invasion when control may still be possible, predictions about which locations are likeliest to be occupied are needed at fine scales but are rarely available. Occupancy modeling could provide such predictions given data of sufficient quality and quantity. We assembled a data set for the macroalga starry stonewort (Nitellopsis obtusa) across Minnesota and Wisconsin, USA, where it is a new and high-priority invader. We used these data to construct a multi-season, single-species spatial occupancy model that included biotic, abiotic, and movement-related predictors. Distance to the nearest access was an important occurrence predictor, highlighting the likely role boats play in spreading starry stonewort. Fetch and water depth also predicted occupancy. We estimated an average detection probability of 63% at sites with mean non-N. obtusa plant cover, declining to ~ 38% at sites with abundant plant cover, especially that of other Characeae. We recommend that surveyors preferentially search for starry stonewort in areas of shallow depth and high fetch close to boat accesses. We also recommend searching during late summer/early fall when detection is likelier. This study illustrates the utility of fine-scale occupancy modeling for predicting the locations of nascent populations of difficult-to-detect species.

Quantifying the effect of habitat availability on species distributions.

1. If animals moved randomly in space, the use of different habitats would be proportional to their availability. Hence, deviations from proportionality between use and availability are considered the tell-tale sign of preference. This principle forms the basis for most habitat selection and species distribution models fitted to use-availability or count data (e.g. MaxEnt and Resource Selection Functions). 2. Yet, once an essential habitat type is sufficiently abundant to meet an individual's needs, increased availability of this habitat type may lead to a decrease in the use/availability ratio. Accordingly, habitat selection functions may estimate negative coefficients when habitats are superabundant, incorrectly suggesting an apparent avoidance. Furthermore, not accounting for the effects of availability on habitat use may lead to poor predictions, particularly when applied to habitats that differ considerably from those for which data have been collected. 3. Using simulations, we show that habitat use varies non-linearly with habitat availability, even when individuals follow simple movement rules to acquire food and avoid risk. The results show that the impact of availability strongly depends on the type of habitat (e.g. whether it is essential or substitutable) and how it interacts with the distribution and availability of other habitats. 4. We demonstrate the utility of a variety of existing and new methods that enable the influence of habitat availability to be explicitly estimated. Models that allow for non-linear effects (using b-spline smoothers) and interactions between environmental covariates defining habitats and measures of their availability were best able to capture simulated patterns of habitat use across a range of environments. 5. An appealing aspect of some of the methods we discuss is that the relative influence of availability is not defined a priori, but directly estimated by the model. This feature is likely to improve model prediction, hint at the mechanism of habitat selection, and may signpost habitats that are critical for the organism's fitness.

A comparison of survey method efficiencies for estimating densities of zebra mussels (Dreissena polymorpha).

Abundance surveys are commonly used to estimate plant or animal densities and frequently require estimating detection probabilities to account for imperfect detection. The estimation of detection probabilities requires additional measurements that take time, potentially reducing the efficiency of the survey when applied to high-density populations. We conducted quadrat, removal, and distance surveys of zebra mussels (Dreissena polymorpha) in three central Minnesota lakes and determined how much survey effort would be required to achieve a pre-specified level of precision for each abundance estimator, allowing us to directly compare survey design efficiencies across a range of conditions. We found that the required sampling effort needed to achieve our precision goal depended on both the survey design and population density. At low densities, survey designs that could cover large areas but with lower detection probabilities, such as distance surveys, were more efficient (i.e., required less sampling effort to achieve the same level of precision). However, at high densities, quadrat surveys, which tend to cover less area but with high detection rates, were more efficient. These results demonstrate that the best survey design is likely to be context-specific, requiring some prior knowledge of the underlying population density and the cost/time needed to collect additional information for estimating detection probabilities.

Circular-linear copulae for animal movement data.

Animal movement is often modelled in discrete time, formulated in terms of steps taken between successive locations at regular time intervals. Steps are characterized by the distance between successive locations (step lengths) and changes in direction (turn angles). Animals commonly exhibit a mix of directed movements with large step lengths and turn angles near 0 when travelling between habitat patches and more wandering movements with small step lengths and uniform turn angles when foraging. Thus, step lengths and turn angles will typically be cross-correlated.Most models of animal movement assume that step lengths and turn angles are independent, likely due to a lack of available alternatives. Here, we show how the method of copulae can be used to fit multivariate distributions that allow for correlated step lengths and turn angles.We describe several newly developed copulae appropriate for modelling animal movement data and fit these distributions to data collected on fishers (Pekania pennanti). The copulae are able to capture the inherent correlation in the data and provide a better fit than a model that assumes independence. Further, we demonstrate via simulation that this correlation can impact movement patterns (e.g. rates of dispersion overtime).We see many opportunities to extend this framework (e.g. to consider autocorrelation in step attributes) and to integrate it into existing frameworks for modelling animal movement and habitat selection. For example, copulae could be used to more accurately sample available locations when conducting habitat-selection analyses.

Generalized functional responses for species distributions.

Researchers employing resource selection functions (RSFs) and other related methods aim to detect correlates of space-use and mitigate against detrimental environmental change. However, an empirical model fit to data from one place or time is unlikely to capture species responses under different conditions because organisms respond nonlinearly to changes in habitat availability. This phenomenon, known as a functional response in resource selection, has been debated extensively in the RSF literature but continues to be ignored by practitioners for lack of a practical treatment. We therefore extend the RSF approach to enable it to estimate generalized functional responses (GFRs) from spatial data. GFRs employ data from several sampling instances characterized by diverse profiles of habitat availability. By modeling the regression coefficients of the underlying RSF as functions of availability, GFRs can account for environmental change and thus predict population distributions in new environments. We formulate the approach as a mixed-effects model so that it is estimable by readily available statistical software. We illustrate its application using (1) simulation and (2) wolf home-range telemetry. Our results indicate that GFRs can offer considerable improvements in estimation speed and predictive ability over existing mixed-effects approaches.

A fresh look at an old concept: home-range estimation in a tidy world.

A rich set of statistical techniques has been developed over the last several decades to estimate the spatial extent of animal home ranges from telemetry data, and new methods to estimate home ranges continue to be developed. Here we investigate home-range estimation from a computational point of view and aim to provide a general framework for computing home ranges, independent of specific estimators. We show how such a workflow can help to make home-range estimation easier and more intuitive, and we provide a series of examples illustrating how different estimators can be compared easily. This allows one to perform a sensitivity analysis to determine the degree to which the choice of estimator influences qualitative and quantitative conclusions. By providing a standardized implementation of home-range estimators, we hope to equip researchers with the tools needed to explore how estimator choice influences answers to biologically meaningful questions.

Estimating the movements of terrestrial animal populations using broad-scale occurrence data.

As human and automated sensor networks collect increasingly massive volumes of animal observations, new opportunities have arisen to use these data to infer or track species movements. Sources of broad scale occurrence datasets include crowdsourced databases, such as eBird and iNaturalist, weather surveillance radars, and passive automated sensors including acoustic monitoring units and camera trap networks. Such data resources represent static observations, typically at the species level, at a given location. Nonetheless, by combining multiple observations across many locations and times it is possible to infer spatially continuous population-level movements. Population-level movement characterizes the aggregated movement of individuals comprising a population, such as range contractions, expansions, climate tracking, or migration, that can result from physical, behavioral, or demographic processes. A desire to model population movements from such forms of occurrence data has led to an evolving field that has created new analytical and statistical approaches that can account for spatial and temporal sampling bias in the observations. The insights generated from the growth of population-level movement research can complement the insights from focal tracking studies, and elucidate mechanisms driving changes in population distributions at potentially larger spatial and temporal scales. This review will summarize current broad-scale occurrence datasets, discuss the latest approaches for utilizing them in population-level movement analyses, and highlight studies where such analyses have provided ecological insights. We outline the conceptual approaches and common methodological steps to infer movements from spatially distributed occurrence data that currently exist for terrestrial animals, though similar approaches may be applicable to plants, freshwater, or marine organisms.

Resampling-based methods for biologists.

Ecological data often violate common assumptions of traditional parametric statistics (e.g., that residuals are Normally distributed, have constant variance, and cases are independent). Modern statistical methods are well equipped to handle these complications, but they can be challenging for non-statisticians to understand and implement. Rather than default to increasingly complex statistical methods, resampling-based methods can sometimes provide an alternative method for performing statistical inference, while also facilitating a deeper understanding of foundational concepts in frequentist statistics (e.g., sampling distributions, confidence intervals, p-values). Using simple examples and case studies, we demonstrate how resampling-based methods can help elucidate core statistical concepts and provide alternative methods for tackling challenging problems across a broad range of ecological applications.

What time is it? Choice of time origin and scale in extended proportional hazards models.

The analysis of telemetry data offers many unique challenges due to both the observation process and the complexity of the underlying system (e.g., risk of mortality may be influenced by both age and a wide range of environmental variables). Although semi-parametric proportional hazards (SPPH) models have been proposed for analyzing ecological data, recent applications have failed to address the importance of choosing an appropriate time origin and scale for analysis. We compared models fit to a long-term deer (Odocoileus spp.) survival data set using three alternative survival timescales: age, time since start of study, and time since 6 June (with a seasonally recurrent timescale). Temporal variability in risk resulted from multiple sources (e.g., changes in hunting pressure, winter severity), and the risk of mortality varied nonlinearly with age (highest risk for young and older individuals). Age-varying hazards were represented well using regression splines, but temporal variability was more difficult to model using parametric assumptions. Annual survival estimates using the three timescales differed considerably. The model using a study-based timescale most closely tracked temporal patterns in risk. Given the difficulties in modeling temporal variability using parametric assumptions, we recommend this approach over an age-based or recurrent timescale when using SPPH models to evaluate the impact of large (naturally occurring or experimental) disturbances or to estimate annual age-specific survival rates. Lastly, we discuss the strengths and limitations of SPPH models relative to fully parametric approaches.