Combining multiple data sources with different biases in state-space models for population dynamics.

The resolution at which animal populations can be modeled can be increased when multiple datasets corresponding to different life stages are available, allowing, for example, seasonal instead of annual descriptions of dynamics. However, the abundance estimates used for model fitting can have multiple sources of error, both random and systematic, namely bias. We focus here on the consequences of, and how to address, differing and unknown observation biases when fitting models.State-space models (SSMs) separate process variation and observation error, thus providing a framework to account for different and unknown estimate biases across multiple datasets. Here we study the effects on the inference of including or excluding bias parameters for a sequential life stage population dynamics SSM using a combination of theory, simulation experiments, and an empirical example.When the data, that is, abundance estimates, are unbiased, including bias parameters leads to increased imprecision compared to a model that correctly excludes bias parameters. But when observations are biased and no bias parameters are estimated, recruitment and survival processes are inaccurately estimated and estimates of process variance become biased high. These problems are substantially reduced by including bias parameters and fixing one of them at even an incorrect value. The primary inferential challenge is that models with bias parameters can show properties of being parameter redundant even when they are not in theory.Combining multiple datasets into a single analysis by using bias parameters to rescale data can offer significant improvements to inference and model diagnostics. Because their estimability in practice is dataset specific and will likely require more precise estimates than might be expected from ecological datasets, we outline some strategies for characterizing process uncertainty when it is confounded by bias parameters.

Improving inference for nonlinear state-space models of animal population dynamics given biased sequential life stage data.

State-space models (SSMs) are a popular tool for modeling animal abundances. Inference difficulties for simple linear SSMs are well known, particularly in relation to simultaneous estimation of process and observation variances. Several remedies to overcome estimation problems have been studied for relatively simple SSMs, but whether these challenges and proposed remedies apply for nonlinear stage-structured SSMs, an important class of ecological models, is less well understood. Here we identify improvements for inference about nonlinear stage-structured SSMs fit with biased sequential life stage data. Theoretical analyses indicate parameter identifiability requires covariates in the state processes. Simulation studies show that plugging in externally estimated observation variances, as opposed to jointly estimating them with other parameters, reduces bias and standard error of estimates. In contrast to previous results for simple linear SSMs, strong confounding between jointly estimated process and observation variance parameters was not found in the models explored here. However, when observation variance was also estimated in the motivating case study, the resulting process variance estimates were implausibly low (near-zero). As SSMs are used in increasingly complex ways, understanding when inference can be expected to be successful, and what aids it, becomes more important. Our study illustrates (a) the need for relevant process covariates and (b) the benefits of using externally estimated observation variances for inference about nonlinear stage-structured SSMs.

Social rank overrides environmental and community fluctuations in determining meat access by female chimpanzees in the Taï National Park, Côte d'Ivoire.

Meat, long hypothesized as an important food source in human evolution, is still a substantial component of the modern human diet, with some humans relying entirely on meat during certain times of the year. Understanding the socio-ecological context leading to the successful acquisition and consumption of meat by chimpanzees (Pan troglodytes), our closest living relative, can provide insight into the emergence of this trait because humans and chimpanzees are unusual among primates in that they both (i) hunt mammalian prey, (ii) share meat with community members, and (iii) form long-term relationships and complex social hierarchies within their communities. However, females in both human hunter-gatherer societies as well as chimpanzee groups rarely hunt, instead typically accessing meat via males that share meat with group members. In general, female chimpanzee dominance rank affects feeding competition, but so far, the effect of female dominance rank on meat access found different results within and across studied chimpanzee groups. Here we contribute to the debate on how female rank influences meat access while controlling for several socio-ecological variables. Multivariate analyses of 773 separate meat-eating events collected over more than 25 years from two chimpanzee communities located in the Taï National Park, Côte d'Ivoire, were used to test the importance of female dominance rank for being present at, and for acquiring meat, during meat-eating events. We found that high-ranking females were more likely to be present during a meat-eating event and, in addition, were more likely to eat meat compared to the subordinates. These findings were robust to both large demographic changes (decrease of community size) and seasonal ecological changes (fruit abundance dynamics). In addition to social rank, we found that other female properties had a positive influence on presence to meat-eating events and access to meat given presence, including oestrus status, nursing of a small infant, and age. Similar to findings in other chimpanzee populations, our results suggest that females reliably acquire meat over their lifetime despite rarely being active hunters. The implication of this study supports the hypothesis that dominance rank is an important female chimpanzee property conferring benefits for the high-ranking females.

Spatio-temporal complexity of chimpanzee food: How cognitive adaptations can counteract the ephemeral nature of ripe fruit.

Ecological complexity has been proposed to play a crucial role in primate brain-size evolution. However, detailed quantification of ecological complexity is still limited. Here we assess the spatio-temporal distribution of tropical fruits and young leaves, two primary chimpanzee (Pan troglodytes) foods, focusing on the predictability of their availability in individual trees. Using up to 20 years of information on monthly availability of young leaf, unripe and ripe fruit in plant species consumed by chimpanzees from tropical forests in East, Central, and West Africa, we estimated: (1) the forest-wide frequency of occurrence of each food type and (2) the predictability of finding ripe fruit-bearing trees, focusing on the timing, frequency, and amount of ripe fruit present. In all three forests, at least half of all encountered trees belonged to species that chimpanzees were known to feed on. However, the proportion of these trees bearing young leaves and fruit fluctuated widely between months. Ripe fruit was the most ephemeral food source, and trees that had more than half of their crown filled were at least nine times scarcer than other trees. In old growth forests only one large ripe fruit crop was on average encountered per 10 km. High levels of inter-individual variation in the number of months that fruit was present existed, and in some extreme cases individuals bore ripe fruit more than seven times as often as conspecifics. Some species showed substantially less variation in such ripe fruit production frequencies and fruit quantity than others. We hypothesize that chimpanzees employ a suite of cognitive mechanisms, including abilities to: (1) generalize or classify food trees; (2) remember the relative metrics of quantity and frequency of fruit production across years; and (3) flexibly plan return times to feeding trees to optimize high-energy food consumption in individual trees, and efficient travel between them. Am. J. Primatol. 78:626-645, 2016. © 2016 Wiley Periodicals, Inc.

Elucidating the significance of spatial memory on movement decisions by African savannah elephants using state-space models.

Spatial memory facilitates resource acquisition where resources are patchy, but how it influences movement behaviour of wide-ranging species remains to be resolved. We examined African elephant spatial memory reflected in movement decisions regarding access to perennial waterholes. State-space models of movement data revealed a rapid, highly directional movement behaviour almost exclusively associated with visiting perennial water. Behavioural change point (BCP) analyses demonstrated that these goal-oriented movements were initiated on average 4.59 km, and up to 49.97 km, from the visited waterhole, with the closest waterhole accessed 90% of the time. Distances of decision points increased when switching to different waterholes, during the dry season, or for female groups relative to males, while selection of the closest waterhole decreased when switching. Overall, our analyses indicated detailed spatial knowledge over large scales, enabling elephants to minimize travel distance through highly directional movement when accessing water. We discuss the likely cognitive and socioecological mechanisms driving these spatially precise movements that are most consistent with our findings. By applying modern analytic techniques to high-resolution movement data, this study illustrates emerging approaches for studying how cognition structures animal movement behaviour in different ecological and social contexts.

Spatial cohesion of adult male chimpanzees (Pan troglodytes verus) in Taï National Park, Côte d'Ivoire.

Group living animals can exhibit fission-fusion behavior whereby individuals temporarily separate to reduce the costs of living in large groups. Primates living in groups with fission-fusion dynamics face numerous challenges in maintaining spatial cohesion, especially in environments with limited visibility. Here we investigated the spatial cohesion of adult male chimpanzees (Pan troglodytes verus) living in Taï National Park, Côte d'Ivoire, to better understand the mechanisms by which individuals maintain group cohesion during fission-fusion events. Over a 3-year period, we simultaneously tracked the movements of 2-4 males for 4-12 hr on up to 12 consecutive days using handheld GPS devices that recorded locations at one-minute intervals. Analyses of the male's inter-individual distance (IID) showed that the maximum, median, and mean IID values across all observations were 7.2 km, 73 m, and 483 m, respectively. These males (a) had maximum daily IID values below the limits of auditory communication (<1 km) for 63% of the observation time, (b) remained out of visual range (≥100 m) for 46% of observation time, and (c) remained within auditory range for 70% of the time when they were in different parties. We compared the observed distribution of IIDs with a random distribution obtained from permutations of the individuals' travel paths using Kolmogorov-Smirnov tests. Observation IID values were significantly smaller than those generated by the permutation procedure. We conclude that these male chimpanzees actively maintain cohesion when out of sight, and that auditory communication is one likely mechanism by which they do so. We discuss mechanisms by which chimpanzees may maintain the level of cohesion observed. This study provides a first analysis of spatial group cohesion over large distances in forest chimpanzees using high-resolution tracking, and illustrates the utility of such data for quantifying socio-ecological processes in primate ecology.

Wild chimpanzees plan their breakfast time, type, and location.

Not all tropical fruits are equally desired by rainforest foragers and some fruit trees get depleted more quickly and carry fruit for shorter periods than others. We investigated whether a ripe-fruit specialist, the chimpanzee (Pan troglodytes verus), arrived earlier at breakfast sites with very ephemeral and highly sought-after fruit, like figs, than sites with less ephemeral fruit that can be more predictably obtained throughout the entire day. We recorded when and where five adult female chimpanzees spent the night and acquired food for a total of 275 full days during three fruit-scarce periods in a West African tropical rainforest. We found that chimpanzees left their sleeping nests earlier (often before sunrise when the forest is still dark) when breakfasting on very ephemeral fruits, especially when they were farther away. Moreover, the females positioned their sleeping nests more in the direction of the next day's breakfast sites with ephemeral fruit compared with breakfast sites with other fruit. By analyzing departure times and nest positioning as a function of fruit type and location, while controlling for more parsimonious explanations, such as temperature, we found evidence that wild chimpanzees flexibly plan their breakfast time, type, and location after weighing multiple disparate pieces of information. Our study reveals a cognitive mechanism by which large-brained primates can buffer the effects of seasonal declines in food availability and increased interspecific competition to facilitate first access to nutritious food. We discuss the implications for theories on hominoid brain-size evolution.

Generalized additive mixed models for disentangling long-term trends, local anomalies, and seasonality in fruit tree phenology.

Quantifying temporal patterns of ephemeral plant structures such as leaves, flowers, and fruits gives insight into both plant and animal ecology. Different scales of temporal changes in fruits, for example within- versus across-year variability, are driven by different processes, but are not always easy to disentangle. We apply generalized additive mixed models (GAMMs) to study a long-term fruit presence-absence data set of individual trees collected from a high-altitude Afromontane tropical rain forest site within Bwindi Impenetrable National Park (BINP), Uganda. Our primary aim was to highlight and evaluate GAMM methodology, and quantify both intra- and interannual changes in fruit production. First, we conduct several simulation experiments to study the practical utility of model selection and smooth term estimation relevant for disentangling intra- and interannual variability. These simulations indicate that estimation of nonlinearity and seasonality is generally accurately identified using asymptotic theory. Applied to the empirical data set, we found that the forest-level fruiting variability arises from both regular seasonality and significant interannual variability, with the years 2009-2010 in particular showing a significant increase in the presence of fruits-driven by increased productivity of most species, and a regular annual peak associated occurring at the end of one of the two dry seasons. Our analyses illustrate a statistical framework for disentangling short-term increases/decreases in fruiting effort while pinpointing specific times in which fruiting is atypical, providing a first step for assessing the impacts of regular and irregular (e.g., climate change) abiotic covariates on fruiting phenology. Some consequences of the rich diversity of fruiting patterns observed here for the population biology of frugivores in BINP are also discussed.

Using diel movement behavior to infer foraging strategies related to ecological and social factors in elephants.

BACKGROUND: Adaptive movement behaviors allow individuals to respond to fluctuations in resource quality and distribution in order to maintain fitness. Classically, studies of the interaction between ecological conditions and movement behavior have focused on such metrics as travel distance, velocity, home range size or patch occupancy time as the salient metrics of behavior. Driven by the emergence of very regular high frequency data, more recently the importance of interpreting the autocorrelation structure of movement as a behavioral metric has become apparent. Studying movement of a free ranging African savannah elephant population, we evaluated how two movement metrics, diel displacement (DD) and movement predictability (MP - the degree of autocorrelated movement activity at diel time scales), changed in response to variation in resource availability as measured by the Normalized Difference Vegetation Index. We were able to capitalize on long term (multi-year) yet high resolution (hourly) global positioning system tracking datasets, the sample size of which allows robust analysis of complex models. We use optimal foraging theory predictions as a framework to interpret our results, in particular contrasting the behaviors across changes in social rank and resource availability to infer which movement behaviors at diel time scales may be optimal in this highly social species. RESULTS: Both DD and MP increased with increasing forage availability, irrespective of rank, reflecting increased energy expenditure and movement predictability during time periods of overall high resource availability. However, significant interactions between forage availability and social rank indicated a stronger response in DD, and a weaker response in MP, with increasing social status. CONCLUSIONS: Relative to high ranking individuals, low ranking individuals expended more energy and exhibited less behavioral movement autocorrelation during lower forage availability conditions, likely reflecting sub-optimal movement behavior. Beyond situations of contest competition, rank status appears to influence the extent to which individuals can modify their movement strategies across periods with differing forage availability. Large-scale spatiotemporal resource complexity not only impacts fine scale movement and optimal foraging strategies directly, but likely impacts rates of inter- and intra-specific interactions and competition resulting in socially based movement responses to ecological dynamics.

A framework for understanding the architecture of collective movements using pairwise analyses of animal movement data.

The study of collective or group-level movement patterns can provide insight regarding the socio-ecological interface, the evolution of self-organization and mechanisms of inter-individual information exchange. The suite of drivers influencing coordinated movement trajectories occur across scales, resulting from regular annual, seasonal and circadian stimuli and irregular intra- or interspecific interactions and environmental encounters acting on individuals. Here, we promote a conceptual framework with an associated statistical machinery to quantify the type and degree of synchrony, spanning absence to complete, in pairwise movements. The application of this framework offers a foundation for detailed understanding of collective movement patterns and causes. We emphasize the use of Fourier and wavelet approaches of measuring pairwise movement properties and illustrate them with simulations that contain different types of complexity in individual movement, correlation in movement stochasticity, and transience in movement relatedness. Application of this framework to movements of free-ranging African elephants (Loxodonta africana) provides unique insight on the separate roles of sociality and ecology in the fission-fusion society of these animals, quantitatively characterizing the types of bonding that occur at different levels of social relatedness in a movement context. We conclude with a discussion about expanding this framework to the context of larger (greater than three) groups towards understanding broader population and interspecific collective movement patterns and their mechanisms.

From moonlight to movement and synchronized randomness: Fourier and wavelet analyses of animal location time series data.

High-resolution animal location data are increasingly available, requiring analytical approaches and statistical tools that can accommodate the temporal structure and transient dynamics (non-stationarity) inherent in natural systems. Traditional analyses often assume uncorrelated or weakly correlated temporal structure in the velocity (net displacement) time series constructed using sequential location data. We propose that frequency and time-frequency domain methods, embodied by Fourier and wavelet transforms, can serve as useful probes in early investigations of animal movement data, stimulating new ecological insight and questions. We introduce a novel movement model with time-varying parameters to study these methods in an animal movement context. Simulation studies show that the spectral signature given by these methods provides a useful approach for statistically detecting and characterizing temporal dependency in animal movement data. In addition, our simulations provide a connection between the spectral signatures observed in empirical data with null hypotheses about expected animal activity. Our analyses also show that there is not a specific one-to-one relationship between the spectral signatures and behavior type and that departures from the anticipated signatures are also informative. Box plots of net displacement arranged by time of day and conditioned on common spectral properties can help interpret the spectral signatures of empirical data. The first case study is based on the movement trajectory of a lion (Panthera leo) that shows several characteristic daily activity sequences, including an active-rest cycle that is correlated with moonlight brightness. A second example based on six pairs of African buffalo (Syncerus caffer) illustrates the use of wavelet coherency to show that their movements synchronize when they are within approximately 1 km of each other, even when individual movement was best described as an uncorrelated random walk, providing an important spatial baseline of movement synchrony and suggesting that local behavioral cues play a strong role in driving movement patterns. We conclude with a discussion about the role these methods may have in guiding appropriately flexible probabilistic models connecting movement with biotic and abiotic covariates.

Likelihood ridges and multimodality in population growth rate models.

A central problem in population ecology is to use time series data to estimate the form of density dependence in the per capita growth rate (pgr). This is often accomplished with phenomenological models such as the theta-Ricker or generalized Beverton-Holt. Using the theta-Ricker model as a simple but flexible description of density dependence, we apply theory and simulations to show how multimodality and ridges in the likelihood surface can emerge even in the absence of model misspecification or observation error. The message for model fitting of real data is to consider the likelihood surface in detail, check whether the best-fit model is located on a likelihood ridge and, if so, evaluate predictive differences of biologically plausible models along the ridge. We present a detailed analysis of a focal data set showing how multimodality and ridges emerge in practice for fits of several parametric models, including a state-space model with explicit accommodation of observation error. Best-fit models for these data are biologically dubious beyond the range of the data, and likelihood ratio confidence regions include a wide range of more biologically plausible models. We demonstrate the broad relevance of these findings by presenting analyses of 25 additional data sets spanning a wide range of taxa. The results here are relevant to information-theoretic and Bayesian methods, which also rely on likelihoods. Beyond presentation of best-fit models and confidence regions around individual parameters, effort toward understanding features of the likelihood surface will help ensure the most robust translation from statistical analysis to biological interpretation.

Disentangling the effects of forage, social rank, and risk on movement autocorrelation of elephants using Fourier and wavelet analyses.

The internal state of an individual-as it relates to thirst, hunger, fear, or reproductive drive-can be inferred by referencing points on its movement path to external environmental and sociological variables. Using time-series approaches to characterize autocorrelative properties of step-length movements collated every 3 h for seven free-ranging African elephants, we examined the influence of social rank, predation risk, and seasonal variation in resource abundance on periodic properties of movement. The frequency domain methods of Fourier and wavelet analyses provide compact summaries of temporal autocorrelation and show both strong diurnal and seasonal based periodicities in the step-length time series. This autocorrelation is weaker during the wet season, indicating random movements are more common when ecological conditions are good. Periodograms of socially dominant individuals are consistent across seasons, whereas subordinate individuals show distinct differences diverging from that of dominants during the dry season. We link temporally localized statistical properties of movement to landscape features and find that diurnal movement correlation is more common within protected wildlife areas, and multiday movement correlations found among lower ranked individuals are typically outside of protected areas where predation risks are greatest. A frequency-related spatial analysis of movement-step lengths reveal that rest cycles related to the spatial distribution of critical resources (i.e., forage and water) are responsible for creating the observed patterns. Our approach generates unique information regarding the spatial-temporal interplay between environmental and individual characteristics, providing an original approach for understanding the movement ecology of individual animals and the spatial organization of animal populations.

Empirical models of pollen limitation, resource acquisition, and mast seeding by a bee-pollinated wildflower.

Synchronous mast seeding is increasingly recognized as common in plant populations. Recent theoretical models show that synchronous mast seeding could be a consequence of resource allocation and storage within individual plants, coupled by pollen limitation in low-flowering years. We used long-term population and weather data to parameterize models of flowering based on stored resources and pollen limitation in Astragalus scaphoides, a bee-pollinated plant that flowers in alternate years. We used these models to test whether internal resource dynamics could explain mast seeding in A. scaphoides and, if so, whether synchrony was caused by pollen limitation and/or fluctuations in precipitation. We compared predictions of models that included all combinations of three factors: constant versus precipitation-dependent resource gain, uniform versus heterogeneous resource gain (among individual plants), and resource-dependent versus resource- and pollen-limited fruit set. Pollen limitation and heterogeneous resource gain were necessary and sufficient to explain alternate-year flowering, but precipitation increased the quantitative match between model predictions and flowering dynamics. Together, our results support the importance of density-dependent pollen limitation as an ultimate and proximate cause of mast seeding in A. scaphoides. Precipitation does not act as a direct cue for synchrony in this species but might affect long-term resource gain and fruiting dynamics.