Extracting information from animal movement data has been an active area of research for the past two decades but insights gained have been primarily restricted to understanding animal space use and the underlying behavioural processes driving these patterns (McLoughlin et al. 2010; Smouse et al. 2010). We expanded the scope of information to be gained from animal movement patterns by developing two quantitative methods to infer rates of parturition and neonate offspring survival, both components of individual fitness and often key drivers of population dynamics in wild animals (Stirling et al. 1999; Mahoney and Schaefer 2002; Ogutu et al. 2010). Our results demonstrate that both methods can yield highly accurate estimates of parturition rates and, when applied to high quality data obtained by modern GPS radio-collars, good estimates of neonate survival using the IBM.
As predicted, a sudden and sustained drop in movement rate was indicative of parturition. While other studies have similarly suggested that parturition is correlated with depressed movement rates in ungulates (Poole et al. 2007; Long et al. 2009; Brook 2010), we validated two objective and quantitative methods for determining parturiency from time-series movement data. Both methods were highly accurate (>97%) in predicting parturition and provided appropriate predictions of parturition dates. Moreover, both methods had extremely low false-negative rates (PBM = 0%; IBM < 3%), which contrasts with the high false-negative rate (46%) that confounded the modelling approach of Dzialak et al. (2011; see Table 3 therein) for inferring parturition in elk.
The PBM performed slightly better for predicting parturition, likely due to its increased sensitivity to short duration changes in movement rates. By only considering movements within a three-day moving window, the PBM may detect parturition even in instances where offspring are lost shortly after birth. In contrast, the IBM considers the entire time-series to calculate likelihoods and discriminate among models. For this reason, it is critical that the time-series be restricted to the expected parturition period of the species because detecting differences in movement rates will become increasingly difficult as the volume of movement data outside of the parturition period increases. Nevertheless, even with this requirement, if parturition is close in time to offspring loss, only a small number of data points will be available to create significant changes in the likelihoods and differences among models. In such instances, the non-parturient model will be the most parsimonious fit to the data because movement rates will have changed relatively little when the entire time-series is considered. We attempted to partially overcome this limitation by constraining parturition and offspring loss break points to be at least 24 time steps apart. This constraint explicitly inhibits the ability of the IBM to detect parturition events where offspring loss is within 4 days of birth, or slightly longer if the data have significant gaps. However, given that the IBM still correctly predicted the parturition status of 33 out of 34 females, offspring losses occurring shortly after birth seem to constitute a small proportion of overall offspring losses, at least for the woodland caribou we monitored.
Both methods likely provide more accurate and cost-effective estimates of true parturition rates than traditional methods such as aerial surveys using radio-telemetry. When considering our 2012 data, only six of 15 females were confirmed to have calved by aerial survey whereas both movement-based methods estimated 12 females to have calved. Nagy (2011) reported a similar finding, suggesting that aerial surveys of woodland caribou underestimated parturition rates by 12–19%. The high correlation of our methods with serum progesterone tests for pregnancy further validates the use of movement-based approaches for estimating population-level parturition rates.
Neonate survival status
For predicting neonate survival, the IBM generally performed better, producing reasonably accurate estimates particularly when using the higher quality data of 2011 and 2012 (87% accuracy across both data sets). We attempted to improve the accuracy of both methods by incorporating information other than step length. We considered changes in turning angles and autocorrelation (Gurarie et al. 2009) as well as spatial information (e.g. net-squared displacement from calving site; Fryxell et al. 2008) but found these additional parameters to be uninformative for predicting neonate survival from caribou movement patterns.
At the sample level, predicted rates of neonate survival were close to true sample rates, particularly for the IBM. It is important to note, however, that predicted survival rates incorporate both correct and false predictions of individual survival. This method of comparing grouped predicted outcomes to grouped known outcomes – known as calibration (Altman and Royston 2000) – is necessary because of the difficulty in translating evaluative measures of individual-based binary classification tests (e.g. accuracy) into estimates of uncertainty for population rates. Calibration yields more explicit insight into potential directional biases associated with each method. Our comparison of predicted to known sample rates of survival suggests that neonate survival is overestimated by the PBM and slightly underestimated by the IBM though a more rigorous evaluation of potential bias would require additional years of data.
The better performance of the IBM was likely due to its predictive ability being less influenced by inter-individual variability. By assigning to each individual a distinct baseline for movement rates, prediction by the IBM is confined to evaluating information solely within each individual. In contrast, the PBM compares individual movement rates to population-level thresholds and is thus contingent on variation within the population. This difference becomes increasingly important as the magnitude of movement variability among individuals increases. Variability in movement rates among females likely increases with offspring age such that the variability among females with 4 week old offspring is much greater than the variability among females in the first few days post-partum (Testa et al. 2000; Odonkhuu et al. 2009). With increasing variability, selecting a threshold that is adequate for all individuals becomes increasingly difficult, particularly in populations where individual personalities may vary widely from “slow” to “active” (Sih et al. 2004; Boon et al. 2008). If a threshold indicative of calf loss is too low, “active” mothers and offspring may exceed the threshold, resulting in an overestimation of offspring loss. Conversely, if a threshold is too high, females with normally “slow” movement rates may not exceed the threshold after offspring loss, resulting in an overestimation of offspring survival. This latter scenario was illustrated by the low sensitivity values recorded when we used the upper bound of our threshold's 95% confidence interval for prediction. Because high inter-individual variation in movement rates is prevalent in many animal populations (Odonkhuu et al. 2009; Olson et al. 2010; Mueller et al. 2011), individual-based approaches such as the IBM will be preferable for predicting neonate survival in most instances.
Misclassification of calf status may also be influenced by the agent of mortality. In most ungulate populations, predation is the primary cause of mortality in neonatal offspring with a relatively small proportion lost to disease and other natural causes (Gustine et al. 2006; Barber-Meyer et al. 2008; Carstensen et al. 2009). In predation events where the predator represents a threat to the female as well as her offspring (e.g. wolves [Canis lupus] for ungulates), the change in maternal movement should be sudden and sustained, creating a break point that is clearly evident. Conversely, if offspring are lost to natural causes or to a predator that does not directly threaten the female, then a break point may be less discernible, particularly if the female remains in the area for a few days before slowly moving away. This latter scenario could result in a false prediction of offspring survival. In our study, we did not have information regarding the true causes of calf mortality to directly assess this potential effect; however, determining whether female movement patterns contain information regarding the possible cause of offspring mortality represents an area for future research.
Due to the analytical framework of both methods, false predictions of offspring survival can result when offspring mortalities occur near the end of the time-series data. For the IBM, this situation results in a small number of post-loss steps being available to differentiate between the models of offspring survival and offspring loss. Moreover, pre-loss and post-loss movement rates will be similar because offspring movement rates are approaching adult rates at this time. Because the IBM uses the entire time-series to compare models, parsimony may favour the model of offspring survival. With the PBM, if offspring loss occurs on the last day of the time-series (i.e. when the calf is 3 weeks and 6 days old), the number of data points post-loss may be insufficient to raise the average of the three-day moving window above the threshold value indicative of calf loss. Overall, when estimating survival rates at the population level, any potential bias resulting from the timing of offspring loss should be small unless true offspring losses are skewed toward the end of the neonatal period (e.g., near 4 weeks of age for caribou).
Data quality was the most significant factor influencing the ability to predict offspring survival. Increasing gappiness in the time-series data negatively affected predictive performance of both methods. On average, the 2004 data set had a 30% reduction in the number of steps available for estimation compared to the other data sets, with some individuals missing complete days of data. Data quality affected each method differently. For the IBM, specificity was reduced because consecutive missed steps could affect the assumption that offspring movement rates increase linearly post-partum. If movement rates after the data gap significantly differed from movement rates before the gap, then a second break point in the time-series could be created regardless of true offspring survival status, resulting in overestimation of offspring loss (see also Appendix S3). For ungulates in particular, data gaps would be especially problematic in the 2–4 week interval post-partum when offspring movement rates can change substantially over a short interval (Testa et al. 2000; Odonkhuu et al. 2009). Alternatively, if the PBM is used, data gaps could result in a small number of data points within the three-day moving window, increasing the probability of sampling error. As a result, estimated movement rates within these data-deficient windows may differ significantly from true values. Because of these issues, data quality needs to be assessed prior to the application of movement-based methods for estimating offspring survival rates. For data sets with fix rates of <90%, estimates of offspring survival may be unreliable, particularly when gaps spanning more than a day are present. However, with fix rates and location accuracy continuing to improve in modern GPS radio-collars (Frair et al. 2010), issues related to data quality should be less problematic with more recent data sets.
The better performance of both methods with the 2011 and 2012 data sets may have been influenced by the carryover of some individuals from 2011 into 2012, creating an issue of non-independence. We note, however, that for the PBM only three of the individuals used to establish the calf loss threshold were included in the 2012 data set and all three had different known statuses in 2012 (e.g. calf survived in 2011, calf lost in 2012). Further, of the 12 females predicted to have calved in 2012 and therefore considered for further analysis of calf survival, only five were carried over from 2011 and of these five, four had different known statuses between years. Based on this information, any non-independence issues likely had minimal impact on our overall results and inferences.