Autocorrelated data in telemetry studies: time to independence and the problem of behavioural effects

Independence of locational fixes, to reduce the effects of autocorrelation, is often deemed a prerequisite for estimation of home range size and utilization when using data derived from telemetric studies. Three methods of estimating times to independence using movement estimates, along with a statistical method of estimating the level of autocorrelation of locational data, were examined for two species of mammal. Attempts to achieve statistically independent data by subsampling resulted in severe redundancy in the data and significant underestimation of range size and rates of movement. Even a sample interval of one fix per week did not guarantee independence and also resulted in underestimation of range size despite range asymptotes being reached. It would appear that the correct strategy for the best possible estimation of range size and use from telemetry would be the repeated use of as short a sampling interval as is possible over an extended period of time. Statistical methods to measure levels of autocorrelation in locational data may be useful for comparing rates of range use between different populations of the same species or between species, as long as the same sample interval is used.     

Population estimates and dispersal of Hydrotaea irritans Fallén

Abstract. 1. Population estimates of Hydrotaea irritans were made by a mark and recapture technique at one site from 1976 to 1978.
2. Population densities of five to 200 thousand ha^-1 were found with large-scale immigration and emigration occurring from the site.
3. The dispersal of marked adults from a point of release was rapid and marked flies were captured up to 3 km from the release point.
4. The distribution of flies along a woodland strip was not homogeneous; certain areas appeared to be more attractive and held more flies over a period of time.
5. The importance of the increasing area within which flies may be found as they move outwards from the release point is discussed.     

BIODIVERSITY RESEARCH: Fidelity to foraging sites,consistency of migration routes and habitat modulation of home range by sea turtles

Aim Resources can shape patterns of habitat utilization. Recently a broad foraging dichotomy between oceanic and coastal sites has been revealed for loggerhead sea turtles (Caretta caretta). Since oceanic and coastal foraging sites differ in prey availability, we might expect a gross difference in home‐range size across these habitats. We tested this hypothesis by equipping nine adult male loggerhead sea turtles with GPS tracking devices. Location National Marine Park of Zakynthos (NMPZ) Greece, central and eastern Mediterranean (Adriatic, Ionian and Aegean seas). Methods In 2007, 2008 and 2009, Fastloc GPS‐Argos transmitters were attached to nine male loggerheads. In addition, a Sirtrack PTT unit was attached to one male in 2007. Four of the turtles were tracked on successive years. We filtered the GPS data to ensure comparable data volumes. Route consistency between breeding and foraging sites of the four re‐tracked turtles was conducted. Foraging site home range areas and within site movement patterns were investigated by the fixed kernel density method. Results Foraging home range size ranged between circa 10 km² at neritic habitats (coastal and open‐sea on the continental shelf) to circa 1000 km² at oceanic sites (using 90% kernel estimates), the latter most probably reflecting sparsely distributed oceanic prey. Across different years individuals did not follow exactly the same migration routes, but did show fidelity to their previous foraging sites, whether oceanic or neritic, with accurate homing in the final stages of migration. Main conclusions The broad distribution and diverse life‐history strategies of this population could complicate the identification of priority marine protected areas beyond the core breeding site.     

Commercial harvest and export of snapping turtles (Chelydra serpentina) in the United States: trends and the efficacy of size limits at reducing harvest

As Asian turtle populations have crashed, China has increasingly turned to international import to meet domestic demand, which has increased pressure on global turtle populations. Snapping turtles (Chelydra serpentina) are being harvested in unprecedented numbers in the United States (US) to meet the needs of this international market. Here we report US snapping turtle live export from 1999 to 2013, and for the first time test the effectiveness of size limits in reducing commercial harvest numbers. Over three million live snapping turtles from farm and wild caught stock were exported from the US to Asia in 2012–14 alone. Increases in the export of wild caught snapping turtles to over 200,000 individuals in 2012 and 2014, compared to under 50,000 in other years, may indicate that farms are becoming unable to keep up with increasing demand. Annual harvest pressure at the state level increased linearly from 1998 to 2013, mirroring trends in federal export over the same time period. Our model estimates that size-limits were effective at reducing harvest by 30–87% in years with high harvest pressure. However, the majority of size limit regulations result in the removal of larger breeding adults, which has been shown to be detrimental to long term population viability. Regulatory approaches dedicated to the long term management of this iconic species will need to balance the short term gains, in the form of reduced harvest rates, with long term population viability.     

Food competition in captive juvenile snapping turtles, Chelydra serpentina

Food-competitive hierarchies and their stability in snapping turtles, Chelydra serpentina, were studied. Nine hatchling turtles were paired against each other in independent tests of food-obtaining dominance. Turtles differed in ability to obtain food. These differences appeared stable over time, and were linear. Neck-stretching, snapping, and clawing were the major behavioural patterns involved in food-appetitive and aggressive encounters.     

Sampling effects, noise, and photobleaching in temporal image correlation spectroscopy

We present an extensive investigation of the accuracy and precision of temporal image correlation spectroscopy (TICS). Using simulations of laser scanning microscopy image time series, we investigate the effect of spatiotemporal sampling, particle density, noise, sampling frequency, and photobleaching of fluorophores on the recovery of transport coefficients and number densities by TICS. We show that the recovery of transport coefficients is usually limited by spatial sampling, while the measurement of accurate number densities is restricted by background noise in an image series. We also demonstrate that photobleaching of the fluorophore causes a consistent overestimation of diffusion coefficients and flow rates, and a severe underestimation of number densities. We derive a bleaching correction equation that removes both of these biases when used to fit temporal autocorrelation functions, without increasing the number of fit parameters. Finally, we image the basal membrane of a CHO cell with EGFP/alpha-actinin, using two-photon microscopy, and analyze a subregion of this series using TICS and apply the bleaching correction. We show that the photobleaching correction can be determined simply by using the average image intensities from the time series, and we use the simulations to provide good estimates of the accuracy and precision of the number density and transport coefficients measured with TICS.     

Estimating environmental effects on population dynamics: consequences of observation error

Within the paradigm of population dynamics a central task is to identify environmental factors affecting population change and to estimate the strength of these effects. We here investigate the impact of observation errors in measurements of population densities on estimates of environmental effects. Adding observation errors may change the autocorrelation of a population time series with potential consequences for estimates of effects of autocorrelated environmental covariates. Using Monte Carlo simulations, we compare the performance of maximum likelihood estimates from three stochastic versions of the Gompertz model (log–linear first order autoregressive model), assuming 1) process error only, 2) observation error only, and 3) both process and observation error (the linear state–space model on log‐scale). We also simulated population dynamics using the Ricker model, and evaluated the corresponding maximum likelihood estimates for process error models. When there is observation error in the data and the considered environmental variable is strongly autocorrelated, its estimated effect is likely to be biased when using process error models. The environmental effect is overestimated when the sign of the autocorrelations of the intrinsic dynamics and the environment are the same and underestimated when the signs differ. With non‐autocorrelated environmental covariates, process error models produce fairly exact point estimates as well as reliable confidence intervals for environmental effects. In all scenarios, observation error models produce unbiased estimates with reasonable precision, but confidence intervals derived from the likelihood profiles are far too optimistic if there is process error present. The safest approach is to use state–space models in presence of observation error. These are factors worthwhile to consider when interpreting earlier empirical results on population time series, and in future studies, we recommend choosing carefully the modelling approach with respect to intrinsic population dynamics and covariate autocorrelation.     

Land-cover data improve bioclimatic models for anurans and turtles at a regional scale

Aim We investigated whether accounting for land cover could improve bioclimatic models for eight species of anurans and three species of turtles at a regional scale. We then tested whether accounting for spatial autocorrelation could significantly improve bioclimatic models after statistically controlling for the effects of land cover. Location Nova Scotia, eastern Canada. Methods Species distribution data were taken from a recent (1999–2003) herpetofaunal atlas. Generalized linear models were used to relate the presence or absence of each species to climate and land‐cover variables at a 10‐km resolution. We then accounted for spatial autocorrelation using an autocovariate or third‐order trend surface of the geographical coordinates of each grid square. Finally, variance partitioning was used to explore the independent and joint contributions of climate, land cover and spatial autocorrelation. Results The inclusion of land cover significantly increased the explanatory power of bioclimatic models for 10 of the 11 species. Furthermore, including land cover significantly increased predictive performance for eight of the 11 species. Accounting for spatial autocorrelation improved model fit for rare species but generally did not improve prediction success. Variance partitioning demonstrated that this lack of improvement was a result of the high correlation between climate and trend‐surface variables. Main conclusions The results of this study suggest that accounting for the effects of land cover can significantly improve the explanatory and predictive power of bioclimatic models for anurans and turtles at a regional scale. We argue that the integration of climate and land‐cover data is likely to produce more accurate spatial predictions of contemporary herpetofaunal diversity. However, the use of land‐cover simulations in climate‐induced range‐shift projections introduces additional uncertainty into the predictions of bioclimatic models. Further research is therefore needed to determine whether accounting for the effects of land cover in range‐shift projections is merited.     

Detecting autocorrelation problems from GPS collar data in livestock studies

Uneven use of grasslands and savannas by livestock has a significant impact on ecosystem productivity, biodiversity, and function. In studies of livestock distribution, global positioning systems (GPS) collars are frequently used and the rapid rate of technological improvement has brought new opportunities to collect extremely large amounts of very accurate spatial information. However, these advances also pose statistical challenges associated with the analysis of large, temporally correlated, datasets. Our main goal was to find the optimal sampling time intervals for GPS collar schedules when studying livestock distribution in semi-arid ecosystems. The schedule must provide maximum spatio-temporal information while avoiding problems of autocorrelation of sequential locations to provide a methodology that is both practical and statistically valid. We used GPS collar data collected in the Southwestern region of the United States. In each study cattle were tracked and data were recorded every 5 min. Location information from the 5-min GPS fixes were subsampled into 10, 20, 30, 60, 90, 120, 150, 180, 240, 300, 360, and 420-min regular intervals. We calculated the Euclidean distance between pairs of successive locations then conducted correlation analyses to determine the degree of similarity between successive traveled distances. We then selected two correlated and two non-correlated time-interval datasets to compare estimates of kernel home range and minimum convex polygon areas. Successive Euclidean distances between GPS locations were significantly correlated when time intervals were <120 min. The calculated distance traveled was significantly reduced as time intervals between successive locations increased. Kernel home range values were smaller in correlated than in non-correlated datasets yet minimum convex polygon values were greater in correlated data than in non-correlated data sets. Our study shows the importance of considering different livestock sampling time intervals using GPS to achieve accurate and meaningful results on animal distributions especially in semi-arid ecosystems. Circumstances in which researchers may elect to use short-time interval autocorrelated data sets are also discussed.