Received: 7 July 2023 | Revised: 4 November 2023 | Accepted: 13 November 2023 DOI: 10.1002/wll2.12026 L E T T E R Inverse relationships between coyote and wild turkey population time series: Implications for future studies of predator – prey interactions Guiming Wang 1 | Adam B. Butler 2 | Xueyan Shan 3,4 1 Department of Wildlife, Fisheries and Aquaculture, Mississippi State University, Mississippi State, Mississippi, USA 2 Mississippi Department of Wildlife, Fisheries, and Parks, Jackson, Mississippi, USA 3 Department of Biochemistry, Molecular Biology, Entomology and Plant Pathology, Mississippi State University, Mississippi State, Mississippi, USA 4 Institute for Genomics, Biocomputing & Biotechnology, Mississippi State University, Mississippi State, Mississippi, USA Correspondence Guiming Wang, Department of Wildlife, Fisheries and Aquaculture, Mail stop 9690, Mississippi State University, Mississippi State, MS 39762, USA. Email: guiming.wang@msstate.edu Funding information Guiming Wang was fi nancially supported by the Forest Wildlife Research Center and Department of Wildlife, Fisheries and Aquaculture, Mississippi State University. Xueyan Shan was fi nancially supported by Mississippi Agricultural and Forestry Experiment Station at Mississippi State University. Abstract Changes in predator communities such as the emergence of new predators alter predator – prey interactions profoundly. Coyotes ( Canis latrans ) have expanded their geographic distributions from the western United States (US) to the Eastern US, potentially suppressing some prey populations as their relative abundance has increased. To assess the relationship between coyotes and one of their prey, the eastern wild turkey ( Meleagris gallopavo silvestris ), we employed time series analysis and multivariate autoregressive state ‐ space models (MARSSMs) to a 23 ‐ year capture per unit effort data set from both species in the state of Mississippi, US. The best MARSSM model indicated density dependence in each species. The competing MARSSM indicated that increases in coyote relative abundance reduced the population growth rate of wild turkeys. We recommend that future studies use long ‐ term time series of multiple coexisting predators and their alternative prey to assess the effects of the predator guild on the dynamics of prey populations. K E Y W O R D S Canis latrans , Meleagris gallopavo silvestris , predator ‐ prey interactions, state space models, time series analysis, two ‐ species interaction models I N T R O D U C T I O N Understanding intrinsic and extrinsic factors in fl uencing the dynamics of wildlife populations is important for science ‐ based management. Additionally, the relative importance of intrinsic (e.g., density dependence) and extrinsic (e.g., interspeci fi c interactions and climate) factors has been debated in population ecology for decades (Hone & Clutton ‐ Brock, 2007; Krebs, 2001; Lack, 1954). The classic views of population ecology have been challenged by the impacts of anthropogenic disturbances at an unprecedented rate and the ever ‐ changing environments (Sutherland et al., 2013). For instance, the geographic range (hereafter, range) of coyote ( Canis latrans ) has expanded eastward from its historic range in the western United States (US) following the extirpation of the red wolf ( Canis rufus ) and translocations by humans (Hill et al., 1987; Hody & Kays, 2018). Evidence has suggested coyote abundance has since increased steadily in the Southeastern US (Bragina et al., 2019; Kilgo et al., 2010), creating questions about the degree to which these increases may alter predator – prey interactions and subsequent in fl uences on the dynamics of prey populations (Gompper, 2002). Previous studies have reported inverse relationships between coyote and white ‐ tailed deer ( Odocoileus virginia- nus ) abundance (Kilgo et al., 2010) or direct predation by Wildl. Lett . 2023;1:171 – 177. onlinelibrary.wiley.com/journal/28325869 | 171 This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2023 The Authors. Wildlife Letters published by Northeast Forestry University and John Wiley & Sons Australia, Ltd. coyotes on deer neonates (Kilgo et al., 2012). Yet, other work has failed to fi nd these relationships at larger spatial scales across six states in the eastern US (Bragina et al., 2019). These inconsistencies call for further studies to examine the possibilities of the area ‐ speci fi c or scale ‐ dependent effects of coyotes on wildlife populations. Miller and Leopold (1992) suggest that coyotes may affect the population dynamics of eastern wild turkeys ( Meleagris gallopavo silvestris ; hereafter, wild turkeys). Predation by coyotes can be a major factor in fl uencing survival of female adult wild turkeys (Byrne & Chamberlain, 2018; Hubbard et al., 1999; Little et al., 2016). However, to the best of our knowledge, no studies have examined whether increases in coyote abundance have reduced the popula- tion growth rates of wild turkey populations using long ‐ term time series. Rigorous statistical time series models for population dynamics and interspeci fi c interactions can shed light on the potential impacts of coyotes on the population dynamics of wild turkeys. Time series models account for temporal autocorrelation to avoid the poten- tial biases in the inferences of population dynamics (Chan & Cryer, 2008; Merritt et al., 2001). In this study, we used time series analysis of autocorrelation functions (ACF) and cross ‐ correlation function (CCF) to detect signals of predation by coyotes on the dynamics of wild turkey populations in Mississippi, US from 1983 to 2005. We also used state ‐ space models (SSMs) for interspeci fi c interactions to estimate the strength of predation by coyotes on the dynamics of wild turkey populations in Mississippi (Bao et al., 2021; Wang, 2009). We tested the prediction that wild turkey population growth rate is inversely related to coyote relative abun- dance. We also tested whether wild turkey and coyote populations were subject to density dependence using the SSMs for two ‐ species interactions (Bao et al., 2021). Additionally, given controversies concerning the strength and the regulating roles of predation in wildlife communi- ties and populations (Estes et al., 2011; Turchin, 2003), we also made several recommendations for future studies of predation using the two species as a case study. METHODS Time series data on annual wild turkey harvest and coyote trapping harvest The Mississippi Department of Wildlife, Fisheries, and Parks (MDWFP) maintained records of annual wild turkey harvests and total hunter days for 16 wildlife management areas (WMAs) during the turkey season from Mid ‐ March to the fi rst of May (Wang, 2018). A single trip a fi eld was counted as a hunter day. Capture per unit effort (CPUE; i.e., the number of harvested birds per hunter day) was calculated to index the annual relative abundance of male adult wild turkeys at each WMA from 1983 to 2005 (Wang, 2018). Wild turkey hunting is recreational in the US although hunters pay fees for annual hunting permits. Hunters may use different weapons to hunt wild turkeys; however, Butler and Wang (2022) found that the choices of weapons did not affect the success of wild turkey hunting. Coyote data were obtained from MDWFP's annual survey of licensed trappers in the state of Mississippi, US. A complete census of all licensed trappers was carried out annually, by mail, to obtain information about their effort and catch (Hunt et al., 2009; Lovell et al., 1998). Licensed trappers harvested coyotes via trapping, that is, primarily leg hold type traps, live traps, or snares. Capture per unit effort (i.e., the number of harvested coyotes per trapper) was calculated as an annual relative abundance index of coyotes in the entire Mississippi from 1983 to 2005. The CPUEs of furbearing wildlife often exhibited temporal trends resulting from market prices. We detrended coyote and wild turkey CPUE time series to remove the trend and minimize the effects of market prices. Coyote captures occurred during November to March, thereby spanning the transition of the calendar year. Conversely, wild turkey harvest occurred from March to May, within a calendar year. Parturition for coyotes typically occurs in mid ‐ spring (Albers et al., 2016), while peak hatching for wild turkeys is late spring to early summer (Miller et al., 1998). The structure of our data can therefore best be considered as being collected within the same biological year for both species, that is, population change did not substantially occur in either species between the collection of harvest data for coyotes (November – March) and wild turkey (March – May). Time series analysis of interspeci fi c interactions between coyotes and wild turkeys The CPUE time series of wild turkeys were averaged over the 16 WMAs to generate a statewide wild turkey CPUE. Likewise, coyote trapper data was averaged across all trappers to create a statewide coyote CPUE for each year from 1983 to 2005. The wild turkey and coyote time series exhibited apparent trends over time (Figure 1). To avoid the spurious correlation caused by the trends, each CPUE time series was detrended by a linear model with year as a covariate (Chan & Cryer, 2008). The normality assump- tion of the detrended time series was checked using the Practitioner points • Predator – prey interactions are important forces shaping wildlife population dynamics. Invasions or emergences of new predators can alter predator – prey interactions and prey communities profoundly. • The geographic distribution of coyotes has expanded into the Eastern United States due to human facilitated dispersal of coyotes and the extinction of native apex predators. • Our fi ndings suggest asymmetric coyote ‐ wild turkey interactions. We offer several sugges- tions for future research of predator – prey systems which may lead to increased inference of the mechanisms interacting within these systems. 172 | WANG ET AL 28325869, 2023, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/wll2.12026 by University Of Florida, Wiley Online Library on [11/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License quantile ‐ quantile (QQ) plot. The autocorrelation function (ACF) was used to check the stationarity assumption (Chan & Cryer, 2008). The ACF of nonstationary time series exhibits a slow decay of ACF with autocorrelation declining or oscillating gradually and slowly over long time lags (Brockwell & Davis, 2002). CCF was used to detect cross correlation between detrended wild turkey and coyote CPUE time series with temporal autocorrelation being accounted for (Brockwell & Davis, 2002; Chan & Cryer, 2008). If wild turkey time series was cross ‐ correlated with coyote time series at a time lag p (= − 10, − 9, ... , − 2, − 1, 0), wild turkey relative abundance was correlated with the coyote CPUE of the previous p year. If cross ‐ correlation is signi fi cant ( p < 0.05) at the lag of p years, wild turkey relative abundance was related to coyote relative abundance of year t + p Cross ‐ correlation of relative abundance does not necessarily suggest the effects of increases in coyote relative abundances on the population growth rate of wild turkeys. We built multivariate autoregressive state ‐ space models (MARSSMs) to assess the effects of changes in coyote relative abundance on the dynamics or population growth rates of wild turkey populations. The MARSSMs were fi t to the two CPUE time series simultaneously, = + − X BX E , t t t 1 (1) where X t is a vertical vector of true relative abundance in year t having bivariate normal distribution; X t − 1 a vertical vector of true relative abundance in year t − 1 (i.e., [coyote t − 1 , turkey t − 1 ]); E t a 2 ‐ element error vector of bivariate normal distributions with zero means and a covariance matrix of process stochasticity; and B is the transition matrix of the form: b b b b 11 12 21 22 Matrix element b 11 quanti fi es the strength of direct density dependence of coyote populations; b 12 the effects of wild turkey populations on the coyotes; b 21 the effect of coyote relative abundance on wild turkey populations; and b 22 the strength of direct density dependence of wild turkey populations. We assumed the observed CPUE Y t is the sum of X t and measurement errors U t : = + Y X U , t t t (2) where U t has a bivariate normal distribution of a mean vector of zeros and a covariance matrix of measurement errors. Equations (1) and (2) were implemented in the form of SSMs with template model builder (TMB; Kristensen et al., 2016). We used the same TMB C++ template codes for the two ‐ species interaction MAR models from Bao et al. (2021). The unknown parameters of Equations (1) and (2) were estimated by the maximum likelihood (ML) methods (Kristensen et al., 2016). We built three candidate models for the detrended CPUE time series of wild turkeys and coyotes: (1) the null model with the interspeci fi c interaction terms b 12 and b 21 being zero (i.e., no predatory – prey interactions) and b 11 and b 22 as free, unknown parameters; (2) asymmetric interaction model with the parameter b 12 for the effects of wild turkey populations on those of coyotes being zero but other three elements b 11 , b 12 , and b 22 being estimated; and (3) the full model with all four elements b 11 , b 12 , b 21 , and b 22 being free to estimate. We scaled the time series to have a mean of 0 and variance of 1.0 before fi tting the MAR models. The best approximating model was selected using information ‐ theoretic approaches. The best model had the lowest Akaike information criterion corrected for small sample size (AICc), and a competing model had the Δ AICc < 2.0 (Burnham & Anderson, 2002). If the estimates of b 11 and b 22 are signi fi cantly less than 1.0 with the 95% con fi dence interval (CI) below 1.0, we concluded that the populations of coyotes and wild turkeys were subjected to density dependence (Royama, 1992; Wang et al., 2009; Xingan & Wang, 2018). We calculated the model ‐ average predictions of coyote and wild turkey annual relative abundances as the weighted means of the predictions of the three candidate models with Akaike weights as weights. Then we regressed observed CPUEs on the model ‐ average predictions for coyote and wild turkey, respectively, using a linear model. We used the R 2 of linear models as a pseudo R 2 to assess the model fi t. RESULTS The relative abundance of male wild turkeys declined from 1983 to 2005, whereas the relative abundance of coyotes increased steadily during the same period (Figure 1). Linear models effectively removed the trends of the two CPUE time series (Figure S1a,b). Detren- ded time series appeared to be normally distributed (Figure S1c,d). Neither detrended coyote nor wild turkey CPUE time series exhibited a slow decay of auto- correlation functions. The ACF of detrended coyote time series declined and became insigni fi cant within 4 years, indicating stationarity (Figure S2). CCF indi- cated that wild turkey CPUE of year t was signi fi cantly correlated with the coyote CPUE of year t (Figure 2a,b), that is, 0 ‐ year time lag. Wild turkey population relative abundance of year t was inversely related to coyote relative abundance of year t The optimization algorithm of all three SSM fi ts converged at the ML estimates. The AICc values were 121.66, 122.68, and 125.41 for the null model, asymmetric model, and full model, respectively (Table S1). Although F I G U R E 1 Annual coyote (solid line) and wild turkey (dashed line) capture per unit effort of Mississippi, USA from 1983 to 2005. WILDLIFE LETTERS | 173 28325869, 2023, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/wll2.12026 by University Of Florida, Wiley Online Library on [11/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License the null model had the lowest AICc (Akaike weight = w 0.57 ), the Δ AICc of the asymmetric model the second ‐ best model, was 1.02 (<2.0, Table S1). We concluded that the asymmetrical interaction model received substantial support from the data ( = w 0.34 ) as a competing model for the alternative explanation of coyote ‐ wild turkey interac- tions. Model ‐ average predictions of both coyote and wild turkey relative abundances fi t CPUE observations well (pseudo ‐ R 2 = 0.99, Figure S1a,b). The ML estimates of the elements of the matrix B matrix of the null model suggested density dependence for coyote (95% CI of b 11 : 0.16 – 0.90 and density dependence of wild turkey populations (95% CI of b 22 : − 0.46 – 0.39): = − b b b b 0.53 0.00 0.00 0.31 . 11 12 21 22 The ML estimates of the matrix B matrix of the asymmetric interaction model suggested density dependence for coyote (95% CI of b 11 : 0.16 – 0.90), negative effects of increasing coyote populations on the populations of wild turkeys (95% CI of b 21 : − 0.85 – 0.21), and density depen- dence of wild turkey populations (95% CI of b 22 : − 1.38 to − 0.14): = − − b b b b 0.53 0.00 0.32 0.76 . 11 12 21 22 Although the asymmetric interactions between coyote and wild turkey populations received substantial support by our data with the Akaike weight being 0.38, there was a notable level of uncertainty in the estimation (i.e., with its 95% CI including zero) of the negative effects of coyotes on the population growth rates of wild turkeys. D I S C U S S I O N Predator – prey interactions are one of the most important ecological forces shaping animal populations and communi- ties (Estes et al., 2011; Lotka, 1925; Turchin, 2003). Predation has most often been ascribed as a top ‐ down regulating mechanism for population dynamics (Estes et al., 2011; Sinclair et al., 2000), yet the relative importance of top ‐ down control (e.g., predation) and bottom up control (e.g., competition, density dependence, and climate effects) has been debated for decades (Estes et al., 2011; Turchin, 2003). The controversy is partially caused by inconsistencies in empirical evidence among studies measur- ing the existence and magnitude of predation. Our time series analysis demonstrated signi fi cant correlation between wild turkey and coyote harvest time series. Our two ‐ species interaction models also detected both the negative effects of predation by coyotes and density dependence of both wild turkey and coyote populations, suggesting the coexistence of top down and bottom ‐ up control. Empirical evidence of the kills and direct consump- tions of wild turkeys by coyotes is intuitively required to support the impacts of coyote populations on wild turkey populations. Studies have ascribed predation by canids, including coyotes, as a major mortality cause of wild turkeys in Arkansas, Kansas, and Missouri, USA (Holdstock et al., 2006; Thogmartin & Schaeffer, 2000; Vangilder & Kurzejeski, 1995), consistent with our fi ndings of the negative impacts of increased coyote abundance on wild turkey population in Mississippi. Wild turkeys were also present in the diet of coyotes, constituting <4% of the diet, in Alabama, Arkansas, Florida, and Mississippi of the Southeastern US (Wagner & Hill, 1994). However, as often seen in the ecological literatures, other studies did not fi nd evidence of the kills or consumption of wild turkeys by coyotes in South Carolina and Texas, US nor in Ontario, Canada (Melville et al., 2015; Niedzielski & Bowman, 2014; Schrecengost et al., 2008). Although we did not aim to conduct an exhaustive literature review of the predation of wild turkeys by coyotes, we suggest that direct predation of wild turkeys by coyotes may vary among different locations and even among different years. Suppression of individual demographic or vital rates, via predation or other means, may or may not be “ translated ” to reductions in population growth rates. For instance, Herrando ‐ Pérez et al. (2012) found that decoupling between component (i.e., single vital rate) and ensemble (i.e., population growth rate) density feedbacks in birds and mammals. The decoupling suggests that increases in population densities may decrease individual vital rates (e.g., survival and F I G U R E 2 Cross correlation of detrended coyote and wild turkey capture per unit effort of Mississippi, USA from 1983 to 2005 (a). Scatterplot of coyote capture per unit effort (CPUE) in year t (the x axis) and wild turkey CPUE in year t (the y axis) (b). Blue dashed line in panel (b) are two times the standard deviation of cross ‐ correlation coef fi cient, approximating a 95% con fi dence band. 174 | WANG ET AL 28325869, 2023, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/wll2.12026 by University Of Florida, Wiley Online Library on [11/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License reproduction rate) but not population growth rates (Herrando ‐ Pérez et al., 2012). Population growth rates have different sensitivities to changes in different vital rates depending on the life history strategies of the species (Sæther et al., 2013). As such, the effect of predation may only be completely assessed by simulta- neously examining the role of predator abundance on both the individual demographic and overall population growth rates of their prey. The former can help understand the ecological mechanisms underlying predator – prey interactions, whereas the latter can evaluate the “ net ” effects of the demographic effects of predation on the dynamics of wildlife populations. Our fi ndings support that increases in coyote relative abundances attenuated wild turkey population growth rates. However, our data do not provide any under- standing of the demographic pathways of the negative impacts. Empirical or simulation studies are warranted to investigate the sensitivities of different demographic rates of wild turkeys, such as stage ‐ speci fi c survival rates, to coyote predation for better understanding coyote ‐ wild turkey interactions. Most studies of coyote ‐ wild turkey population interactions have used the CPUE time series or harvest data to infer the interactions between the two species. Our fi ndings suggest that inverse relationships between the population time series cannot be used as the sole evidence for predator – prey interactions. A potential bias of this approach is measurement errors or other inconsistency between relative abundance indices and true abundance. For instance, changes in hunter demo- graphics (young, inexperienced vs. experienced hunters) may in fl uence average hunting success over time. The potential inferential bias warrants future studies to estimate the abundances of predator and prey at multiple sites for 5 – 10 years using remote ‐ sensing data collection methods (e.g., camera trapping, on ‐ board cameras of unmanned aerial vehicles, and environmental DNA) and rigorous statistical estimators. Furthermore, climate changes and changes in land use and land cover may affect the population dynamics of predators and their prey, which may mask the effects of predation on the dynamics of prey populations. For instance, summer temperature and proportion of forests may affect spatiotemporal dynamics and relative abundances of wild turkeys in Mississippi (Davis et al., 2017; Wang, 2018). We either include climate variables in the population models or use state ‐ space models to include process variance E t in Equation (1) to account for population variability induced by environmental variations. Many factors contribute to the controversy and elusiveness of research conclusions regarding the roles of predation in the population and community dynamics. Here we make a few recommendations to improve future studies of the impacts of predation on the dynamics of wildlife populations and communities. First, we need to determine appropriate spatial scales to assess the roles of predation in shaping the dynamics of wildlife populations and communities. A fundamental theoretical question needs to be addressed: how much space is required to support stable, detectable predator – prey interactions (McIntosh et al., 2018; McWilliams et al., 2019)? Our study used the time series data collected from the state of Mississippi (125,460 km 2 in size), which was apparently suf fi cient to detect the signal of coyote relative abundance on the population growth rate of wild turkeys. However, it is unclear whether this relationship would exist, or be detectable, at a more localized site. Two possible approaches can be used to determine the minimum space required to support sustainable predatory – prey interactions. We can compile multiple existing time series such as CPUE and harvest time series from a large area and divide the data set to different subsets that cover a series of space extents. We can fi t time series models to those subsets of time series to determine the minimum spatial extent in which predator – prey interactions can be detected. Additionally, we can use presence and absence data on predator and prey species to build joint species distribution models in conjunction with GPS tracking data to determine the spatial extent, in which the joint occupancy probability of predator and prey is above a threshold (e.g., 0.05 or 0.1). Second, our fi ndings suggest that cross correlation between time series is not equivalent to the negative effects of increased predator abundances on the popula- tion growth rates of prey. Our approach requires long ‐ term time series to precisely estimate the strength of interspeci fi c interactions. A relevant theoretical ecologi- cal question is: how many years are needed until the impacts of predation on prey are manifested or are statistically detectable at a population level? In an analogy, the length of time series affected the decoupling between the component and ensemble density depen- dence when detecting the density ‐ dependent feedback at the population level (Herrando ‐ Pérez et al., 2012). The spatial and temporal scales may be critically important for the studies of predator – prey interactions, particularly for large ‐ sized apex predators. Lastly, we need a system approach to evaluating the impacts of predation on prey population dynamics. Most studies, including ours, focus on a pair of predator and prey populations. In reality, a guild of multiple potential predators and a guild of multiple potential prey may exist and interact. For instance, coyotes prey on multiple small mammal species, which are also the prey of other coexisting mesocarnivores, which prey on wild turkeys (Nielsen et al., 2018). It is theoretically possible that the increased consumption of small mammals by coyotes would make the bobcat ( Lynx rufus ), another mesocar- nivore, to kill more wild turkeys. Complex relationships among multiple predators and their potential prey switches may result in the indirect effects of “ apparent ” predation or competition (Mittelbach & McGill, 2019). While apparent predation may not be the actual ecological process causing the observed dynamic pat- terns, the apparent or indirect relationship can prompt for the further studies of complex, direct, and indirect interspeci fi c interactions in the predator and prey communities. Therefore, indirect or apparent interac- tions revealed by time series analysis like ours should not be ignored, particularly when long ‐ term experimental studies of predator – prey interactions are logistically impractical. WILDLIFE LETTERS | 175 28325869, 2023, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/wll2.12026 by University Of Florida, Wiley Online Library on [11/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License A U T H O R C ON T R I B U T I O N S Guiming Wang : Conceptualization (equal); formal anal- ysis (equal); investigation (equal); methodology (lead); writing — original draft (lead). Adam B. Butler : Concep- tualization (equal); writing — review and editing (equal). Xueyan Shan : Formal analysis (equal); methodology (equal); visualization (equal); writing — review and edit- ing (equal). AC KNOWLE DGMENTS The authors thank Dr. Marcus Lashley for the discus- sion. We thank two anonymous reviewers for their constructive comments on this manuscript. This publica- tion is a contribution of the Forest and Wildlife Research Center, Mississippi State University. Guiming Wang was fi nancially supported by the Forest Wildlife Research Center and Department of Wildlife, Fisheries and Aquaculture, Mississippi State University. Xueyan Shan was fi nancially supported by Mississippi Agricultural and Forestry Experiment Station at Mississippi State University. CONFLI CT OF I NTE RES T STAT EME NT The authors declared no con fl ict of interest. DATA AVA IL ABI LI TY ST ATE MENT Data available on request from the authors. ORCID Guiming Wang http://orcid.org/0000-0001-5002-0120 Adam B. Butler http://orcid.org/0009-0005-5664-255X Xueyan Shan http://orcid.org/0000-0003-0144-9371 RE FER ENCES Albers, G., Edwards, J.W., Rogers, R.E. & Mastro, L.L. 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(2018) Bayesian spatiotemporal dynamic models for regional dynamics of avian populations. Ecological Informatics , 45, 31 – 37. Wang, G., Hobbs, N.T., Twombly, S., Boone, R.B., Illius, A.W., Gordon, I.J. et al. (2009) Density dependence in Northern ungulates: interactions with predation and resources. Population Ecology , 51, 123 – 132. Xingan & Wang, G. (2018) Spatiotemporal dynamics of mesocarnivore populations. Wildlife Biology , 2018, 1 – 7. AUTHOR BIOGRAPHY Guiming Wang is the Dale H. Arner Professor in Wildlife Ecology and Man- agement in the Department of Wildlife, Fisheries and Aquaculture at Mississippi State University. He is interested in wildlife population ecology, computa- tional statistics, applied data science, and applications of machine learning in wildlife ecology. S U P P O R T I N G I N F O R M A T I O N Additional supporting information can be found online in the Supporting Information section at the end of this article. How to cite this article: Wang, G., Butler, A.B. & Shan, X. (2023) Inverse relationships between coyote and wild turkey population time series: implications for future studies of predator – prey interactions. Wildlife Letters , 1, 171 – 177. https://doi.org/10.1002/wll2.12026 WILDLIFE LETTERS | 177 28325869, 2023, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/wll2.12026 by University Of Florida, Wiley Online Library on [11/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for ru