Integrated population models poorly estimate the demographic contribution of immigration

Quantifying the relative contribution of demographic parameters to population growth is essential for understanding processes influencing dynamics (Caswell, 2000; Coulson et al., 2005; Koons 2016). This important in research, where identifying these relationships not only can help predict effectiveness targeted conservation measures on but also provide information about spatial scale at which management should be taken (Schaub 2012; Zipkin & Saunders, 2018). For example, if local reproduction a strong contributor growth, this suggests that supporting may an effective strategy managing population, while immigration would instead suggest supportive undertaken larger scale. However, acquiring data all and their temporal variation often challenging. In particular, are limited or absent from datasets (Abadi 2010). reason, modelling approaches such as integrated models (IPMs) have been developed use other estimate missing rates 2010; Schaub Fletcher, 2015; 2013). IPMs combine with size allow: (a) changes both rate joint analysis, some cases (b) additional (Riecke 2019) no explicitly collected by integrating available (Kéry Schaub, 2011; Abadi, 2011). Therefore, offer exciting possibility investigate how parameter associated rate, even explicit (Millon 2019). Hence, rapidly increasing number recent studies used parameters, typically (e.g. Taylor 2018; Weegman 2017), productivity breeding success when populations assumed closed (Baillie 2009; e.g. Besbeas 2002; Nuijten 2020). since used, estimating must based particular assumptions. It has shown estimation mean sensitive parametrization priors chosen 2015), systematic bias results biased Similarly, (and consequently its growth) could depend parameterized presence any parameters. Indeed, residual random noise detection probability, density dependence, trends), considered models, will likely result growth. Given this, caution needed interpreting findings many show strongest (70% 44 estimated 23 compiled Table 1). Because it ‘missing’ like (together variance observation model), model parameterization influence estimates (Paquet 2019; Saunders Despite vast majority IPM interpret exclusively (Table Thus, there obvious need what proportion truly due component variation. Here we combination simulated empirical assess accuracy driver measured directly. First, simulation scenarios confirm existence examine cause within framework. Using ‘perfect datasets’ known immigration, whether parametrization, specification method immigration. Demographic values than were open northern wheatear, Oenanthe oenanthe, near Uppsala, Sweden. The study allows us quantify under various scenarios. Second, long-term real order compare IPM-estimated versus true More specifically, either (Soay sheep Ovis aries island Hirta Mauritius kestrels Falco punctatus) immigrants very small (grey wolf Canis lupus Scandinavia). To accurate using fecundity, apparent survival (i.e. accounting emigration mortality), We then applied compared modelled (see Appendix 1 scripts simulate fit data). series underlying time-varying parameters) structure adapted real-data example Kéry (2011) time varying (random) vital rates, stochasticity accounted Poisson Binomial distributions distribution count data. rather suggested better particularly populations, whereas lead unrealistically high dependency obtain realistic simulations, fitted same dataset wheatear central Sweden except (for further details given below), posterior medians values). immigrants, two most formulations each first, widely type (hereafter IPMPois), strictly positive allowed vary around value according log-normal 2012, 2013; second IPMNoConst), fixed independently year (Brommer 2017; Szostek 2014), without constraining positive, nor randomly mean. common methods. calculated correlation coefficient between annual sample, well coefficients 2012). computed recently transient Life Response Experiment (LTRE) contributions (Koons 2016, advantage summing into meaningful quantity, approximate therefore explained limitations ad hoc approach, notably comparisons among present LTRE main text refer approach Figures S3 S6. six scenarios, 100 datasets. 600 datasets, above-mentioned types Bayesian (IPMPois IPMNoConst, see IPM, obtained three independent MCMC chains after adaptation period 5,000 iterations, burn 1,000 sampling every 30th iteration 30,000 iterations. vague initial was initially set 0.02 did vary. correlations yearly samples, comparison. looked 2018), had rate. Note because size, hence still varies fixed. 2 sample sizes, methods references describing collection). built rates. female breeders only, assuming females limiting sex (Rankin Kokko, 2007). A detailed description provided 3. chains. Details prior distribution, values, convergence assessment predictive checks found 4. All simulations estimations performed JAGS, version 4.2.0 (Plummer, 2003, 2015) run rjags package 2013) Program R, 3.3.1 (R Core Team, R code compute 5. Both parameterizations satisfactorily predicted 32 320 sizes) Figure S1 illustration one scenario). Nevertheless, overestimated (Figure 1; S2, panels D) S3) S1; 2). overestimated, uncertainty combined fact standard deviation constrained 3). When varied moderately strongly over time, IPMPois gave unbiased 3) clearly different absence 1: 95% CrI panel B C [with immigration] largely overlap those [no variation]). differences more pronounced, although unclear, sizes increased 10-fold 1d–f). IPMNoConst poorly case studies, numbers credible intervals almost always included zero S4). Their (estimated parameterization) low deviate S5). kestrel occur twice, close ?3.46 × 10–5 (95% CrI: ?0.16.8 10–5, 6.83 10–5). samples formulation 4). Computing similar S6). formulation, analyses average 19.1% 4.2% 84.0% 4, as: mean(ContribImm)/mean(ContribImm + ContribOther rates)). dramatically representing 98.2% 36.1% 99.2% overestimate happened our negligible. strength overestimation formulated size. (simulated) substantial = 0.2 0.4 log scale). despite distinguishable Below, discuss implications guidelines informed inference importance (or little data) IPMs. Although previous work acknowledged mismatch, lack unmodelled 2013), shows biases. 3; S1a) contributing (LTRE 63% 30–95) total parameterization, S2). least studies. uniform year, induce spurious rarely recommended expected (as studies), negative unlike formulation. While does perform performs compromise Normal likelihood (cf. IPMNoConst) having constant IPMPois; Fay presumably leads occurrence (not negative) substantially, good indistinguishable contribute growth; Only and/or huge precise enough distinguish Similar wild (IPMNoConst, Such driven factors, including process data, non-random mismatch components Knowledge biology needs minimize note applies indirectly Riecke 2019), and, potentially lesser extent, variation, shape clear zero. issues raised carefully comparing differing amounts What done get parameter, IPMs? recommend first look evidence before investigating evaluating assessing peak differs computationally time-consuming, recommendation proceed study. That is, interest) time. Then interest. step-by-step procedure script do so 6. As illustration, highlights far highly (Appendix 6). inclusion prevent likewise regarding useful better-informed being said, biologically otherwise. Calling ‘additional parameter’ throughout define describes immigration) biological misinterpretation. An application practical (relative survival) necessarily (supporting consequence. Yet sometimes (mean) interpreted Ullrich, 2020) subsequent suggestions scales. Our greatly 6), tools indicating If aim advisable empirically collect rare situations, monitored offspring marked, unmarked animals recruited (Link Barker, 2005). subpopulations monitored, towards subpopulation multi-state (Seward Moreover, individuals’ locations spatially movements (Chandler Clark, 2014; Chandler Paquet 2020), extrapolation area problematic. Spatially allow autocorrelation accommodate scales avoid single framework, genetic authors thank Michael Editors anonymous reviewers helpful comments suggestions. Bambou Mountains part species recovery program conducted Mauritian Wildlife Foundation National Parks Conservation Service (Government Mauritius), support Institute Zoology (ZSL), University Kent, Durrell Trust, Peregrine Fund, Vallee de Ferney landowners fieldworkers engaged monitoring last 30 years. Soay project St Kilda supported UK Natural Environment Research Council they field workers invaluable collecting They people who laboratory fieldwork administrated wolves Scandinavia during 40 years Swedish Environmental Protection Agency (5855/2019) Marie-Claire Cronstedt's Foundation. D.A. J.K. financed FORMAS, M.L. VR (2017-03963) FORMAS (2017-00384) T.P. Carl Tryggers None. conceived idea discussion M.P., J.K., P.F.; Ø.F., C.G.J., M.A.C.N., K.N., J.M.P., H.S., L.S., V.T., P.W., C.W. M.Å. data; M.P. study; analysed J.K.; led writing manuscript together D.A., contributed drafts final approval submission. peer review history article https://publons.com/publon/10.1111/2041-210X.13667. Data accessed Dryad Digital Repository https://doi.org/10.5061/dryad.xd2547dh0 2021). Please note: publisher responsible content functionality supplied authors. Any queries (other content) directed corresponding author article.