Bayesian population models can be exceedingly slow due, in part, to the choice to simulate discrete latent states. Here, we discuss an alternative approach to discrete latent states, marginalization, ...that forms the basis of maximum likelihood population models and is much faster. Our manuscript has two goals: (1) to introduce readers unfamiliar with marginalization to the concept and provide worked examples and (2) to address topics associated with marginalization that have not been previously synthesized and are relevant to both Bayesian and maximum likelihood models. We begin by explaining marginalization using a Cormack- Jolly-Seber model. Next, we apply marginalization to multistate capture–recapture, community occupancy, and integrated population models and briefly discuss random effects, priors, and pseudo-R². Then, we focus on recovery of discrete latent states, defining different types of conditional probabilities and showing how quantities such as population abundance or species richness can be estimated in marginalized code. Last, we show that occupancy and site-abundance models with auto-covariates can be fit with marginalized code with minimal impact on parameter estimates. Marginalized code was anywhere from five to >1,000 times faster than discrete code and differences in inferences were minimal. Discrete latent states and fully conditional approaches provide the best estimates of conditional probabilities for a given site or individual. However, estimates for parameters and derived quantities such as species richness and abundance are minimally affected by marginalization. In the case of abundance, marginalized code is both quicker and has lower bias than an N-augmentation approach. Understanding how marginalization works shrinks the divide between Bayesian and maximum likelihood approaches to population models. Some models that have only been presented in a Bayesian framework can easily be fit in maximum likelihood. On the other hand, factors such as informative priors, random effects, or pseudo-R² values may motivate a Bayesian approach in some applications. An understanding of marginalization allows users to minimize the speed that is sacrificed when switching from a maximum likelihood approach. Widespread application of marginalization in Bayesian population models will facilitate more thorough simulation studies, comparisons of alternative model structures, and faster learning.
Breeding dispersal, the movement from one breeding territory to another, is rare for philopatric species that evolved within relatively stable environments, such as the oldgrowth coniferous forests ...of the Pacific Northwest. Although dispersal is not inherently maladaptive, the consequences of increased dispersal on population dynamics in populations whose historical dispersal rates are low could be significant, particularly for a declining species. We examined rates and possible causes of breeding dispersal based on a sample of 4,118 northern spotted owls (Strix occidentalis caurina) monitored in seven study areas over 28 yr, 1990–2017, in Oregon and Washington, USA. Using a multistate mark–resight analysis, we investigated the potential impacts of an emergent congeneric competitor (barred owl Strix varia) and forest alteration (extrinsic factors), and social and individual conditions (intrinsic factors) on 408 successive and 1,372 nonsuccessive dispersal events between years. The annual probability of breeding dispersal increased for individual owls that had also dispersed in the previous year and decreased for owls on territories with historically high levels of reproduction. Intrinsic factors including pair status, prior reproductive success, and experience at a site, were also associated with breeding dispersal movements. The percent of monitored owls dispersing each year increased from ∼˜7% early in the study to ∼25% at the end of the study, which coincided with a rapid increase in numbers of invasive and competitively dominant barred owls. We suggest that the results presented here can inform spotted owl conservation efforts as we identify factors contributing to changing rates of demographic parameters including site fidelity and breeding dispersal. Our study further shows that increasing rates of breeding dispersal associated with population declines contribute to population instability and vulnerability of northern spotted owls to extinction, and the prognosis is unlikely to change unless active management interventions are undertaken.
Slow ecological processes challenge conservation. Short-term variability can obscure the importance of slower processes that may ultimately determine the state of a system. Furthermore, management ...actions with slow responses can be hard to justify. One response to slow processes is to explicitly concentrate analysis on state dynamics. Here, we focus on identifying drivers of Northern Spotted Owl (Strix occidentalis caurina) territorial occupancy dynamics across 11 study areas spanning their geographic range and forecasting response to potential management actions. Competition with Barred Owls (Strix varia) has increased Spotted Owl territory extinction probabilities across all study areas and driven recent declines in Spotted Owl populations. Without management intervention, the Northern Spotted Owl subspecies will be extirpated from parts of its current range within decades. In the short term, Barred Owl removal can be effective. Over longer time spans, however, maintaining or improving habitat conditions can help promote the persistence of northern spotted owl populations. In most study areas, habitat effects on expected Northern Spotted Owl territorial occupancy are actually greater than the effects of competition from Barred Owls. This study suggests how intensive management actions (removal of a competitor) with rapid results can complement a slower management action (i.e., promoting forest succession).
Estimates of species' vital rates and an understanding of the factors affecting those parameters over time and space can provide crucial information for management and conservation. We used ...mark–recapture, reproductive output, and territory occupancy data collected during 1985–2013 to evaluate population processes of Northern Spotted Owls (Strix occidentalis caurina) in 11 study areas in Washington, Oregon, and northern California, USA. We estimated apparent survival, fecundity, recruitment, rate of population change, and local extinction and colonization rates, and investigated relationships between these parameters and the amount of suitable habitat, local and regional variation in meteorological conditions, and competition with Barred Owls (Strix varia). Data were analyzed for each area separately and in a meta-analysis of all areas combined, following a strict protocol for data collection, preparation, and analysis. We used mixed effects linear models for analyses of fecundity, Cormack-Jolly-Seber open population models for analyses of apparent annual survival (φ), and a reparameterization of the Jolly-Seber capture–recapture model (i.e. reverse Jolly-Seber; RJS) to estimate annual rates of population change (λRJS) and recruitment. We also modeled territory occupancy dynamics of Northern Spotted Owls and Barred Owls in each study area using 2-species occupancy models. Estimated mean annual rates of population change (λ) suggested that Spotted Owl populations declined from 1.2% to 8.4% per year depending on the study area. The weighted mean estimate of λ for all study areas was 0.962 (± 0.019 SE; 95% CI: 0.925–0.999), indicating an estimated range-wide decline of 3.8% per year from 1985 to 2013. Variation in recruitment rates across the range of the Spotted Owl was best explained by an interaction between total winter precipitation and mean minimum winter temperature. Thus, recruitment rates were highest when both total precipitation (29 cm) and minimum winter temperature (−9.5°C) were lowest. Barred Owl presence was associated with increased local extinction rates of Spotted Owl pairs for all 11 study areas. Habitat covariates were related to extinction rates for Spotted Owl pairs in 8 of 11 study areas, and a greater amount of suitable owl habitat was generally associated with decreased extinction rates. We observed negative effects of Barred Owl presence on colonization rates of Spotted Owl pairs in 5 of 11 study areas. The total amount of suitable Spotted Owl habitat was positively associated with colonization rates in 5 areas, and more habitat disturbance was associated with lower colonization rates in 2 areas. We observed strong declines in derived estimates of occupancy in all study areas. Mean fecundity of females was highest for adults (0.309 ± 0.027 SE), intermediate for 2-yr-olds (0.179 ± 0.040 SE), and lowest for 1-yr-olds (0.065 ± 0.022 SE). The presence of Barred Owls and habitat covariates explained little of the temporal variation in fecundity in most study areas. Climate covariates occurred in competitive fecundity models in 8 of 11 study areas, but support for these relationships was generally weak. The fecundity meta-analysis resulted in 6 competitive models, all of which included the additive effects of geographic region and annual time variation. The 2 top-ranked models also weakly supported the additive negative effects of the amount of suitable core area habitat, Barred Owl presence, and the amount of edge habitat on fecundity. We found strong support for a negative effect of Barred Owl presence on apparent survival of Spotted Owls in 10 of 11 study areas, but found few strong effects of habitat on survival at the study area scale. Climate covariates occurred in top or competitive survival models for 10 of 11 study areas, and in most cases the relationships were as predicted; however, there was little consistency among areas regarding the relative importance of specific climate covariates. In contrast, meta-analysis results suggested that Spotted Owl survival was higher across all study areas when the Pacific Decadal Oscillation (PDO) was in a warming phase and the Southern Oscillation Index (SOI) was negative, with a strongly negative SOI indicative of El Niño events. The best model that included the Barred Owl covariate (BO) was ranked 4th and also included the PDO covariate, but the BO effect was strongly negative. Our results indicated that Northern Spotted Owl populations were declining throughout the range of the subspecies and that annual rates of decline were accelerating in many areas. We observed strong evidence that Barred Owls negatively affected Spotted Owl populations, primarily by decreasing apparent survival and increasing local territory extinction rates. However, the amount of suitable owl habitat, local weather, and regional climatic patterns also were related to survival, occupancy (via colonization rate), recruitment, and, to a lesser extent, fecundity, although there was inconsistency in regard to which covariates were important for particular demographic parameters or across study areas. In the study areas where habitat was an important source of variation for Spotted Owl demographics, vital rates were generally positively associated with a greater amount of suitable owl habitat. However, Barred Owl densities may now be high enough across the range of the Northern Spotted Owl that, despite the continued management and conservation of suitable owl habitat on federal lands, the long-term prognosis for the persistence of Northern Spotted Owls may be in question without additional management intervention. Based on our study, the removal of Barred Owls from the Green Diamond Resources (GDR) study area had rapid, positive effects on Northern Spotted Owl survival and the rate of population change, supporting the hypothesis that, along with habitat conservation and management, Barred Owl removal may be able to slow or reverse Northern Spotted Owl population declines on at least a localized scale.
We conducted a range‐wide investigation of the dynamics of site‐level reproductive rate of northern spotted owls using survey data from 11 study areas across the subspecies geographic range collected ...during 1993–2018. Our analytical approach accounted for imperfect detection of owl pairs and misclassification of successful reproduction (i.e., at least one young fledged) and contributed further insights into northern spotted owl population ecology and dynamics. Both nondetection and state misclassification were important, especially because factors affecting these sources of error also affected focal ecological parameters. Annual probabilities of site occupancy were greatest at sites with successful reproduction in the previous year and lowest for sites not occupied by a pair in the previous year. Site‐specific occupancy transition probabilities declined over time and were negatively affected by barred owl presence. Overall, the site‐specific probability of successful reproduction showed substantial year‐to‐year fluctuations and was similar for occupied sites that did or did not experience successful reproduction the previous year. Site‐specific probabilities for successful reproduction were very small for sites that were unoccupied the previous year. Barred owl presence negatively affected the probability of successful reproduction by northern spotted owls in Washington and California, as predicted, but the effect in Oregon was mixed. The proportions of sites occupied by northern spotted owl pairs showed steep, near‐monotonic declines over the study period, with all study areas showing the lowest observed levels of occupancy to date. If trends continue it is likely that northern spotted owls will become extirpated throughout large portions of their range in the coming decades.
Barred owls (
Strix varia) have recently expanded their range and now encompass the entire range of the northern spotted owl (
Strix occidentalis caurina). This expansion has led to two important ...issues of concern for management of northern spotted owls: (1) possible competitive interactions between the two species that could contribute to population declines of northern spotted owls, and (2) possible changes in vocalization behavior and detection probabilities of northern spotted owls induced by presence of barred owls. We used a two-species occupancy model to investigate whether there was evidence of competitive exclusion between the two species at study locations in Oregon, USA. We simultaneously estimated detection probabilities for both species and determined if the presence of one species influenced the detection of the other species. Model selection results and associated parameter estimates provided no evidence that barred owls excluded spotted owls from territories. We found strong evidence that detection probabilities differed for the two species, with higher probabilities for northern spotted owls that are the object of current surveys. Non-detection of barred owls is very common in surveys for northern spotted owls, and detection of both owl species was negatively influenced by the presence of the congeneric species. Our results suggest that analyses directed at hypotheses of barred owl effects on demographic or occupancy vital rates of northern spotted owls need to deal adequately with imperfect and variable detection probabilities for both species.
Northern spotted owls (Strix occidentalis caurina) have been studied intensively since their listing as a threatened species by the U.S. Fish and Wildlife Service in 1990. Studies of spotted owl site ...occupancy have used various binary response measures, but most of these studies have made the assumption that detectability is perfect, or at least high and not variable. Further, previous studies did not consider temporal variation in site occupancy. We used relatively new methods for open population modeling of site occupancy that incorporated imperfect and variable detectability of spotted owls and allowed modeling of temporal variation in site occupancy, extinction, and colonization probabilities. We also examined the effects of barred owl (S. varia) presence on these parameters. We used spotted owl survey data from 1990 to 2002 for 3 study areas in Oregon, USA, and we used program MARK to develop and analyze site occupancy models. We found per visit detection probabilities averaged <0.70 and were highly variable among study years and study areas. Site occupancy probabilities for owl pairs declined greatly on 1 study area and slightly on the other 2 areas. For all owls, including singles and pairs, site occupancy was mostly stable through time. Barred owl presence had a negative effect on spotted owl detection probabilities, and it had either a positive effect on local-extinction probabilities or a negative effect on colonization probabilities. We conclude that further analyses of spotted owls must account for imperfect and variable detectability and barred owl presence to properly interpret results. Further, because barred owl presence is increasing within the range of northern spotted owls, we expect to see further declines in the proportion of sites occupied by spotted owls.
Northern spotted owls (Strix occidentalis caurina) are known to be associated with late-successional forests in the Pacific Northwest of the United States, but the effects of habitat on their ...demographic performance are relatively unknown. We developed statistical models relating owl survival and productivity to forest cover types within the Roseburg Study Area in the Oregon Coast Range of Oregon, USA. We further combined these demographic parameters using a Leslie-type matrix to obtain an estimate of habitat fitness potential for each owl territory (n = 94). We used mark–recapture methods to develop models for survival and linear mixed models for productivity. We measured forest composition and landscape patterns at 3 landscape scales centered on nest and activity sites within owl territories using an aerial photo-based map and a Geographic Information System (GIS). We also considered additional covariates such as age, sex, and presence of barred owls (Strix varia), and seasonal climate variables (temperature and precipitation) in our models. We used Akaike's Information Criterion (AIC) to rank and compare models. Survival had a quadratic relationship with the amount of late- and mid-seral forests within 1,500 m of nesting centers. Survival also was influenced by the amount of precipitation during the nesting season. Only 16% of the variability in survival was accounted for by our best model, but 85% of this was due to the habitat variable. Reproductive rates fluctuated biennially and were positively related to the amount of edge between late- and mid-seral forests and other habitat classes. Reproductive rates also were influenced by parent age, amount of precipitation during nesting season, and presence of barred owls. Our best model accounted for 84% of the variability in productivity, but only 3% of that was due to the habitat variable. Estimates of habitat fitness potential (which may range from 0 to infinity) for the 94 territories ranged from 0.74 to 1.15 (x̄ = 1.05, SE = 0.07). All but 1 territory had 95% confidence intervals overlapping 1.0, indicating a potentially stable population based on habitat pattern. Our results seem to indicate that while mid- and late-seral forests are important to owls, a mixture of these forest types with younger forest and nonforest may be best for owl survival and reproduction. Our results are consistent with those of researchers in northern California, USA, who used similar methods in their analyses. However, we believe that given the low variability in survival and productivity attributed to habitat, further study is needed to confirm our conclusions before they can be used to guide forest management actions for spotted owls.
We analyzed demographic data from northern spotted owls (Strix occidentalis caurina) from 14 study areas in Washington, Oregon, and California for 1985–2003. The purpose of our analyses was to ...provide an assessment of the status and trends of northern spotted owl populations throughout most of their geographic range. The 14 study areas made up approximately 12% of the range of the subspecies and included federal, tribal, private, and mixed federal and private lands. The study areas also included all the major forest types that the subspecies inhabits. The analyses followed rigorous protocols that were developed a priori and were the result of extensive discussions and consensus among the authors. Our primary objectives were to estimate fecundity, apparent survival (φ), and annual rate of population change (λ) and to determine if there were any temporal trends in these population parameters. In addition to analyses of data from individual study areas, we conducted 2 meta-analyses on each demographic parameter. One meta-analysis was conducted on all 14 areas, and the other was restricted to the 8 areas that constituted the Effectiveness Monitoring Plan for northern spotted owls under the Northwest Forest Plan. The average number of years of reproductive data per study area was 14 (range = 5–19), and the average number of recapture occasions per study area was 13 (range = 4–18). Only 1 study area had <12 years of data. Our results were based on 32,054 captures and resightings of 11,432 banded individuals for estimation of survival and 10,902 instances in which we documented the number of young produced by territorial females. The number of young fledged (NYF) per territorial female was analyzed by testing a suite of a priori models that included (1) effects of age, (2) linear or quadratic time trends, (3) presence of barred owls (Strix varia) in spotted owl territories, and (4) an even-odd year effect. The NYF varied among years on most study areas with a biennial cycle of high reproduction in even-numbered years and low reproduction in odd-numbered years. These cyclic fluctuations did not occur on all study areas, and the even–odd year effect waned during the last 5 years of the study. Fecundity was highest for adults (x̄ = 0.372, SE = 0.029), lower for 2-year-olds (x̄ = 0.208, SE = 0.032), and very low for 1-year-olds (x̄ = 0.074, SE = 0.029). Fecundity was stable over time for 6 areas (Rainier, Olympic, Warm Springs, H. J. Andrews, Klamath, and Marin), declining for 6 areas (Wenatchee, Cle Elum, Oregon Coast Range, Southern Oregon Cascades, Northwest California, and Simpson), and slightly increasing for 2 areas (Tyee, Hoopa). We found little association between NYF and the proportion of northern spotted owl territories where barred owls were detected, although results were suggestive of a negative effect of barred owls on the Wenatchee and Olympic study areas. The meta-analysis on fecundity indicated substantial annual variability with no increasing or decreasing trends. Fecundity was highest in the mixed-conifer region of eastern Washington (x̄ = 0.560, SE = 0.041) and lowest in the Douglas-fir (Pseudotsuga menziesii) region of the Oregon coast (x̄ = 0.306, SE = 0.039). We used Cormack–Jolly–Seber open population models and Program MARK to estimate apparent survival rates of owls >1 year old. We found no differences in apparent survival rates between sexes except for 1 area (Marin), which had only 6 years of data. Estimates of apparent survival from individual study areas indicated that there were differences among age classes with adults generally having higher survival than 1- and 2-year-olds. Apparent survival rates ranged from 0.750 (SE = 0.026) to 0.886 (SE = 0.010) for adults, 0.626 (SE = 0.073) to 0.886 (SE = 0.010) for 2-year-olds, and 0.415 (SE = 0.111) to 0.860 (SE = 0.017) for 1-year-olds. These estimates were comparable to survival rates from previous studies on the subspecies. We found evidence for negative time trends in survival rates on 5 study areas (Wenatchee, Cle Elum, Rainier, Olympic, and Northwest California) and no trends in survival on the remaining areas. There was evidence for negative effects of barred owls on apparent survival on 3 study areas (Wenatchee, Cle Elum, and Olympic). Survival rates of adult owls on the 8 Monitoring Areas generally were high, ranging from 0.85 (SE = 0.009) to 0.89 (SE = 0.010), but were declining on the Cle Elum, Olympic, and Northwestern California study areas. The meta-analysis of apparent survival indicated differences among regions and changes over time with a downward trend in the mixed-conifer and Douglas-fir regions of Washington. The meta-analysis of apparent survival also indicated that there was a negative association between fecundity and survival the following year, suggesting a cost of reproduction on survival. This effect was limited to the Douglas-fir and mixed-conifer regions of Washington and the Douglas-fir region of the Oregon Cascade Mountains. We used the reparameterized Jolly–Seber method (λRJS) to estimate annual rate of population change of territorial owls in the study areas. This estimate answers the question, Are these territorial owls being replaced in this geographically open population? Point estimates of λRJS were <1.0 for 12 of 13 study areas. The analyses provided strong evidence that populations on the Wenatchee, Cle Elum, Rainier, Olympic, Warm Springs, H. J. Andrews, Oregon Coast Ranges, and Simpson study areas were declining during the study. The mean λ̂RJS for the 13 study areas was 0.963 (SE = 0.009), suggesting that populations over all the areas were declining about 3.7% per year during the study. The mean λ̂RJS for the 8 monitoring areas for the Northwest Forest Plan was 0.976 (SE = 0.007) compared to a mean of 0.942 (SE = 0.016) for the other study areas, a 2.4-versus-5.8% decline per year. This suggested that owl populations on federal lands had higher demographic rates than elsewhere; thus, the Northwest Forest Plan appeared to have a positive effect on demography of northern spotted owls. Populations were doing poorest in Washington, where apparent survival rates and populations were declining on all 4 study areas. Our estimates of λRJS were generally lower than those reported in a previous analysis (λ̂RJS = 0.997, SE = 0.003) for many of the same areas at an earlier date. The possible causes of population declines include but are not limited to habitat loss from timber harvest and fires, competition with barred owls, and weather patterns.
PDF
