Factors affecting the distribution and abundance of autumn vagrant New World warblers in northwestern California and southern Oregon

Birds found outside their typical range, or vagrants, have fascinated naturalists for decades. Despite broad interest in vagrancy, few attempts have been made to statistically examine the explanatory variables potentially responsible for the phenomenon. In this study, we used multiple linear regression to model the occurrence of 28 rare warbler species (family Parulidae) in autumn in northern California and southern Oregon as a function of migration distance, continental population size, distance, and bearing to both closest breeding population and breeding population center. In addition to our predictive model, we used capture data from the California coast to 300 km inland to examine relationships between the presence of vagrant warblers, regional warbler species richness and age class distribution. Our study yielded three important results: (1) vagrancy is strongly correlated with larger North American population size; (2) vagrants are more common at some coastal sites; and (3) where young birds are over-represented, vagrants tend to occur—such as on the coast and at far inland sites. Of the many explanations of rare and vagrant individuals, we feel that the most likely is that these birds represent the ends of the distributions of a normal curve of migration direction, bringing some few migrants to locations out of their normal migratory range as vagrants. We also examine the underrepresented species that, according to our model, are overdue for being recorded in our study area.


INTRODUCTION
Bird observers have been long fascinated by the appearance of rare or out of range birds, and the opportunity to speculate on the causes of such vagrants.
"The erratic wanderings of migratory birds, resulting in their appearance in countries far removed from their accustomed haunts, and off the routes followed to reach them, are in many cases to be attributed to their failure, from some cause or other, predicting which warbler species have likely been missed by observers. Second, we used capture data from northern California and southern Oregon to determine if vagrancy asymmetrically influenced warbler species richness across the landscape. Third, we used capture data to test the prediction that young and vagrant warblers probably represent lost birds subject to the vagaries of geography, and their abundances are, therefore, statistically correlated across the landscape.

METHODS
Vagrancy is a site-specific phenomenon, as one area's common bird is another's rare vagrant, or out of range species, so we limited our study to two overlapping study areas. The first study area is delineated by the 28 bird banding stations used in this study (from our network of 239 banding stations known as the Klamath Bird Monitoring Network; Alexander & Ralph, 2004) in northern California and southern Oregon (Fig. 1). The second study area is based on the meticulous compilation of all available records from all observers in northwestern California by Harris (2006) that includes the western half of Siskiyou County, all of Del Norte, Humboldt, and Trinity counties, and the northern half of Mendocino County. From this, we retrieved fall sightings (September-November) of all vagrant warbler species (Table 1)  We defined a vagrant as a species that was detected at least once, and with a maximum of a total of 500 records, over a 36 year period (Harris, 2006). We felt that this was a useful number that differentiated relatively rare migrant birds from vagrant species that are occurring outside their normal range. For example, we did not consider the Palm Warbler (see Table 1 for scientific names) a vagrant, but a regular, yet rare, migrant with some 1,100 fall records. We found that 28 warbler species could be classified as vagrants because of their rarity (Table 1). For our predictive model, the response variable was a log transformation (to normalize the distribution) of the total number of individuals of each vagrant species detected during fall migration from Harris (2006). For example, Black-throated Blue Warbler had 51 and Blue-winged Warbler had three individuals documented during fall migration in northern California; each of these values represented a single datum. Explanatory variables were chosen based on their probability of affecting vagrant warbler occurrence in northern California and southern Oregon. Broadly, we included explanatory variables that measured three influential factors: migratory distance, population size, and direction to breeding population (Thorup, 2004;McLaren et al., 2006). Based on these three factors, we selected six explanatory variables to explain fall vagrant warbler sightings: migration distance, size of the North American breeding population (log), distance to closest population (log), bearing to closest population, distance to population center (log), and bearing to population center (Pfeifer, Stadler & Brandl, 2007). Distances were estimated by taking digital measurements from the centroid of our study area to the edge of the closest breeding range, as well as the center of the breeding population. Migration distance class was calculated by the number of degrees latitude between the breeding and wintering ranges using BirdLife range maps (http://www.birdlife.org/datazone/species). Our use of degrees latitudes likely underestimated migrant birds that move across longitudes as well as latitudes. However, given that long-distance warbler migration is characterized by changes in latitude, we felt comfortable that degrees latitude serves as an excellent index of migratory distance among our study species. We also calculated distance to  closest population, bearing to closest population, distance to population center, and bearing to population center. The inclusion of distance and bearing to closest breeding population accounted for distant, yet westerly populations of breeding vagrants. Distance estimates were to the nearest 100 km, from the combined center of the four counties of our study area to the center of each species' breeding range. North American population estimates were taken from Rich et al. (2004). We formulated 16 competitive multiple-linear regression models (Table 2), including a null (no explanatory variables) and global model (all explanatory variables) using program R (R Core Team, 2012). Models were formulated a priori based on a combination of explanatory variables we believed most influenced vagrancy. Next, we ranked each model using Akaike information criterion values corrected for small sample sizes (AICc) where the top model was selected if it was at least two AICc values lower, and/or had fewer parameters relative to the next most competitive model (Arnold, 2010). We also included 95% confidence intervals with explanatory variable beta estimates and adjusted R 2 with each model to provide additional information regarding how well each model performed and fit the data. Once the top model was selected, we used covariate data from ten other warbler species (Table 1) that had not yet been documented in the study area, Next, we used capture and banding data from 28 stations across southern Oregon and northern California, representing eight geographic regions, to explore relationships between location and warbler species occurrences. Each of the stations had at least a total of 10,000 mist-net hours of banding data during fall migration, and for convenience, were subjectively grouped into regions based on empirical criteria of distance to coast, latitude, altitude, and habitat ( Fig. 1; Table 3). Most nets were amongst riparian vegetation to achieve higher capture rates, irrespective if they were near oak woodland or dense coniferous forest.
To estimate the number of species of both all warblers and vagrant warblers, we generated Chao1 estimates of total and vagrant warbler richness, using program EstimateS (Colwell, 2005), at each banding station to examine the influence of vagrancy on warbler richness across southern Oregon and northern California. The Chao1 diversity index uses the ratio of species detected only once or twice to generate predicted estimates of species richness. The formula used for Chao1 estimates are based on Chao (1987) where S observations refers to total number of species observed in all samples pooled and F 1 and F 2 refer to species detected only once or twice: Finally, we used the same Klamath banding dataset (described above) to test the hypothesis that the proportion of young birds and vagrant bird abundances are correlated across the landscape (DeSante, 1973;Ralph, 1981). To examine this hypothetical relationship, we performed a simple linear regression to examine the correlation between the percent of all warbler species pooled that were young, and the abundance of vagrant warblers captured per 1,000 net-hours across the eight geographic regions in southern Oregon and northern California during fall migration.

Factors affecting the occurrence of vagrants
Using the number of fall records of the 28-vagrant species as a response variable (Table 1), we investigated combinations of six likely explanatory variables. We selected the top model based on being within two AICc values of the lowest value, while having the fewest number of parameters (Arnold, 2010). Based on these criteria, we selected North American population size as the most competitive explanatory variable explaining vagrancy in northern California (Table 2). Specifically, we found that vagrancy was positively correlated with the North American breeding population (Fig. 2), indicating that the larger the species' breeding population, the more likely it is to occur in northern California as a vagrant (β = 0.719; SE = 0.135; CI = [0.45-0.98]). Based on our model selection

Species recorded less or more often than expected
We detected a strong linear relationship between the number of fall records for the 28 species and the size of their North American breeding population, with most falling near the regression line (Fig. 2). The possibly instructive exceptions include those underrepresented, seen much less often than the population size would predict, with their values below the regression line (i.e, the largest negative residuals), including Connecticut Warbler, Cerulean Warbler, and Mourning Warbler. Conversely, "overrepresented" species tending to be recorded more often than would be predicted (the largest positive residuals) included Prairie Warbler, Virginia's Warbler, Black-and-White Warbler, and Black-throated Blue Warbler. We included the predicted number of records of 10 species of warblers that have never been recorded in northern California to identify what species, according to our model, should have been detected (Fig. 2). Painted Redstart, Swainson's Warbler, Red-faced Warbler, and Louisiana Waterthrush would have been predicted to be detected fewer than three times, but Grace's Warbler had ∼7 predicted records and Pine Warbler possibly more than 50 records. The other four species with no records had populations of less than 40,000 and would have a low probability of occurring in northwest California.

Influence of vagrancy on warbler species richness
When comparing the number of warbler species at the 11 stations that had at least one vagrant species occurring (Fig. 3), we found that vagrant warblers were most common   at the HOME station (in the Coastal Region) where vagrant warblers accounted for 9 of the 26 estimated species (36%). This was our highest ratio of vagrant to total species; this finding indicates that vagrancy strongly influenced total warbler richness at our most species-rich site. Conversely, vagrants at inland stations generally accounted for a smaller proportion of total warbler species richness, with 17 stations having none or relatively few vagrants. These species-poor stations could be located just inland from the coast, such as 7% at the RED2 station in the Redwood Region, only 4.5 km from the coast. At the much farther inland sites, however, the estimated proportion of vagrants rose again sharply to 19% at CABN and 20% at ODES on the western shore of Upper Klamath Lake in the Upper Klamath Region (Fig. 3).

Associations between young birds of all species and vagrants
Previous evidence suggests that banding stations along coasts have a high proportion of young birds (the "coastal effect" of Ralph, 1971Ralph, , 1978Ralph, , 1981. To examine if both young birds in general, and vagrant abundances, are similarly over-represented in certain regions across the study area, we employed linear regression using percent of young (all non-vagrant warblers pooled) as the response and vagrant warbler abundance captured across the regions as the explanatory variables. Our analysis found a moderately-significant relationship between the percent of young birds and the abundance of vagrant warblers captured across the eight geographic regions. Specifically, while beta estimate confidence intervals slightly overlapped zero (β = 0.299; SE = 0.163; CI = [0.02-0.62]), associated adjusted R 2 values were high, where vagrant records explained 25% of the variance in non-vagrant age ratios. Thus, areas with higher proportions of young warblers tended to have more vagrant warblers. As expected, the region with both the highest proportion of young and the highest proportion of vagrant warblers was the coastal region ( Fig. 4; Table 3).

DISCUSSION
Our analysis revealed three major insights: (1) vagrancy is largely driven by large population size-species with more individuals increased the likelihood of being detected outside a species' normal range. This is a logical confirmation and extension of other studies (Stake, 2012); (2) vagrancy drives warbler richness in some coastal sites and does not affect warbler richness at other, more inland sites; and (3) stations where young warblers account for a higher proportion of total captures, vagrant warblers also tend to occur-such as on the coast. Our findings suggest that young and vagrant birds have something in common: they both may be more prone to navigational mistakes, and therefore more often occur on the coast, an inherently dangerous place for these nocturnal migrants.
In an early analysis of California warblers, DeBenedictis (1971) also presented some subjective evidence that continental population size accounted for some variation in abundance of vagrants in California. He also suggested involvement of the angle of deviation from normal migration routes needed to reach California. By contrast, DeSante (1983b) suggested that on the Farallon Islands, some 30 km offshore, the abundance of vagrant warblers might be related to their respective commonness in North America. Another analysis by Hampton (1997) examining patterns of vagrancy relied on a linear model to explore factors that may have influenced the occurrence of 84 rare species throughout coastal and central northern California. Of the six explanatory variables included in a linear model, he found support for the following variables in explaining the occurrence of vagrants: westernmost longitude of a species' breeding range, taxonomic status, distance to the nearest edge of the breeding range, and easterly migratory route. Interestingly, unlike our findings, Hampton found little support for population size. Differences in Hampton's (1997) and our findings may reflect statistical methodologies, that is, we ranked a series of competitive models using AICc, while Hampton explored a single model. Our study area and taxonomic unit, wood warblers in northern California, was also much smaller relative to Hampton's that included all vagrant landbirds across much of the state.
Interestingly, we found four warbler species with no records in northern California (Harris, 2006) that, according to our model, should have been recorded at least once. Two species would be predicted to have a single individual Louisiana Waterthrush and Red-faced Warbler; but two others would be much more abundant: Grace's Warbler with seven records and the Pine Warbler with 45 records predicted. However, the facultative migratory behavior of the Pine Warbler-meaning some populations may not migrate-could be partly responsible for the overestimation of their potential occurrence in our study area (F. Moore, 2018, personal communication). Assuming that our predictive model is robust, both Grace's Warbler and Pine Warbler might not have occurred in our study area because they are more accurate in their navigation, or they could have been missed by observers because of identification problems, as both species are relatively cryptic. Pine Warbler resembles the somewhat more common Blackpoll Warbler, and other species, such as the Orange-crowned Warbler (Oreothlypis celata).
Interestingly, Pine Warbler has been detected south of the study area along the central coast of California, thereby suggesting the species has likely occurred in our study area (see ebird citizen science records: https://ebird.org/map/pinwar). Grace's Warbler is a southwestern species, and may be confused with immature Townsend's Warbler (Setophaga townsendi), a common species in the study area. Several other species appear to be relatively under-detected, and below the trend line. These are generally either cryptic or hard to detect (e.g., Mourning Warbler, underrepresented by almost an order of magnitude, and Connecticut Warbler both of which are likely confused with the common migrant MacGillivray's Warbler (Geothlypis tolmiei). In addition to appearing similar to MacGillivray's Warbler, Connecticut Warbler prefers thick vegetation near the ground making them inherently difficult to find (Pitocchelli et al., 2012). According to our model, other underrepresented vagrants include Ovenbird and Cerulean Warbler, both of which may be challenging to detect because Ovenbirds prefer forested understories and the Cerulean Warbler frequents forest canopies-an arduous stratum to look for birds in the oftentowering trees of the north coast. By contrast, overrepresented species, seen relatively more often than their population size would indicate, are typically conspicuous, or easily identified species, such as Black-and-white Warbler, Prairie Warbler, Chestnut-sided Warbler, American Redstart, and Black-throated Blue Warbler. It is also possible that, in addition to being conspicuous, these overrepresented species may be more prone to misorientation or have produced more young during the years of this study, relative to other species, thereby increasing the probability of young vagrants being detected on the coast. A high proportion of young birds on the Pacific coast, the "coastal effect" (Ralph, 1978(Ralph, , 1981 is suggested to be primarily due to misorientation of the relatively naïve young individuals at the edge of their migratory flyway. Several hundred kilometers farther inland is another periphery of many migrant species' routes, the eastern portion of our study area, where the habitat is less salubrious, and on the eastern edge of a major habitat type, the coniferous Cascade Mountains, and on the western edge of the relatively inhospitable Great Basin. In this portion of our study area, we found an increase in the number of vagrants, but did not find a concomitant high proportion of young. The increase of vagrants here along the western shore of Upper Klamath Lake may be related to this shoreline, acting as a "coast" analogous to the shore of the Pacific Ocean. In addition, it is quite possible that young birds on the coast may be due to one phenomenon, and the occurrence of vagrants might be associated with a different phenomenon. For example, Austin (1971) found that migrants which breed east of the Rockies typically occur approximately three weeks later in migration than migration dates in the east. A high percentage of these lost vagrants were immature. He suggested that they were transported westward, by airflows from east across the southwestern states, that could have played a role, as well as misorientation. However, DeSante (1973) clearly found that vagrant wood warblers in California occurred on time, relative to their average timing on their normal migration route.
While today's vagrant might be tomorrow's model citizen, destined to become a colonizer and perhaps an established resident, as Grinnell (1922) asserted, most vagrants might be viewed as "failed colonization attempts". Newton (2008: 267-299) summarized quite well the various explanations of the causes of vagrancy put forward over the past century or so. They include: normal dispersal over long distances, population growth or expansion, drift by winds, migration overshoots, deviant directional tendencies (right time but wrong direction), mirror-image migration, and reversed direction migration. While all explanations probably play a role and explain the occurrence of some vagrant individuals, we address the latter three explanations as they likely involve the vast majority of landbirds. The mirror-image misorientation theory, originally developed by DeSante (1973), and described by Diamond (1982), proposed that vagrants are misoriented by confusion of right and left in relating an inherited migration direction to a compass reference direction. Mirror-image misorientation theory accounts for observations made by DeSante (1983a) that in certain situations large-angle misorientations seem more frequent than small or intermediate deviations from the normal migration course (Alerstam, 1990). Misorientation by the wind has long been suggested as a cause of accidentals (Austin, 1971), but Thorup et al. (2012) found differently, as the authors used radio telemetry to track individual migratory flights of several species of songbirds from the Faroe Islands, approximately halfway between Norway and Iceland, far west of their normal migration route. Birds with expected easterly and south-easterly migration direction departed westward out over the Atlantic Ocean, indicating that these birds are actively flying in the "wrong" direction and that their occurrence is not caused by wind drift. However, on Attu Island, in the Aleutian Islands off Alaska, Hameed et al. (2009) found statistical evidence that the occurrence of spring Asian vagrants on this North Pacific island were correlated with storm winds from the west.
Perhaps none of our proposed explanatory variables captured the essence of either simple misorientation or mirror-image misorientation in determining the abundance of vagrants, because they do not include information on the normal fall migration routes of the various species. For example, American redstart and Black-and-white Warbler may be more abundant than predicted from source populations because they commonly winter in southern Baja California, much farther west than other species with similar breeding ranges, and thus require much smaller degrees of simple misorientation from their normal fall migration route to reach northern California. Similarly, Prairie, Black-throated Blue and Blackpoll Warblers may be more abundant than predicted due to their easterly fall migration routes which facilitates mirror-image vagrants in California.
We would advance that perhaps a more parsimonious explanation of the phenomenon, and certainly part of some of the mechanisms listed above, is that these vagrants represent the ends of the distributions of a normal curve of the migration direction of the species, thus bringing some few migrants to unaccustomed locations. As to the other explanations that have been advanced, as Newton (2008: 299) notes "possible bias in observer coverage throws doubt on some apparent examples of mirror-image and reversed-direction migration, and neither mechanism can be considered as proven or disproven". Our explanation of misorientation of young along the coast as being the result of deviant directional tendencies remains well-demonstrated (Ralph, 1978). Hence, it remains quite likely that the probability of an individual migrant suffering from deviant directional tendencies increases with population size, leading to our documented correlation between the abundance of vagrant warblers and total population size.