Pairing functional connectivity with population dynamics to prioritize corridors for Southern California spotted owls

Land use change, climate change, and shifts to disturbance regimes make successful wildlife management challenging, particularly when ongoing urbanization constrains habitat and movement. Preserving and maintaining landscape connectivity is a potential strategy to support wildlife responding to these stressors. Using a novel model framework, we determined the population‐level benefit of a set of identified potential corridors for spotted owl population viability.


| INTRODUC TI ON
Corridors are a promising conservation strategy because of their potential to limit the negative impacts of fragmentation (e.g., inbreeding), to allow individuals to reorganize after a disturbance, and to promote species' response to habitat degradation, including degradation due to climatic change (Beier & Gregory, 2012;Heller & Zavaleta, 2009;Hilty et al., 2006;Noss, 1991). Because of the importance of connectivity to metapopulation persistence, corridor modelling is an essential component of reserve design and implementation (Keeley, Ackerly, et al., 2018). Given limited conservation resources (as in Cushman et al., 2018;Torrubia et al., 2014), there is considerable interest in understanding where to establish or protect corridors or linkages, and which provide the most benefit to a population network.
Analytical approaches to specify corridor location have benefited from considerable attention in the literature (Beier et al., 2015).
Innovations in least cost path (Cushman et al., 2013), connectivity circuit flow (Littlefield et al., 2017;McRae et al., 2012), centrality (Pinto & Keitt, 2009) and spatial redundancy (Rubio & Saura, 2012) have led to detailed assessments of habitat and corridor quality across a landscape. Once key areas for connectivity have been identified, there is an additional need to prioritize among potential areas often with little information on the actual or potential rate of immigration between habitat patches, termed functional connectivity (in Hodgson et al., 2009). Quantifying functional connectivity can be challenging.
Although an ideal test of functional connectivity would be in situ field comparisons of communities in the presence and absence of a given corridor, such empirical testing is rare (Gilbert-Norton et al, 2010, Kool et al., 2013 and unable to address the future impacts of climate change. Thus, an analytical approach is needed to explore the impact of current and future functional connectivity and apply it within a metapopulation network. Quantifying the population-level benefit of functional connectivity can be even more challenging, where connectivity benefit can be defined as the increase in the abundance of a target population given the presence of a corridor. As an extreme example, a population sink (as described in Furrer & Pasinelli, 2016) would have no connectivity benefit. With a long history in the ecological literature (Hanski, 1998), metapopulation models provide a framework to consider changes in populations due to the addition or removal of a corridor (Kitzes & Merenlender, 2013;Mestre et al., 2017). There are a number of analytical approaches that consider spatial flow and centrality within a metapopulation (Littlefield et al., 2017;McRae et al., 2012;McRae & Kavanagh, 2011), but translating the flow of individuals into increased metapopulation abundance requires a model that explicitly incorporates functional connectivity and population dynamics. Once metapopulation patch and linkage networks have been specified, a corridor's benefit depends on whether the corridor connects patches that are otherwise functionally isolated from the broader population network. To address this, individual corridors can be removed from a fully connected network, or added to an unconnected network to determine their irreplaceability or redundancy. To date, most redundancy analyses rely primarily on landscape pattern and flow (as in Pinto & Keitt, 2009;Rubio & Saura, 2012).
Because landscape connectivity is scale-dependent (Maciejewski & Cumming, 2016) and conservation objectives are often determined locally (e.g., cactus wren in San Diego; Conlisk et al., 2014), it can be informative to consider a corridor's benefit to a local network even if the corridor has limited value to the regional metapopulation. In such cases, common reserve design priorities-for example, connecting large, robust habitat patches-may give way to promoting benefits within localized networks. Thus, corridor prioritization techniques need to be able to define a localized network (e.g., graph theory approaches; Pinto & Keitt, 2009) and quantify the benefit of individual corridors to that local network. In the absence of such analysis, the benefit of one corridor to a local population may be obscured by another corridor's benefit to the larger metapopulation.
Finally, long-term conservation planning requires that the benefit of a corridor be resilient to future landscape change including climate change, landscape development, and habitat restoration (Alagador et al., 2016). While connectivity analyses have historically been designed to connect similar locations in space, rapidly changing landscapes demand resilience assessments across both time and space. New modelling approaches have emerged to combine the strengths of species distribution models (SDMs) and dynamic metapopulation models (Conlisk et al., 2012(Conlisk et al., , 2013, offering a novel way to prioritize potential corridors. Linked species distributionpopulation models incorporate direct and indirect effects of climate change, disturbance, and species' population dynamics and dispersal, allowing the benefit of individual corridors to be examined within an evolving network. Approaches that consider multiple global change phenomena are recognized as under-represented in the literature (Beier et al., 2008;Keeley, Basson, et al., 2018).
The need to plan for landscape connectivity is particularly relevant in Southern California, a global biodiversity hotspot (Myers et al., 2000), where the climate is expected to change dramatically (Klausmeyer & Shaw, 2009), a 25% increase in the human population is expected by 2050, and climate and land use changes are projected to alter disturbance regimes (Mann et al., 2016). In this study, we demonstrate how estimated functional connectivity can be used to identify and prioritize corridors that support a metapopulation.
In particular, we incorporate ecological processes that determine a corridor's irreplaceability across local and regional networks under global change. We use the California spotted owl as a model species corridor identification, corridor prioritization, expected minimum abundance, functional connectivity, metapopulation model, redundancy, spotted owl because long-term survival and fecundity data are available and can be used to assess climate change impacts on suitable habitat and population-level connectivity. In particular, we asked which corridors for the Southern California spotted owl metapopulation: (1) are most beneficial; (2) are irreplaceable; (3) are locally versus regionally beneficial; and (4) are beneficial now and in a future climate in 2100. Pairing functional connectivity assessments with population dynamics, we demonstrate a method for identifying and prioritizing the population-level benefit of local and regional corridors under climate change.

| Study system
Our target area was the South Coast ecoregion of Southern California, a geographically and biologically diverse region with a Mediterranean climate. Spotted owls inhabit high-elevation, coniferdominated sites in these mountain ranges. The area is bounded in the north by the Transverse Mountains and in the east by the Peninsular Range ( Figure S1). While already including a broad set of habitats-grasslands, coastal sage and chaparral shrublands, and conifer forests-we further extended our study area to include desert to the east, the north to central coast, and southern Sierra Nevada to describe connectivity in and out of the study region. The study area included elevations below sea level to >3,500 metres at the highest point.  Elevation Model (Flint & Flint, 2014) to calculate the 19 bioclim variables typically employed in distribution modelling (described in Hijmans et al., 2005). When we found pairs of highly correlated variables, we retained the variable with a stronger influence on suitability in univariate tests. Finally, because non-climate variables can also influence habitat suitability, we included variables describing land use (impervious surface), water resources (distance to perennial and seasonal streams and stream density), and topography (roughness and per cent slope) (see Table S1).

| Metapopulation and model development
Species presence (n = 1,865) and absence (trimmed to three times the number of presence points, or n = 5,595) points were acquired from eBird (Sullivan et al., 2009) , 2017). Absence points were a combination of scientistcollected callback absences in owl habitat (CNDDB data) and of eBird observations in non-owl habitat (see Figure S2), where the utility of eBird absences in non-target habitat has been shown across bird taxa (Robinson et al., 2020). We computed ensemble suitability predictions, weighted by AUC (Area Under the receiver operating characteristic Curve), using generalized linear models, boosted regression trees, and random forest in the biomod2 package (Thuiller et al., 2005(Thuiller et al., , 2016 in R (R Core Team 2017), the mgcv package for generalized additive models (Wood, 2017), and the stand alone MaxEnt software (Phillips et al., 2006). To project the distribution of future suitable habitat, we substituted future climate variables into the ensemble models for two general cir-  Table S2 and Figure S4) changing climate, we included a third, more optimistic, future climate projection focused on forest vulnerability under future climatic conditions. Briefly, our vegetation vulnerability projection is based on the ensemble, across four climate projections, of a statewide vegetation assessment (described in Thorne et al., 2016) that quantifies vulnerability based on the degree to which forests are exposed to marginal climates (defined as extreme quantiles of their existing range).
For a given year, we used a habitat suitability map to assign a continuous suitability value (ranging from 0 to 1) to each cell.  Table 1 in LaHaye & Gutiérrez, 2005). We then input our core maps into the software package RAMAS GIS ® 6.0 (described in Akçakaya & Root, 2005). RAMAS translates the suitability values within a pixel, summed across a habitat patch, to the carrying capacity of the patch, where patches could grow or shrink through time with concomitant changes to dispersal distances between patches (see Supporting Information S1). In addition to climate-driven changes in carrying capacity, we imposed random fluctuations (15%) in the carrying capacity to reflect environmental stochasticity. We ran all projections for 100 years (discussed here) and 40 years (discussed in Supporting Information S4).  Peery et al. (2012). Because the goal of our model was to explore the potential of connectivity to influence viability, we adjusted vital rates upward (see equation S1), such that the owl population was at equilibrium when habitat suitability did not change with climate change (no change). Fecundity and survival were drawn each year from a distribution with specified mean and standard deviation.

| Connectivity parameterization and scenarios
We made dispersal between patches inversely proportional to the time-evolving edge-to-edge distances between patches (see Supporting Information S1). Mean and maximum dispersal distance were 25 km and 150 km, respectively, based on Forsman et al. (2002) which measured dispersal within intact forest. In addition, we fixed dispersal between any two patches such that (1) less than 10% of individuals in the giving patch went to any one adjacent receiving patch (although patches could be connected to more than one adjacent patch), (2) the larger the abundance in the giving patch the larger the fraction dispersing, and (3)

| Spotted owl distribution and population trajectories
SDM predictions showed substantially less suitable owl habitat by the year 2100 as compared to historically suitable habitat (Figure 1).
Historical ensemble models of habitat suitability achieved high AUC values (0.95-0.96 across ten validation datasets) because of the clear climatic distinction of mountainous owl habitat from lowlands within the study region (see Figure S2). Suitable habitat reduction under future climate projections drove a decline in population abundance ( Figure 3) despite parameterizing fecundity to increase by 75% by the end of the century (as modelled by Peery et al., 2012). Under the most optimistic (vegetation vulnerability) future projection, the population was roughly halved; under the CNRM CM5 and MIROC5 future projections the population was reduced by more than 90% (see Figure S3).

| Corridor benefit under the current climate
Under a no climate change future projection, we saw a maximum increase in the overall metapopulation of 6% in the full dispersal compared to the no dispersal scenario. Two Southern California (2) the East Los Padres to San Gabriel patches, and (3) Sierra West to Sierra East patches (see Table S2 for all corridor results, including additional patches labelled in Figure S4). The same corridors were even more beneficial in the fire scenarios ( Figure S5).
These corridors involved the most populous patches in the model

| Corridor irreplaceability
The value of the three most beneficial corridors is shown in Figure 4 as the per cent difference in expected minimum abundance achieved by subtracting the corridor from an otherwise full dispersal landscape-what we call reduction-by-subtraction-as well as the per cent difference achieved by adding the corridor to an otherwise no dispersal landscape-what we call improvement-by-addition. All corridors were more beneficial in the improvement-by-addition case, where all achieved the threshold (1.7%) above which we assume that change is due to the addition of the corridor as opposed to random chance. In the reduction-by-subtraction case, the Sierra West-Sierra East corridor had slightly lower benefit and the East Los Padres-San Gabriel corridor had much lower benefit. The difference between improvement-by-addition and reduction-by-subtraction suggests that when other corridors are present they can compensate for the loss of the redundant East Los Padres-San Gabriel corridors but not the irreplaceable San Gabriel-San Bernardino corridor. Considering the San Bernardino-San Jacinto corridor, we see that the San Jacinto patch consistently acted as a sink. All corridors not shown in Figure 4 (23 other corridors) were modelled but did not exceed the 1.7% threshold in the owl expected minimum abundance (see Table S2 in Supporting Information S2).

| Local versus regional benefits
Some corridors that demonstrated little benefit across the entire population were beneficial within local population clusters. Identifying clusters by graph theory (Figure 5b), we performed local-scale tests that mirrored the tests performed on the entire metapopulation.
Assessing a cluster's regional importance within the metapopulation, we found that patch connectivity within clusters 2 and 4 increased the expected minimum abundance by 5.3% and 2.0%, respectively, over the no dispersal scenario (green bars, Figure 5a). The large, central San Gabriel patch was included in both cluster 2 and 4 (see Figure 2 and 4) because parts of the patch fell in both clusters; however, since the patch's population is well-mixed, we included the entire population in both clusters. Testing local population networks that included only the patches of a specified cluster, we found that retaining all corridors within the cluster increased the expected minimum abundance of the patches within the cluster by 6.4%-10.2% (grey bars, Figure 5b), more than the 5.1% change in expected minimum abundance between the full dispersal versus no dispersal tested on the entire metapopulation. Within each local network, we found that a single corridor drove the lion's share of the connectivity benefit for the cluster (blue bars,

| Resilient connectivity benefits
Across climate change future projections, the owl population declined precipitously in both the full dispersal and no dispersal scenarios. Climate change, especially the CNRM CM5 and MIROC5 future projections, was predicted to reduce suitable habitat and increase dispersal distances between patches resulting in lower overall flow of owls among habitat patches. Because of declining populations with increasing dispersal distances, the corridors that provided benefits under the current climate were not able to compensate for the loss of habitat due to climate change (Figure 4). In the MIROC5 future projection, the Sierra West-Sierra East corridor provided some benefit, although still below the 1.7% threshold (Figure 4a,b). Interestingly, the San Bernardino-San Jacinto corridor, between two of the few remaining habitat patches under the CNRM CM5 and MIROC5 future projection, was no longer a pronounced sink. The vegetation vulnerability future projection, while retaining more suitable habitat, still resulted in long dispersal distances that decreased the benefit of connectivity.

| D ISCUSS I ON
Using the Southern California spotted owl as a model species, we described a framework to estimate the benefit of corridors to an overall metapopulation, determining which corridors were irreplaceable, locally versus regionally beneficial, and beneficial now and in a future climate in 2100. Our models allow for the flexible introduction of new disturbances, such as disease, as well as alterations in the timing of these events, to explore uncertainty in potential outcomes. Further, our methodology considers both the regional and local benefits of corridors. Taken together, these approaches offer robust tools for connectivity decision-making, a widely recognized challenge in the literature.

| Beneficial and irreplaceable corridors
We found that a corridor between the large, centrally located San Gabriel and San Bernardino populations was both beneficial in isolation and irreplaceable based on our metrics of improvementby-addition and reduction-by-subtraction. The ability to distinguish between these two properties is an important benefit of our modelling approach. For example, the most beneficial corridors we identified, the San Gabriel-San Bernardino and East Los Padres-San Gabriel corridors, differed with respect to irreplaceability. When the San Gabriel-San Bernardino corridor was lost from a full dispersal scenario, the overall metapopulation abundance declined; whereas, when the East Los Padres-San Gabriel F I G U R E 5 Fraction increase in expected minimum abundance, or EMA (a), across clusters displayed in inset (b) and identified by graph theory. Across the bars in (a), All Patches shows the increase in EMA for retaining connectivity between the patches within a cluster as compared to the no dispersal scenario across the entire metapopulation; Subset Patches looks at the benefit of full dispersal compared to no dispersal within the subset of patches within the cluster (as if the cluster were its own metapopulation); and Best Corridor in Subset identifies the improvement of the single best corridor within each of the subsets of patches defined by the clusters. The entire bi-coloured San Gabriel patch (SG) was included in clusters 2 and 4, and the bi-coloured Palomar patch (PM) was in clusters 2 and 3. The greyed out Sierra West and Sierra East populations composed their own cluster, but were not considered since the value of that corridor was described in the metapopulation modelling. The single best corridors are labelled above the bars in (a) and coloured red. Patches are labelled as follows: NLP = North Los Padres, CLP = Central Los Padres, ELP = East Los Padres, SG = San Gabriel, SB = San Bernardino, and SJ = San Jacinto mountains, PM = Palomar mountain, and VL = Volcan-to-Laguna. Dashed line shows threshold above which differences in models are not likely to be due to random variation across model runs corridor was removed, the overall abundance was unchanged.
Examining the metapopulation network, the East Los Padres and San Gabriel populations each retained considerable connectivity in the absence of a corridor between them; making the corridor between them redundant. Depending on conservation goals, redundant networks may be beneficial in vulnerable landscapes or when functional connectivity of a corridor through time is highly variable.

| Local versus regional corridors
By testing local clusters of corridors, we were able to identify redundancy at the local level as well as individual corridors that were uniquely beneficial to local networks. For example, in cluster 4, the East Los Padres-San Gabriel corridor increased the expected minimum abundance by 4.6% when added to the cluster under no dispersal, compared with the full dispersal cluster scenario where expected minimum abundance increased by 6.4%. This difference in relative benefit suggests that there is local redundancy in connectivity where full dispersal provided more benefit than any single corridor. In contrast, a single corridor, the irreplaceable San Bernardino-San Gabriel corridor, increased minimum expected abundance by 10.1% in cluster 2 as compared with 10.2% under full dispersal, suggesting this particular corridor is a conservation priority.
Our local network assessment also revealed two corridors with potential local benefit that were not apparent in the full metapopulation assessment: the North-Central Los Padres and Palomar-Volcan corridors. These corridors did not emerge in the metapopulation scenarios because they connect patches with relatively few individuals: clusters 1 and 3 had less than half as many female owls as clusters 2 and 4. When considering the entire metapopulation, the demographic signal from the biggest clusters obscured the signal in the smallest clusters. The value of this multi-scale approach to evaluating corridors is that we can identify regional priorities based on expected importance to the entire metapopulation (e.g., San Gabriel-San Bernardino corridor) while also recognizing the benefits of conserving local corridors for subpopulations and individuals within those clusters.
These findings provide a quantitative assessment that supports the central premise of Hodgson et al. (2009), that the best course of action is to make conservation decisions focusing on locations of large contiguous habitat. At both the regional and local scales, connecting large, centrally located patches was most beneficial.
Further, when we compare our output to more traditional metrics of cost-weighted distance, we see that the two largest populations are within relatively contiguous habitat. The distance between the San Gabriel and San Bernardino patches is relatively short (less than 5.2 km), with a ratio of cost-weighted to Euclidean distance of 24:1 (because of the need to traverse the five-lane interstate I-15 highway), less than the 37:1 cost-weighted to Euclidean distance ratio for the East Los Padres-San Gabriel corridor.

| Global change resilience
Given the modelled decline in owl habitat under climate change, we did not find any corridors that increased metapopulation abundance in 2100. Because owls depend on long-lived trees and SDMs implicitly assume instant climatic equilibration, the CNRM CM5 and MIROC5 projections are likely an extreme, pessimistic future.
Instead of seeing rapid declines in adult trees, a more likely scenario is forest decline over hundreds of years due to recruitment failure (Conlisk et al., 2017a(Conlisk et al., , 2017bDobrowski et al., 2015). To consider a less dire future projection, we included the vegetation vulnerability future projection where owls might persist in resilient conifer forests (Thorne et al., 2016) which occupy a relatively larger set of climatic conditions than owls. However, even in the vegetation vulnerability future projection, we did not see a benefit of connectivity because of dramatic habitat loss. While it is generally assumed that species with fragmented metapopulations are most likely to need well-designed connectivity networks (Beier et al., 2008) (Davis et al., 2019). Further, protecting a wider diversity of vegetation types, including high-productivity, low-elevation live oak-Douglas fir forests (LaHaye et al., 1997), can improve owl roosting, nesting, and foraging habitat (Roberts, 2017).

| Population Sink
Our evaluation also identified a corridor that could potentially lead to a population sink for owls, a phenomenon hypothesized in the literature . Specifically, we found that the San A corridor could create a temporary sink-as the San Gabriel-San Bernardino linkage did in the 40-year vegetation vulnerability projection (Supporting Information S4)-or a current sink might become a hold-out population in the future. In the latter case, the San Jacinto patch retained much of its suitable habitat by the end of the century under the MIROC5 future projection which translated to a nearly significant (i.e., greater than 1.7%) increase in overall owl population in the reduction-by-subtraction scenario (Figure 4). The ability to identify where corridors are maladaptive or detrimental can be particularly valuable when evaluating conservation investments in connectivity.

| Model parameterization and generalizability
One limitation of our modelling framework is the difficulty in generalizing the results of our species-specific approach across ecological communities, where single-species analyses are over-represented in the conservation design literature (Reside et al., 2018). Because our goal was to prioritize corridors, we chose a species with a distinct set of habitat patches and high dispersal capacity, parameterizing dispersal rates from intact forest (Forsman et al., 2002 Jennings et al., 2020).
Another drawback of our approach is that it is relatively data intensive, lending itself to implementation with species with enough available data to parameterize the model. However, others have found ways around this by defining archetypal species based on dispersal ability (Kitzes & Merenlender, 2013;Littlefield et al., 2017).
Our approach could be treated in a similar fashion with the added benefit of considering archetypal regeneration times in addition to different dispersal capabilities. However, this "archetypal species" approach lacks specificity for some conservation and model validation purposes. One advantage of using a well-studied species is there is likely to be additional data-analytic, genetic, and dispersal data-that can be used to validate models.
In addition to our choice of study species, we parameterized the model to provide an upper estimate of the benefit of connectivity. was that patches were more likely to diverge from one another, making the reorganization of individuals among patches more beneficial. This type of risk spreading has been shown to be beneficial in regions with high fire frequencies and localized damage (Regan et al., 2010). Similarly, in our fire simulations ( Figure S5 and Table S3), we found that adding fire increased the benefit of all of the identified corridors. Under the fire scenarios we found an additional corridor, the East to Central Los Padres corridor, increased overall abundance by 1.4%, approaching the threshold above which results were unlikely due to chance. One side effect of introducing considerable environmental stochasticity is that we saw abundances change across multiple sets of 5,000 runs. To account for this between-set variability, we chose the highest threshold (1.7%) from the CNRM CM5 when adjacent to roads (Hayward et al., 2011) and limited evidence of inter-mountain dispersal in Southern California owls (Gutiérrez et al., 2017). Regardless, preserving high-quality forested habitat is important to spotted owl resilience and would likely benefit additional species, where a 43% overlap in mountain lion and spotted owl least cost corridors has been observed (Beier et al., 2009).

| CON CLUS ION
Using metapopulation models to estimate functional connectivity of spotted owls, we identified and prioritized redundant and irreplaceable corridors that benefited regional and local population resilience. Both regionally and locally, we found that beneficial corridors were typically between two similarly sized, centrally located, large patches. Although we saw a dramatic decrease in modelled metapopulation abundance and increase in inter-patch distances when we introduced climate change into the model, evaluating connectivity under different scenarios is informative to consider the long-term value of conservation investments. Overall, our approach provides a framework and workflow that can support resilient connectivity planning in changing landscapes.

PEER R E V I E W
The peer review history for this article is available at https://publo ns.com/publo n/10.1111/ddi.13235.