Climate oscillation and the invasion of alien species influence the oceanic distribution of seabirds

Abstract Spatial and temporal distribution of seabird transiting and foraging at sea is an important consideration for marine conservation planning. Using at‐sea observations of seabirds (n = 317), collected during the breeding season from 2012 to 2016, we built boosted regression tree (BRT) models to identify relationships between numerically dominant seabird species (red‐footed booby, brown noddy, white tern, and wedge‐tailed shearwater), geomorphology, oceanographic variability, and climate oscillation in the Chagos Archipelago. We documented positive relationships between red‐footed booby and wedge‐tailed shearwater abundance with the strength in the Indian Ocean Dipole, as represented by the Dipole Mode Index (6.7% and 23.7% contribution, respectively). The abundance of red‐footed boobies, brown noddies, and white terns declined abruptly with greater distance to island (17.6%, 34.1%, and 41.1% contribution, respectively). We further quantified the effects of proximity to rat‐free and rat‐invaded islands on seabird distribution at sea and identified breaking point distribution thresholds. We detected areas of increased abundance at sea and habitat use‐age under a scenario where rats are eradicated from invaded nearby islands and recolonized by seabirds. Following rat eradication, abundance at sea of red‐footed booby, brown noddy, and white terns increased by 14%, 17%, and 3%, respectively, with no important increase detected for shearwaters. Our results have implication for seabird conservation and island restoration. Climate oscillations may cause shifts in seabird distribution, possibly through changes in regional productivity and prey distribution. Invasive species eradications and subsequent island recolonization can lead to greater access for seabirds to areas at sea, due to increased foraging or transiting through, potentially leading to distribution gains and increased competition. Our approach predicting distribution after successful eradications enables anticipatory threat mitigation in these areas, minimizing competition between colonies and thereby maximizing the risk of success and the conservation impact of eradication programs.

In the Indian Ocean (IO), several studies have explored linkages between oceanographic and geomorphic conditions and seabird distribution derived from single-year surveys (e.g., Kappes, Weimerskirch, Pinaud, & Le Corre, 2011;Mendez et al., 2017; Weimerskirch, Le Corre, . Hyrenbach et al. (2007) explored drivers of seabird distribution in the southern IO, identifying the influence of sea surface temperature (SST) and proximity to sub-Antarctic Islands.  found that their distribution in the southwest IO was closely related to persistent oceanographic conditions and that time-averaged values over the long term (>7 years) were more predictive of distribution than those averaged over the shortterm (1 week).
Multiyear studies can provide managers with useful information needed to anticipate how interannual climate oscillations such as El Niño Southern Oscillation (ENSO; Sprogis, Christiansen, Wandres, & Bejder, 2018) and the IO Dipole (Saji, Goswami, Vinayachandran, & Yamagata, 1999) may impact seabird distribution. Interannual and climate variability in the tropical IO is to a large degree characterized by oscillations in SST gradient between the eastern and western basin, referred to as the IO Dipole (Saji et al., 1999). This gradient is represented by the Dipole Mode Index (DMI), where positive values correspond to cooler waters in the eastern basin and warmer in the west, whereas negative values correspond to warmer waters in eastern basin and colder in the west. Although the influence of climate oscillations and seabird dynamics has been the subject of a vast body of work (reviewed in Oro, 2014), the effects of the dipole on higher trophic levels remain poorly understood. A few studies have explored linkages between the IO Dipole and seabird population dynamics and behavior (Rivaland, Barbraud, Inchausti, & Weimerskirch, 2010;Tryjanowski, Stenseth, & Matysioková, 2013), due in part to its relatively recent discovery (Ashok, Guan, & Yamagata, 2003). Recent research on land birds has shown a positive correlation between the IO Dipole and bird community composition (Mehta & Wilby, 2018). However, to our knowledge, the influence of climate variability on seabird distribution in the central Indian Ocean has not been studied.
While seabird distribution at sea may fluctuate as a function of climatic variability, such as that reflected by the IO Dipole (Dias et al., 2019), distribution at sea is likely also impacted by invasive species on nearby islands. Island invasion by rodents, such as the ship rat Rattus rattus, is one of the greatest threats to seabird populations (Dias et al., 2019;Jones et al., 2008;King, 1985). Seabirds are central place foragers and thus sensitivity to rats may restrict their distributions in the water adjacent to invaded islands. Seabirds require islands to rest and breed, and both survival and breeding success rates are highest on islands with limited disturbance (King, 1985). Rats successfully invade islands by quickly adapting to new habitats, in part because of their omnivorous diet. Rats prey on both chicks and adults, causing population declines which can lead to extirpation (Fleet, 1972;Jones et al., 2008;King, 1985;Major, Jones, Charette, & Diamond, 2007). The impact of rat invasion on seabirds is species-dependent and depends upon a combination of biological traits, such as breeding strategy, body weight, and life history. For example, small seabirds nesting in burrows such as storm-petrels are particularly vulnerable to rat predation (Jones et al., 2008;Woodward, 1972). Rat-eradication programs are considered a major component of successful island restoration and seabird population recovery (Borrelle, Boersch-Supan, Gaskin Towns, 2018;Hutton, Parkes, & Sinclair, 2007;Le Corre et al., 2012;Towns et al., 2009).
The IO has 27 archipelagos that are considered hotspots of marine biodiversity (Carr et al., 2020, Danckwerts et al., 2014Le Corre et al., 2012), most of which are particularly important to seabirds . In the central IO, the Chagos Archipelago, encompassed within the British Indian Ocean Territory (BIOT), is comprised of 55 tropical islands and was designated a no-take marine protected area (MPA) in 2010.
The majority of the archipelago has been closed to human activities since 1971 and is therefore relatively undisturbed (Everaarts et al., 1999;Readman et al., 2013;Sheppard & Sheppard, 2019).
The archipelago is considered of great importance for seabird conservation, harboring eighteen species of resident breeders, and ten designated and two proposed "Important Birds Areas" (Hilton & Cuthbert, 2010;McGowan, Broderick, & Godley, 2008 (Harper & Bunbury, 2015;Harper, Carr, & Pitman, 2019;Hilton & Cuthbert, 2010). Seabird densities on rat-free islands are up to 760 times greater than that on invaded islands, leading to nutrient subsidies and increased productivity on adjacent coral reefs (Graham et al., 2018). Notably, these subsidized reefs may recover faster following coral bleaching (Benkwitt, Wilson, & Graham, 2019), primarily enhanced by biodiversity richness and ecosystem functionality (Benkwitt, Wilson, & Graham, 2020). As productivity near rat-free islands is enriched, it is therefore conceivable that seabirds on these islands have greater opportunities to feed in proximity to their colonies.
After the successful eradication of rats from Île Vache Marine in 2017 (Harper et al., 2019), further rat eradication has been designated a priority target within the conservation framework of the BIOT Draft Conservation Management Plan 2018-2023(BIOT Administration, 2018. Here, we expand on previous work done in the IO (i.e., Hyrenbach et al., 2007; by using a multiyear seabird survey (from 2012 to 2016) within the BIOT MPA to identify drivers of distribution. First, we modeled seabird distribution using oceanographic variables, and distance to the nearest island, in order to make general seabird distribution predictions and to establish the influence of oceanography and interannual variability. Then, having established that the at-sea distribution of these species is in fact sensitive to the nearest island, we built new models considering distance to closest rat-free island or to closest rat-invaded island.
Finally, predictions based on the rat-invaded island model were subtracted from those of the rat-free model to infer the spatial effect of rats on seabird distribution at sea during transiting or foraging. This approach enables us to estimate potential suitable marine habitats (i.e., distribution gain) in a scenario of a successful archipelago-wide rat-eradication program and possible factors relevant to island restoration priorities.

| Study area
The Chagos Archipelago is located in the central IO at 6°S and 72°E at the southern limit of the Chagos-Laccadive ridge and is over 1,500 km from the nearest continental land mass (Carr, 2012). Fiftyfive islands are clustered within the atolls of Diego Garcia, Peros Banhos, Salomon, Egmont, and on the Great Chagos Bank ( Figure 1a) and constitute combined approximately 60 km 2 of land area. The territory encompasses approximately 60,000 km 2 of shallow photic reefs and 580,000 km 2 of primarily oceanic habitat, with a maximum depth over 6,000 m (Carr, 2011;Dumbraveanu & Sheppard, 1999).
The climate is tropical, characterized by oceanic conditions and the seasonal reversal monsoon (Sheppard, 1999). Situated in the intertropical convergence zone (ITCZ), the archipelago has moderate winds generally from the northwest (October to April) and the southeast (May to September). Sea surface temperature has an approximately bimodal distribution with maxima in December-January and March-April with a yearly mean of 28°C (Pfeiffer, Dullo, Zinke, & Garbe-Schönberg, 2008) oscillating between 24.8 and 30.5°C.

| Seabird observations
In order to identify the influence of oceanographic conditions and island on seabird distribution, we conducted a multiyear survey of the archipelago's seabirds at sea. The survey ran from 2012 to 2016 between November and April, to overlap with the moderate phase of the monsoon. This period generally coincides with peak seabird breeding activity in the Chagos Archipelago (Carr, 2011(Carr, , 2015Carr et al., 2020 Figure 1). Each year during the survey, sampling effort was a trade-off between partial replacement of the previous years to en- supported by 1-2 field assistants. This consistency in the same lead observer with multiple field assistants and the use of transects with limited strip (i.e., 300 m) reduced potential sources of bias (Spear, Ainley, Hardesty, Howell, & Webb, 2004).

| Variables selection
We retained the most frequent and abundant seabird species (total sum of observations > 100) in the BIOT MPA in order to model oceanic distributions. These distributions were modeled based on geomorphic and oceanographic variables using Boosted Regression Tree models (BRT), an advanced form of regression (Friedman, Hastie, & Tibshirani, 2000) that use boosting to combine and adapt large numbers of relatively simple tree models, enabling model performance optimization (Elith, Leathwick, & Hastie, 2008).
The BRTs were fitted using individual species count per sample (a proxy for abundance) as the response variables, against explanatory variables that previously have been shown to contribute to seabird distribution (Fox et al., 2017;Mannocci, Catalogna, et al., 2014;Vilchis et al., 2006;Yen, Sydeman, & Hyrenbach, 2004). Slope and distance to nearest island were calculated using QGIS version 3.8. Slope was derived from seabed depth values from a GEBCO 30-arc seconds bathymetry grid (Becker et al., 2009) shown to be more predictive of apex predators than short-term values (Mannocci et al., 2017;Suryan, Santora, & Sydeman, 2012) and are more directly related to habitat consistency and thus ecologically relevant . We also included an index of climatic variability, as represented by the Dipole Mode Index [DMI] and oceanic Niño index [ONI]. ONI and DMI were downloaded from NOAA (2020, 2020b) repository.

| Species distribution models
We first constructed full BRT models that included all explanatory variables (seven variables) for each species. Secondly, we observed the individual contribution of each variable and rebuilt the models selecting the variables with contributions greater than 5%.
We then used the total explained deviance (TED) to evaluate the explanatory power of the models. TED was calculated dividing the

F I G U R E 2
Year-to-year sampling effort in the Chagos Archipelago. Each 300-m transect is represented by a black dot as the spatial resolution does not allowed us to perfectly draw lines residual deviance by the null deviance resulting from each selected species models. BRT models were fitted using the package gbm on R (R Development Core Team 2018 version R version 3.5.2) with code modifications provided by Elith et al. (2008). As recommended by Elith et al. (2008) and D'agata et al. (2014), we did an analytical exploration of BRT models in order to find a "trade-off" between numbers of trees (nt; number of interactions), learning rate (lr; the shrinkage parameter), and tree complexity (tc; depth of interactions between factors of each tree). This approach required investigation of the bag fraction term (bg) that controls overfitting via the introduction of stochasticity to the models (Friedman, 2002). Model parameters were chosen while considering the goodness of fit, as determined via cross-validation (CV , Table S2). Finally, we used the dependence plots resulted from the BRT models to understand the shape of the influence of every variable in every species.

| Predictions of seabird distribution
Spatial predictions in unsampled areas were limited to the convex hull defined within the BIOT MPA and restricted by the range values of the variables used to build each model and the max recorded value of distance from coast (~137 km). This constraint ensured that predictions were only made in areas with similar environmental conditions (see Figure S1 and Table S1). Using this approach, we avoided extrapolating beyond the range of the model, while generating meaningful predictions beyond our sampled area (Yates et al., 2018).
Whenever ONI or DMI was retained in the model, we rendered predictions based on the values for the last year of sampling, 2016. We rendered predictions on a 0.4 × 0.4 decimal degree resolved grid.
This resolution was considered a reasonable trade-off in order to capture distribution for species with uncertain range sizes (Seo, Thorne, Hannah, & Thuiller, 2008).

| Modeling the effect of rat invasion
We hypothesize that the presence of rat-invaded islands will influence the distribution of seabirds at sea. We modeled the effect of rat invasion on seabird distribution at sea by modifying our BRTs.
We first exchanged the variable distance to coast from each transect with either the distance to the closest rat-free island or the closest rat-invaded island. This resulted in two additional models. The model that included "distance to the closest rat-free islands (km)" was considered to represent bird distribution at its theorized maximum abundance, in the absence of any rat invasion. The model that included "distance to the closest rat-invaded islands (km)" was considering to represent bird distribution assuming total invasion.
These two models were then used to identify thresholds based on a broken-line regression analysis of the effect of rat invasion or absence. This analysis gave us the chance to quantify the degree to which seabird distribution is influenced by the distance to rat-free or rat-invaded islands using a Davies' test (Davies, 2002). Davies' test enabled us to find the inflexion point of the partial dependence plots by testing the difference in the slopes. The test was done using the R package segmented (Muggeo, 2008). This analysis has been previously used to find thresholds on the response to explanatory variables (e.g., Clausen, Christensen, Gundersen, & Madsen, 2017;D'agata et al., 2014;Isles, Xu, Stockwell, & Schroth, 2017;Picard, Rutishauser, Ploton, Ngomanda, & Henry, 2015). As a result, the test provided with break points (BP) of the dependence plots with a range of the 95% confidence intervals (CI). We contrasted the BP and the CI of the ratfree model, the rat-invaded model, and the original distribution model.
The final objective of our analysis was to identify possible distribution shifts, after a rat-eradication scenario. In order to determine the potential net gain in distribution following a scenario of an archipelago-wide rat-eradication program, we subtracted the predictions of the rat-invaded models from the predictions of the rat-free models. The predictions were mapped only where the nearest island was rat-invaded since we assume that no new islands will be invaded, showing net gain and net loss in seabird abundance and habitat suit- ability. An eradication program will not increase a seabird population immediately, as islands may first need to be recolonized, and only after several years of high reproductive output can substantial population increases be expected (e.g., Jones, 2010). Depending on whether an island is actually occupied by a species or not, the initial recolonization may also spill over the abundance elsewhere (as the colonizing birds must come from somewhere). As such, these predictions should be considered as potential only.

| Seabird sightings
In total, 7,008 seabirds were observed during the five expeditions (Table 2) Figure 3g and h). These species were retained for further distribution modeling (Figure 4).

| Oceanic drivers of distribution and spatial patterns
Total deviance explained for each BRT was 80% for red-footed booby, 89% for brown noddy, 88% for white tern, and 99% for wedge-tailed shearwater. Distance to coast was an important variable for all species, explaining between 17.6% and 41.1% of the deviance (Figure 5b, 5g, 5k and 5q). Slope was a particularly important variable influencing for red-footed booby (22.3% contribution, Figure 4a) whereas sea surface temperature was the most important for wedge-tailed shearwater (29.4%). Chlorophyll a concentration explained between 6.4% and 23.5% for all species. DMI was retained for red-footed booby (6.7%, Figure 6a) and wedge-tailed shearwater Spatial predictions for red-footed booby, brown noddy, and white tern revealed a strong coast signature (Figure 7a-c), while wedge-tailed shearwater distribution was more uniform with higher abundance levels near high slope areas and toward the northeast of the Archipelago (Figure 7d). Brown noddy and white tern abundance was pronounced over shallow seabeds (<1,000 m) in proximity to islands and atolls (Figure 7b,c). Red-footed booby abundance was more pronounced in pelagic and deeper areas and in areas with intermediate slope (ca. 15º, Figure 7a).
The presence of rats on nearby islands reduced the suitable habitat of seabirds ( Figure 10). Following rat eradication, abundance at sea of red-footed booby, brown noddy, white tern, and wedgetailed shearwater increased by 14%, 17%, 3%, and 4% respectively.
However, the models for wedge-tailed shearwater distribution were weak and the effect was negligent. Hence, it is not reported in figure.

| D ISCUSS I ON
Using our at-sea observations in the Chagos Archipelago over a 5-year period, we have identified spatiotemporal trends in seabird

| Drivers of seabird distribution within the Chagos Archipelago
The red-footed booby showed a primarily oceanic distribution,   Harrison & Stone-Burner, 1981;King, 1974). Therefore, this response is likely an artifact of the observed birds commuting to foraging areas, rather than actually foraging in the relatively near-coast areas. Wedge-tailed shearwater return to burrows only at night, so that their distribution appears independent from islands may be due to a predominantly scattered and remote distribution during the day (Dias, Alho, Granadeiro, & Catry, 2015). Although we found no significant effect of rat invasion on wedge-tailed F I G U R E 5 Partial dependence plots of each variable modeled in the BRTs for all four species red-footed booby (a-e), brown noddy (f-g), white tern (k-o) and wedge-tailed shearwater (p-s). The green solid line in each graph represents the response of the species to the variables. The relative contribution of the model is showed from the greatest to the least. Plots manifest that nonmonotonic responses were found shearwater distribution, many shearwater species and allies are particularly vulnerable to invasive land predators (Dias et al., 2019;Smith, Polhemus, & VanderWerf, 2002), because they nest in ground burrows. The pelagic behavior and large foraging range which our sampling range failed to capture may mask any distribution shift related to rat invasion and the other environmental variables, as indicated by the weaker models.
Constant competition over prey is expected to lead to a prey depredation zones around colonies, otherwise known as Ashmole's Halo (Ashmole, 1963). Halos vary as a function of colony, size, and bird foraging range (Birt, Birt, Goulet, Cairns, & Montevecchi, 1987).
Within the Chagos Archipelago, many islands are <100 km apart and are clustered close together (<20 km between islands) within atolls. The range to which the abundant red-footed booby, brown noddy, and white tern distributions radiate out from islands (i.e., 263, 136, and 133 km respectively) makes it therefore very likely that neighboring colonies compete, either by overlapping in distribution or by expressing behavior to minimize foraging overlap (Mendez et al., 2017;Wakefield et al., 2013). The wider distribution range and lower abundance of the wedge-tailed shearwater make competition between colonies less likely than for other seabirds (Gaston, Ydenberg, & Smith, 2007).

F I G U R E 7
Predicted distribution of red-footed booby, brown noddy, white tern, and wedge-tailed shearwater as a function the BRT models. Color scales represent the seabird abundance response, ranging from highest predicted value (red) to zero (blue). Scales differ between species as a function of difference in abundance. Predictions were run within the convex hull of the variables F I G U R E 8 Contribution of the distance to coast on the distribution model, rat-free model, and rat-invaded model for red-footed booby (RFT), brown noddy (BN), white tern (WT), and wedge-tailed shearwater (WTS). Contribution of distance to a near rat-free island was greater in red-footed booby and brown noddy. White tern showed that rat-invaded island has a greater contribution. Wedge-tailed shearwater showed difference in contribution between rat-free and rat-invaded island but the contribution of distance to coast in the distribution model was greater F I G U R E 9 Sensitivity of seabird distribution to presence or absence of rats on nearby islands. Partial dependence plot (a, c, e, g) of the effects of rat-free (blue lines) and rat-invaded (red lines) islands contrasted with the original distribution model (green lines For example, Kumar, Pillai, and Manjusha (2014) identified a positive association between IO tuna productivity and the Dipole Index. In the southern IO, albatross breeding success has also been positively correlated with the Dipole Index (Rivaland et al., 2010). The knowledge of mechanisms driving these patterns is at present limited and any explanation must remain speculative at this stage. There is evidence that equatorial upwellings in the IO are more pronounced and that westerly winds decrease in intensity during positive Dipole events (Du & Zhang, 2015). In the Chagos Archipelago, it is thus possible that negative Dipole events result in weakened regional upwelling and therefore require seabirds to forage further afield, leading to a drop in regional abundance. This would be consistent with present understanding regarding other climate oscillations such as ENSO, which is known to influence forage species productivity (Lehodey, Bertignac, Hampton, Lewis, & Picaut, 1997), with implications for higher trophic levels. For example, common bottlenose dolphin (Tursiuops trunctatus) migrate offshore during strong ENSO years, possibly due to a lack of inshore prey (Sprogis et al., 2018).

| Influence of climate oscillation
Use of telemetry and satellite tracking is currently being deployed on red-footed boobies in BIOT (Carr, pers. obs.), which will enable mechanisms to be explored in more detail. The greater sensitivity of wedge-tailed shearwater to both oceanographic variables and to the Dipole suggests this family may be the most vulnerable to global environmental change.
Any linkage between the Dipole and mobile megafauna is likely mediated by multiple trophic links (Oro, 2014). As foragers commensal with subsurface predators, seabirds could be impacted by the Dipole both directly, for example, by a reduction in forage species abundance, and indirectly, by an increase in tuna abundance (Kumar et al., 2014;Maxwell & Morgan, 2013). It is beyond our scope to distinguish these processes here; however, we are currently expanding our analysis of seabird distribution to include data on subsurface prey and predator abundance collected simultaneously to the seabird observations, using midwater baited videography (Letessier, Bouchet, & Meeuwig, 2017;Letessier et al., 2019).

| Implication for rat-eradication programs
Past rat-eradication efforts in the Chagos Archipelago include a failed attempt on Eagle Island (Meier, 2006) and successful attempts on Îles Vache Marine, du Sel, and Jacobin (Harper et al., 2019). The latter attempts were focussed on small islands to test the feasibility of eradication and appropriate methodologies on a small scale. Island rodent eradication is increasingly recognized as a powerful strategy for the preservation and recovery of avian populations (Brooke et al., 2018;Jones et al., 2016;Lavers, Wilcox, & Donlan, 2010).
However, eradication is technically challenging and expensive (Warren, 2018), requiring the application of toxic rodenticide posing a risk to humans, livestock, pets, and wildlife (Pickrell, 2019;Van den Brink, Elliott, Shore, Rattner, and (Eds.)., 2018). Eradication is more likely to fail in the tropics, with high mean annual temperatures and constant precipitation , and in the presence of land crabs and coconut palms , making a program in the Chagos Archipelago challenging. Eradication on the largest island of Diego Garcia is likely to be particularly complex and expensive as it is inhabited (Harper & Carr, 2015).
Our analysis has revealed potential increases in habitat usage following rat eradication and that these habitats are spatially and species-specific. On the basis of our study, we propose that eradication Our results here aim to form part of a far wider set of considerations, with the ultimate aim of eradicating rats from all islands in the archipelago, in order to achieve full conservation impact.

| Concluding remarks
Seabird abundance and distribution at sea in BIOT are driven by geomorphology and oceanographic conditions. Our distribution pre- To our knowledge, this is the first attempt at predicting the potential response of seabird distribution by predicting potential shifts in habitats usage following a rat-eradication scenario. We have demonstrated areas of potential distribution gain and have predicted new hotspots at sea following a rat-eradication program. There is considerable impetus for eradicating invasive species on islands (Brooke et al., 2018;Dawson et al., 2015;Holmes et al., 2019;Jones et al., 2016;Lavers et al., 2010), further supported by our research here and other related research in the Chagos Archipelago (Benkwitt et al., 2019(Benkwitt et al., , 2020Graham et al., 2018;Harper et al., 2019). In addition to practical considerations such as cost and probability of success, eradication programs should identify where eradication can have the greatest conservation potential and ecological impact. This is particularly important for seabirds, whose niche extends beyond terrestrial breeding colonies.

ACK N OWLED G M ENTS
We acknowledge Dr. David Curnick for helping us with the variable extractions and the BIOT Administration for support and access to the BIOT patrol vessel. We want to thank all field assistants for their help and Nicholas Dunn for valuable comments on the manuscript. We are grateful to the Master, Chief engineer, and crew of the BIOT patrol vessels for their hard work and assistance.

O PE N R E S E A RCH BA D G E S
This article has earned an Open Materials Badge for making publicly available the components of the research methodology needed to reproduce the reported procedure and analysis. All materials are available at https://github.com/juper ez/Seabi rdChagos. F I G U R E 1 0 Predicted areas of increase in seabird abundance under a scenario of rat eradication. Rat-free distribution predicted from BRT model using a rat-free scenario (a-c), and a rat-invaded scenario (d-f), where each island is set as either "rat-free" or "rat-invaded," respectively. These models represent the distribution predictions under complete eradications of rats and a full invasion of rats, respectively. Hence, an approach to understand the variations of distribution is calculated by subtracting the rat-invaded minus the rat-free models. This yielded to the net gain in bird abundance under a scenario of rat eradication (g-i). The upper 95% quantile increase of the net gain is also showed (j-l). White shaded areas indicate areas nearby currently rat-free islands in which a rat-eradication program would not have any effect since they are already at the theorized maximum abundance