Appendix A. Detailed derivation of the game theoretic model and a table summarizing the variables and parameters in the game-theory model.

Detailed derivation of the game theoretic model and a table summarizing the variables and parameters in the game-theory model

Appendix A. Coexistence conditions and derivation of w.

Coexistence conditions and derivation of w

Linking Dynamic Habitat Selection with Wading Bird Foraging Distributions across Resource Gradients.

Species distribution models (SDM) link species occurrence with a suite of environmental predictors and provide an estimate of habitat quality when the variable set captures the biological requirements of the species. SDMs are inherently more complex when they include components of a species' ecology such as conspecific attraction and behavioral flexibility to exploit resources that vary across time and space. Wading birds are highly mobile, demonstrate flexible habitat selection, and respond quickly to changes in habitat quality; thus serving as important indicator species for wetland systems. We developed a spatio-temporal, multi-SDM framework using Great Egret (Ardea alba), White Ibis (Eudocimus albus), and Wood Stork (Mycteria Americana) distributions over a decadal gradient of environmental conditions to predict species-specific abundance across space and locations used on the landscape over time. In models of temporal dynamics, species demonstrated conditional preferences for resources based on resource levels linked to differing temporal scales. Wading bird abundance was highest when prey production from optimal periods of inundation was concentrated in shallow depths. Similar responses were observed in models predicting locations used over time, accounting for spatial autocorrelation. Species clustered in response to differing habitat conditions, indicating that social attraction can co-vary with foraging strategy, water-level changes, and habitat quality. This modeling framework can be applied to evaluate the multi-annual resource pulses occurring in real-time, climate change scenarios, or restorative hydrological regimes by tracking changing seasonal and annual distribution and abundance of high quality foraging patches

Determining habitat quality for species that demonstrate dynamic habitat selection

Determining habitat quality for wildlife populations requires relating a species' habitat to its survival and reproduction. Within a season, species occurrence and density can be disconnected from measures of habitat quality when resources are highly seasonal, unpredictable over time, and patchy. Here we establish an explicit link among dynamic selection of changing resources, spatio‐temporal species distributions, and fitness for predictive abundance and occurrence models that are used for short‐term water management and long‐term restoration planning. We used the wading bird distribution and evaluation models (WADEM) that estimate (1) daily changes in selection across resource gradients, (2) landscape abundance of flocks and individuals, (3) conspecific foraging aggregation, and (4) resource unit occurrence (at fixed 400 m cells) to quantify habitat quality and its consequences on reproduction for wetland indicator species. We linked maximum annual numbers of nests detected across the study area and nesting success of Great Egrets (Ardea alba), White Ibises (Eudocimus albus), and Wood Storks (Mycteria americana) over a 20‐year period to estimated daily dynamics of food resources produced by WADEM over a 7490 km2 area. For all species, increases in predicted species abundance in March and high abundance in April were strongly linked to breeding responses. Great Egret nesting effort and success were higher when birds also showed greater conspecific foraging aggregation. Synthesis and applications: This study provides the first empirical evidence that dynamic habitat selection processes and distributions of wading birds over environmental gradients are linked with reproductive measures over periods of decades. Further, predictor variables at a variety of temporal (daily‐multiannual) resolutions and spatial (400 m to regional) scales effectively explained variation in ecological processes that change habitat quality. The process used here allows managers to develop short‐ and long‐term conservation strategies that (1) consider flexible behavioral patterns and (2) are robust to environmental variation over time

Daily mean landscape flocks and individuals (fourth-root transformed) predicted by the model-averaged terms for the White Ibis.

<p>Predicted presence and abundance are highest with an average landscape depth (within available depths) of 10–17 cm and when White Ibis are using an average DSD of ~450 days.</p

Ranking of candidate models describing variables influencing daily mean flock abundance of Great Egrets, White Ibises, and Wood Storks in the Florida Everglades (Proc Mixed).

<p>Models are ranked by differences in Akaike’s information criterion and only candidate models within ΔAIC_c^d ≤ 4.0 are presented. Model selection results are followed by model averaging results for each species. The R² represents the model fit for the estimated daily flock abundance vs. model averaged predicted values.</p><p>Ranking of candidate models describing variables influencing daily mean flock abundance of Great Egrets, White Ibises, and Wood Storks in the Florida Everglades (Proc Mixed).</p

Ranking of candidate models describing variables influencing daily mean depth use of Great Egrets, White Ibises, and Wood Storks in the Florida Everglades (Proc Mixed).

<p>Models are ranked by differences in Akaike’s information criterion and only candidate models within ΔAIC_c^d ≤ 4.0 are presented. Model selection results are followed by model averaging results for each species. The R² represents the model fit for the estimated mean daily depth use vs. model averaged predicted values.</p><p>Ranking of candidate models describing variables influencing daily mean depth use of Great Egrets, White Ibises, and Wood Storks in the Florida Everglades (Proc Mixed).</p

Ranking of candidate models describing variables influencing daily mean days since drydown (DSD) use of Great Egrets, White Ibises, and Wood Storks in the Florida Everglades (Proc Mixed).

<p>Models are ranked by differences in Akaike’s information criterion and only candidate models within ΔAIC_c^d ≤ 4.0 are presented. Model selection results are followed by model averaging results for each species. The R² represents the model fit for the estimated mean daily DSD use vs. model averaged predicted values.</p><p>Ranking of candidate models describing variables influencing daily mean days since drydown (DSD) use of Great Egrets, White Ibises, and Wood Storks in the Florida Everglades (Proc Mixed).</p

Ranking of candidate models describing variables influencing frequency of cell use (i.e., spatial occurrence) over the study period for the Great Egret, White Ibis, and Wood Stork (Proc Glimmix).

<p>Models are ranked by differences in Akaike’s information criterion and only candidate models within ΔAIC_c^d ≤ 4.0 are presented. Model selection results are followed by model averaging results for each species. The R² represents the model fit for the estimated spatial occurrence vs. model averaged predicted values.</p><p>Ranking of candidate models describing variables influencing frequency of cell use (i.e., spatial occurrence) over the study period for the Great Egret, White Ibis, and Wood Stork (Proc Glimmix).</p