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https://github.com/cadam00/egcorrs

Evolutionary Game Corridors
https://github.com/cadam00/egcorrs

corridors evolutionary-game-theory game-theory graph-theory r r-package

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Evolutionary Game Corridors

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README 

        

[![CRAN status](https://www.r-pkg.org/badges/version/EGCorrs)](https://CRAN.R-project.org/package=EGCorrs)

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**This research was conducted at the Department of Marine Sciences, University

of the Aegean, Greece, supported by the European Union’s Horizon 2020 research

and innovation programme HORIZON-CL6–2021-BIODIV-01–12, under grant agreement

No 101059407, “MarinePlan – Improved transdisciplinary science for effective

ecosystem-based maritime spatial planning and conservation in European Seas”.**



## **Introduction to the EGCorrs Package (tutorial)**



Biodiversity conservation can be substantially enhanced through the modeling of

species corridors based on predicted behaviors. In this package, a dynamic

evolutionary congestion game is formulated to generate species corridors. The

primary advantage of this model lies in its utilization of vector fields as

input layers, rendering it particularly suitable for simulating species

distributions in marine environments characterized by current layers. The

population of hypothetical agents is transported from an origin to a destination

in space using a directed weighted graph, with each agent's utility being

maximized. An equilibrium state is reached after numerous iterations,

illustrating the paths selected by the agents. Furthermore, a congestion

parameter is incorporated to represent the tendency of populations to aggregate.

Detailed presentation of the algorithm and its theoretical background is done by

Nagkoulis et al. ([forthcoming](#ref-nagkoulisforthcomingevolutionary)).



## **Installation**



Development version of the package can be installed using:

``` r

if (!require(remotes)) install.packages("remotes")

remotes::install_github("cadam00/EGCorrs")

```



## **Illustration example**



Packages required in this vignette are listed and imported below:



``` r

# Import packages

library(EGCorrs)

library(sf)

```

```

## Linking to GEOS 3.12.1, GDAL 3.8.4, PROJ 9.3.1; sf_use_s2() is TRUE

```

```r

library(terra)

```

```

## terra 1.7.83

```

``` r

library(tmap)

```

```

## Breaking News: tmap 3.x is retiring. Please test v4, e.g. with

## remotes::install_github('r-tmap/tmap')

```

``` r

tmap_mode("view")

```

```

## tmap mode set to interactive viewing

```



Currents information about the flow directions is usually split into horizontal

($u$) and vertical ($v$) components, regarding the horizontal and the vertical

flow of the currents, respectively. As an example we use a cropped subset of the

Aegean Sea site (Clementi et al., [2021](#ref-clementi2021mediterranean))

provided in the form of `SpatRaster` elements. In Figure [1](#fig-Figure1) these

two directions of components $u$ and $v$ are presented. This can be plotted

using the following:



``` r

# Get example u and v components

component_u <- get_component_u()

component_v <- get_component_v()



# Plot each component

par(mfrow=c(1,2), las=1)

plot(component_u, main="u")

plot(component_v, main="v")

```





  Figure 1: Currents u (left) and v (right) components





Figure 1: Currents $u$ (left) and $v$ (right)

components.




In Figure [2](#fig-Figure2) an example of one origin and one

destination area is used, using a subset of the NATURA 200 data (European

Environment Agency, [2023](#ref-european2023natura)) at this cropped area of

Aegean Sea is utilized. For illustration purposes, the area around the left

island (Kythira) -in neon green- is considered as the origin area and the area

around the right island (Milos) -in mikado yellow- as the destination area.

Additional rows on each area could be added using `rbind`, indicating more areas

of the origin or destination area should be taken into consideration by the

analysis.



```r

# Read origin area

origin_areas      <- get_origin_areas()

```

```

## Reading layer `origin_areas' from data source 

##   `C:\Program Files\R\R-4.4.2\library\EGCorrs\external\origin_areas\origin_areas.shp' 

##   using driver `ESRI Shapefile'

## Simple feature collection with 1 feature and 1 field

## Geometry type: POLYGON

## Dimension:     XY

## Bounding box:  xmin: 22.86969 ymin: 36.04912 xmax: 23.13855 ymax: 36.39421

## Geodetic CRS:  WGS 84

```

```r

# Read destination area

destination_areas <- get_destination_areas()

```

```

## Reading layer `destination_areas' from data source 

##   `C:\Program Files\R\R-4.4.2\library\EGCorrs\external\destination_areas\destination_areas.shp' 

##   using driver `ESRI Shapefile'

## Simple feature collection with 1 feature and 1 field

## Geometry type: POLYGON

## Dimension:     XY

## Bounding box:  xmin: 24.3053 ymin: 36.62173 xmax: 24.49323 ymax: 36.75966

## Geodetic CRS:  WGS 84

```

```r

# Plot both of them

tm_shape(origin_areas) +

  tm_polygons(col="#1AFF1A") +

  tm_shape(destination_areas) +

  tm_polygons(col="#FFC20A")

```





  Figure 2: Origin on the left (Kythira) and destination on the right
<br />  (Milos).





Figure 2: Origin on the left (Kythira) -neon

green- and destination in the right (Milos) -mikado yellow.




Therefore, horizontal and vertical currents' components, as well as origin and

destination areas, are the minimum spatial data requirements for conducting an

analysis using the `EGCorrs` package. Additional non-spatial arguments of the

function are about used like the number of nearest neighbors (`k_neighbors` and

`nearest_grid_nodes`). For each one of the `niters` iterations, `npoints` agents

are added in the game, whose behavior is affected by the setting of a parameter

named `lambda` ($\lambda$).



``` r

set.seed(42)

# Warnings are thrown because of reassuring that components u/v and

# origin/destination areas are intersecting

corridors <- EGCorrs(component_u       = component_u,

                      component_v       = component_v,

                      origin_areas      = origin_areas,

                      destination_areas = destination_areas,

                      npoints           = 10, 

                      niters            = 100)

```

```

## |================================================================================================| 100%

## Warning messages:

## 1: attribute variables are assumed to be spatially constant throughout all

## geometries

## 2: attribute variables are assumed to be spatially constant throughout all

## geometries

```

The final corridors and origin/destination points produced from the algorithm

can be plotted using the following:



```r

names(corridors$solution_edges)[6] <- "uₗ"



tm_shape(st_as_sf(corridors$net_result_congestion, "edges"))+

  tm_lines(col = "black",alpha = 0.05) +

  tm_shape(corridors$solution_edges) +

  tm_lines(col = "uₗ",lwd="uₗ", scale=10,

           palette=colorRampPalette(c("blue", "red"))(10), n=10)+

  tm_shape(corridors$origin_points) + tm_dots(col="#1AFF1A", size=0.1) +

  tm_shape(corridors$destination_points) + tm_dots(col="#FFC20A", size=0.1)

```

```

## Legend for line widths not available in view mode.

```



  Figure 3: Final solution of the algorithm. Stronger corridors origin on
<br />  the left (Kythira) to the destination on the right (Milos) are indicated with
<br />  more red and wider lines. The origin random points are in neon green and the
<br />  destination points in mikado yellow.





Figure 3: Final solution of the algorithm.

Stronger corridors origin on the left (Kythira) to the destination on the right

(Milos) are indicated with more red and wider lines. The origin random points

are in neon green and the destination points in mikado yellow.




Convergence of the algorithm can be seen using, for example, the following plot

of $RMSE(u_{l_{perc}})$:



```r

# Restore device to a single plot

par(mfrow=c(1,1), las=1)



# Plot convergence of rmse_u_l_perc

plot(x    = corridors$metrics_df$niters,

     y    = corridors$metrics_df$rmse_u_l_perc,

     main = expression(RMSE(u[l[perc]])),

     xlab = "Number of iterations",

     ylab = "",

     lwd  = 2,

     type = "l")

```



  Figure 4: Convergence of the RMSE(u_{l_{perc}}), representing the
<br />  convergence of the selected corridors from the algorithm.





Figure 4: Convergence of the $RMSE(u_{l_{perc}})$,

  representing the convergence of the selected corridors from the algorithm.




## **References**





Clementi, E., Aydogdu, A., Goglio, A. C., Pistoia, J., Escudier, R., Drudi, M.,

Grandi, A., Mariani, A., Lyubartsev, V., Lecci, R., Cretí, S., Coppini, G.,

Masina, S., & Pinardi, N. (2021). Mediterranean Sea Physical Analysis and

Forecast (CMEMS MED-Currents, EAS6 system) (Version 1) [Data set]. Copernicus

Monitoring Environment Marine Service (CMEMS).

https://doi.org/10.25423/CMCC/MEDSEA_ANALYSISFORECAST_PHY_006_013_EAS8.

Last Access: 16/10/2024.





European Environment Agency. (2023). Natura 2000 data - the European network of

protected sites. European Environment Agency. Retrieved from 

https://www.eea.europa.eu/en. Last Access: 16/10/2024.





Nagkoulis N, Mazaris A, Adam C, Katsanevakis S. (forthcoming).

An Evolutionary Game Theoretic Model for Species Corridors Estimation.