Introduction

• Period: Oct 2015 - May 2016

• State Wildlife Grants - Iowa Department of Natural Resources

• Run predictive models using R package RMark

• Produce predictive maps using ArcGIS

• Develop an interactive web application using Shiny

Outline

• Project overview: data source and objectives

• Methods: model fit and covariates

• Model Validation: AUC

• Results: example of estimates table and predictive maps

• Demonstrate Shiny application

Data Collection

• Multiple Species Inventory and Monitoring (MSIM) Program

  • Iowa DNR and Iowa State University

• Sampling Interval

  • Primary: 2006-2014

  • Secondary: survey occasions (days)

• Survey Objects

  • 414 SGCN, only 69 SGCN where sufficient data were available

  • Birds, mammals, reptiles, amphibians, odonates and butterflies

Objectives

• Predict the distribution of species of conservation need

  • robust design occupancy model

• Create predictive species maps for priority SGCN

  • ArcGIS raster files

  • Shiny interactive web application

• Prioritize areas of conservation action for SGCN

  • habitat restoration and management

Methods

• Robust design occupancy model (MacKenzie et al. 2003)

  • package RMark

• Parameters of Interest

  • probability of occupancy ( $\psi$ )

  • probability of colonization ( $\gamma$ )

  • probability of extinction ( $ϵ$ )

  • probability of detection ( $p$ )

• Model types

  • RDOccupEG, RDOccupPE, RDOccupPG, ...

Statistical Model

$$Pr\left(X_i\right)={\varphi }_0\{\prod _{t=1}^{T=1}D\left(p_{X,t}\right){\varphi }_t\}{p}_{X,T}$$

• $p_{X,t}$ : vector denoting probability of observing the detection history $X_{i,t}$ in primary period $t$
• ${\varphi }_t$ : matrix of transition probabilities between states of occupancy from primary period $t$ to $t+1$ $$\begin{array}{cc}{\varphi }_t& =\left[\begin{array}{cc}P(X_{t+1}=1|X_t=1)& P(X_{t+1}=0|X_t=1)\\ P(X_{t+1}=1|X_t=0)& P(X_{t+1}=0|X_t=0)\end{array}\right]\\ & =\left[\begin{array}{cc}1-{ϵ}_t& {ϵ}_t\\ {\gamma }_t& 1-{\gamma }_t\end{array}\right],t=1,...,\text{T-1}\end{array}$$

$${\varphi }_0=\left[\begin{array}{cc}{\psi }_1& 1-{\psi }_1\end{array}\right]$$

Example

$$\begin{array}{cc}Pr(X_{i,1}=010)& ={\psi }_1(1-p_{1,1})p_{1,2}(1-p_{1,3})\\ Pr(X_{i,2}=000|X_{i,1})& =(1-{ϵ}_1)\prod _{j=1}^3(1-p_{2,j})+{ϵ}_1\\ Pr(X_i=\text{010 000})& ={\varphi }_{0}D\left(p_{010,1}\right){\varphi }_1{p}_{000,2}\\ & =\left[\begin{array}{cc}{\psi }_1& 1-{\psi }_1\end{array}\right]\left[\begin{array}{cc}(1-p_{1,1})p_{1,2}(1-p_{1,3})& 0\\ 0& 0\end{array}\right]\\ & \times \left[\begin{array}{cc}1-{ϵ}_1& {ϵ}_1\\ {\gamma }_1& 1-{\gamma }_1\end{array}\right]\left[\begin{array}{c}{\prod }_{j=1}^3(1-p_{2,j})\\ 1\end{array}\right]\\ & ={\psi }_1(1-p_{1,1})p_{1,2}(1-p_{1,3})[(1-{ϵ}_1)\prod _{j=1}^3(1-p_{2,j})+{ϵ}_1]\end{array}$$

Statistical Model (cont'd)

• Including Covariates $$\theta =\frac{\exp \left(Z^{\prime }\beta \right)}{1+\exp \left(Z^{\prime }\beta \right)}$$

  • $\theta$ is the probability of interest

  • $Z$ is the matrix of covariate information

  • $\beta$ is the vector of logistic model coefficients to be estimated

Covariates

• Landscape habitat variables ^[1]

  • Radius of sampled site: 200m, 500m and 1km

  • Land use classification:
    Water, Wetland, Grassland, Woodland and Agriculture

  • Landscape configuration:
    percentage of landscape (PLAND), large patch index (LPI), edge density (ED), patch density (PD) and interspersion-juxtaposition (IJI)

• Climate variables ^[2]

  • Wind speed (km/h), Cloud cover (%), Temperature ( ${}^{\text{o}}\text{C}$ )

Model Selection and Validation

• Akaike's Information Criterion adjusted for small sizes ( ${\text{AIC}}_c$ )

  • Models with $\Delta {\text{AIC}}_c\le 2\Rightarrow$ strong support
    (Burnham and Anderson 2002)

• Area under the receiver operating characteristic curve (AUC)

  • evaluate performance of predicting occupancy

  • training data set: survey years 2006-2012, 2014

  • test data set: survey year 2013 (better representative)

  • package pROC

  • $\text{AUC}=0.5\Rightarrow$ random guess

  • $\text{AUC}=1.0\Rightarrow$ perfect prediction
    (Jimenez-Valverde 2012)

ROC Curve

Results

Results Summary

Results (Cont'd)

Best Models for Each Specie

Results (Cont'd)

AUC and Coefficients Estimates under Best Model

Shiny

• Shiny by RStudio is a web application framework for R.

• No HTML, CSS or JavaScript knowledge required to turn your analyses into interactive web applications.

install.packages("shiny")
library("shiny")
runExample("01_hello")

• ui.R defines the page layout and user interface

• server.R contains the R code to create any output

• More information available at Shiny Webpage

About Our Shiny Application

• Interactive web application to display predictive maps and parameter estimates for each SGCN

• Easy to download personalized data and maps

• Available to researchers and managers across Iowa (credentials needed)

• Hosted by CSSM for 1-2 years

• The URL for accessing the application is https://dnrswg.cssm.iastate.edu/