# Presentation: 623393

## Sample Design

- Michael DeBacker
- and Lloyd Morrison

## Important Underlying Themes of Sample Design:

- Ability to make inferences
- Whether or not to stratify
- Co-location/co-visitation

## We can only sample a very small proportion (often <1%) of most natural areas, but: 
Our job is to protect, restore, understand, and inform others about the entire area, not just some convenient portion of it.
We need to make scientifically defensible inferences to areas beyond the limited sites we sample.
Statistical, design-based inferences can only be made to areas that have a chance of being included in the sample.

- We can only sample a very small proportion (often <1%) of most natural areas, but:
- Our job is to protect, restore, understand, and inform others about the entire area, not just some convenient portion of it.
- We need to make scientifically defensible inferences to areas beyond the limited sites we sample.
- Statistical, design-based inferences can only be made to areas that have a chance of being included in the sample.

## Stratification

- Stratification is a powerful method of decreasing variance among sample sites, but:
- Strata must be carefully chosen in long-term studies, so criteria for strata do not change.
- Multiple protocols may need to use different criteria for stratification.
- Later addition of protocols may not fit within defined strata.
- In general, stratification is not recommended for long-term studies measuring multiple response variables.

## Co-location (Co-visitation)

- Co-location will provide information on multiple vital signs for the same sites.
- Co-visitation will aid overall sampling efficiency, as multiple vital signs can be sampled at the same time.

## Status of an Overall Sampling Framework for the First Twelve Networks

## Summary of Spatial Designs Utilized by the First Twelve Networks

## Example 1: Integrated Terrestrial DesignHeartland Network & Prairie Cluster Prototype 

_**Protocols Spatially Integrated:**_
**Vegetation communities**
**Bird communities**
**Invasive plants**
_**Protocols Temporally Integrated:**_
**None**
_**Strata:**_
** ****soils, slope aspect (vegetation monitoring only)**

**Example 1: Integrated Terrestrial Design****Heartland Network & Prairie Cluster Prototype **

## Monitoring projects are integrated using an underlying grid for multiple purposes  

**Monitoring projects are integrated using an underlying grid for multiple purposes****  **
**Step one: overlay the sample frame with a relatively fine scale grid, the vertices of which create a systematic sample. **

**Notes:**
By sharing a common underlying grid, multiple protocols using different approaches to spatial allocation may maximize co-location of sample sites.  Figure 4-6 illustrates a hypothetical example of superimposing several different survey designs on a single systematic grid.  (While the study unit in Figure 4-6 is simplified for demonstration purposes, the HTLN faces the real challenge of implementing invasive non-native plant, breeding bird, and vegetation community monitoring simultaneously in member parks.)  The example begins by overlaying a relatively fine scale grid (e.g., cell size 100 x 100m) over the study unit (i.e., reference frame).  Vertices of the grid form a pool of potential sample points, and those falling outside the reference frame are removed from consideration.  For invasive non-native plant species monitoring, the HTLN is developing rapid data collection methods to maximize spatial coverage.  In this case, all sample points in the reference frame (i.e., all filled circles) would be utilized in a systematic sample. 
Protocols for monitoring breeding birds utilize a systematic survey design, although at a larger spatial scale (400 x 400m).  In this example, the initial grid would be subsampled to the desired scale as indicated by blue circles.  Initially establishing a relatively fine-scale grid allows
flexibility in scaling up to meet different design requirements.

Finally, vegetation community monitoring methods are time consuming and intensive; therefore, total sample sizes must remain small.  Given relatively small sample sizes and the desire to capture heterogeneity in vegetation communities that reflects underlying differences in soil type and aspect, a stratified random sample is drawn.  In this example, three sample sites are drawn at random from strata A and B with the number of sites per strata proportionate to the area of the strata, creating equal probability for selection.  At points represented by solid red dots, invasive non-native plant species and vegetation community monitoring are co-located. 

## Invasive plant monitoring:

**Invasive plant monitoring:**
**- rapid data collection**
**- maximum spatial coverage**
**- all points in the reference frame are sampled****  **

- Invasive plant species (INP) sample site

## Protocols for monitoring breeding birds utilize a systematic survey design at a larger spatial scale.  In this example, the initial grid would be sub-sampled to the desired scale as indicated by blue circles. 

**Protocols for monitoring breeding birds utilize a systematic survey design at a larger spatial scale.  In this example, the initial grid would be sub-sampled to the desired scale as indicated by blue circles.**** **

- Invasive plant species (INP) sample site
- INP _and_ bird community sample site

## For vegetation community monitoring, the grid vertices form a pool of potential sample sites from which a stratified random sample is drawn.

**For vegetation community monitoring, the grid vertices form a pool of potential sample sites from which a stratified random sample is drawn.**

- Invasive plant species (INP) sample site
- INP and bird community sample site
- INP and vegetation community sample site

**Notes:**
vegetation community monitoring methods are time consuming and intensive; therefore, total sample sizes must remain small.  Given relatively small sample sizes and the desire to capture heterogeneity in vegetation communities that reflects underlying differences in soil type and aspect, a stratified random sample is drawn.  In this example, three sample sites are drawn at random from strata A and B with the number of sites per strata proportionate to the area of the strata, creating equal probability for selection 

## Example 2: Systematic, Unequal Probability Sampling Design

**Northern Colorado Plateau Network (NCPN)**

_**Protocols Spatially Integrated:**_
**Vegetation**
**Soil/Site Stability**
**Hydrologic Function**
**Soil Crust Structure**
**Nutrient Cycling**
_**Protocols Temporally Integrated:**_
**TBD**
_**Probability of site inclusion determined by:**_
**Accessibility**
**“****Ecological Sites”**

## Accessibility Model Example  from Zion National Park

**Accessibility Model Example  from Zion National Park**
**Selection probabilities for sample plots are defined by accessibility (high or low)**

## Selection probabilities for sample plots are also determined by “ecological sites”

**Selection probabilities for sample plots are also determined by “ecological sites”**
**Ecological sites are defined by climate, geology, and soils.**

## Sample grid overlaid on an 

**Sample grid overlaid on an **
**Ecological Site map**
** ****A final sample is drawn from this pool of points utilizing the inclusion probabilities.****  **

## Example 3:  Two Stage Systematic Sampling,  Central Alaska Network (CAKN)

_**Protocols Spatially Integrated:**_
**Vegetation**
**Passerine Birds**
**Snow depth**
_**Protocols Temporally Integrated:**_
**Vegetation and Passerine Birds (~50%)**
_**Strata:**_
**Road corridor at DENA**

## Stage one - a systematic grid, 20 x 20 km

**Stage one - a systematic grid, 20 x 20 km**
**Stage two – a 25 point “mini grid,” 500 x 500 m**

## Benefits of the two-stage systematic grid design:

**effectively samples both regional and meso-scale gradients in resource conditions**

**relies on a sampling frame that is not tied to any preconceived  **
**      ****notions of  how changes in the ecosystem will occur**

**concentrates landscape-scale sampling effort within study areas**

**provides a multiple-scale sampling frame that allows for **
**     “****nesting” of  monitoring efforts that occur at different spatial scales or at different levels of  intensity**

**- access cost per data point is lower **
**- fewer trips into wilderness are required per sample**

**if funding is interrupted prior to completion of the full park-wide sample, partial data set remains a valid network of monitoring sites with interpretable data – and a subset of sites may be continued into the future**

## Temporal Design for Vegetation and Snow Depth Monitoring Projects

## Temporal Design for the Passerine Birds Monitoring Project

- Group A – sites near the main road

- Group B – sites dispersed throughout parks, provides statistical “connectivity”

- Group C – sites dispersed throughout parks, provides broad spatial coverage

**Temporal Design for the Passerine Birds Monitoring Project**

## Example 4:  GRTS Design for Aquatic Resources Monitoring – Heartland Network (HTLN)

_**Protocols Spatially Integrated:**_
**Fish Communities**
**Water Chemistry**
**Aquatic Invertebrates**
**Geomorphology**
**Ozark Hellbender (T&E)**
_**Protocols Temporally Integrated:**_
**Fish, Invertebrates, and Water Chemistry**
_**Strata:**_
**None**

## Ozark National Scenic Riverways Stream Network = 508 KM 

**GRTS: spatially-balanced sample, ****n = 50**

## Slide 24

## Temporal Design for Hellbender, Fish, Geomorphology, and Aquatic Invertebrate Monitoring Projects

**Temporal Design for Hellbender, Fish, Geomorphology, and Aquatic Invertebrate Monitoring Projects**

## Acknowledgments:

- Trent McDonald (West, Inc.),
- Tony Olsen (EPA),
- Paul Geissler (USGS),
- and others.