Why model abundance spatially? Why model abundance spatially?
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Maps Maps
3 / 52 3 / 52 Black bears in Alaska Heterogeneous spatial distribution 4 / 52
Spatial decision making Spatial decision making
5 / 52 5 / 52 Block Island, Rhode Island First offshore wind in the USA Spatial impact assessment 6 / 52
Back to regular distance sampling Back to regular distance sampling
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How many animals are there? (500!)
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Plot sampling
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Strip transect
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Detectability matters!
We've assumed certain detection so far This rarely happens in the field Distance to the object is important Detectability should decrease with increasing distance 11 / 52
Distance and detectability
Credit Scott and Mary Flanders
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Line transect
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Line transects - distances
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Distance sampling animation
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Detection function
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Distance sampling estimate
Surveyed 5 lines (each area 1 2 0.025) Total covered area 5 1 (2 0.025) = 0.25 Probability of detection 0.546 Saw 76 animals Inflate to 139.198 Estimated density 556.8 Total area Estimated abundance 556.8
∗ ∗ 𝑏 = ∗ ∗ ∗ = 𝑞̂ 𝑜 = 𝑜/ = 𝑞̂ = = 𝐸 ̂
𝑜/𝑞̂ 𝑏
𝐵 = 1 = 𝐵 = 𝑂̂ 𝐸 ̂
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Reminder of assumptions
- 1. Animals are distributed independent of lines
- 2. On the line, detection is certain
- 3. Distances are recorded correctly
- 4. Animals don't move before detection
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What are detection functions?
"Integrate out distance" == "area under curve" == Many different forms, depending on the data All share some characteristics
ℙ (detection | animal at distance 𝑦) 𝑞̂
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Fitting detection functions (in R!)
Using the package Distance Function ds() does most of the work More on this in the practical!
library(Distance) df_hn <- ds(distdata, truncation=6000)
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Horvitz-Thompson-like estimators
Once we have how do we get ? Rescale the (flat) density and extrapolate are group/cluster sizes is the detection probability (from detection function)
𝑞̂ 𝑂̂ = 𝑂̂ study area covered area ∑
𝑗=1 𝑜
𝑡𝑗 𝑞̂
𝑗
𝑡𝑗 𝑞̂
𝑗
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Hidden in this formula is a simple assumption
Probability of sampling every point in the study area is equal Is this true? Sometimes. If (and only if) the design is randomised 22 / 52
Many faces of randomisation
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Randomisation & coverage probability
H-T equation above assumes even coverage (or you can estimate) 24 / 52
Extra information
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Extra information - depth
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Extra information - SST
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We should model that! We should model that!
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DSM ow diagram
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Modelling requirements
Account for effort Flexible/interpretable effects Predictions over an arbitrary area Include detectability 30 / 52
Accounting for eort Accounting for eort
31 / 52 31 / 52 Have transects Variation in counts and covars along them Want a sample unit w/ minimal variation "Segments": chunks of effort
Eort
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Chopping up transects
Physeter catodon by Noah Schlottman 33 / 52
Flexible, interpretable eects Flexible, interpretable eects
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Smooth response
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Explicit spatial eects
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Predictions Predictions
37 / 52 37 / 52 Don't want to be restricted to predict on segments Predict within survey area Extrapolate outside (with caution) Working on a grid of cells
Predictions over an arbitrary area
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Detection information Detection information
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Including detection information
Two options: adjust areas to account for effective effort use Horvitz-Thompson estimates as response 40 / 52
Count model
Area of each segment, use 💮 effective strip width ( ) Response is counts per segment "Adjusting for effort"
𝐵𝑘 𝐵𝑘𝑞̂
𝑘
= 𝑥 𝜈̂ 𝑞̂
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Estimated abundance
Effort is area of each segment Estimate H-T abundance per segment (where the observations are in segment )
= 𝑜̂
𝑘
∑
𝑗
𝑡𝑗 𝑞̂
𝑗
𝑗 𝑘
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Detectability and covariates
2 covariate "levels" in detection function "Observer"/"observation" -- change within segment "Segment" -- change between segments "Count model" only lets us use segment-level covariates "Estimated abundance" lets us use either 43 / 52
When to use each approach?
Generally "nicer" to adjust effort Keep response (counts) close to what was observed Unless you want observation-level covariates 44 / 52
Data requirements Data requirements
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What do we need?
Need to "link" data ✅ Distance data/detection function Segment data Observation data (segments 🔘 detections) More info on course website. 46 / 52 47 / 52
Example data Example data
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Example data
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Example data
50 / 52 Hang out near canyons, eat squid Surveys in 2004, US east coast Thanks to Debi Palka (NOAA NEFSC), Lance Garrison (NOAA SEFSC) for data. Jason Roberts (Duke University) for data prep.
Sperm whales
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Recap
Model counts or estimated abundance The effort is accounted for differently Flexible models are good Incorporate detectability 2 tables + detection function needed 52 / 52
Lecture 1: distance sampling & density surface Lecture 1: distance sampling & density surface models models
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