Extra information - SST What are detection functions? Distance and detectability What do we need? Line transect Line transects - distances Distance sampling animation When to use each approach? Detection function Distance sampling estimate Detectability and covariates DSM �ow diagram Estimated abundance Reminder of assumptions Fitting detection functions (in R!) Strip transect Count model Horvitz-Thompson-like estimators Including detection information Predictions over an arbitrary area Explicit spatial e�ects Smooth response Hidden in this formula is a simple assumption Chopping up transects Many faces of randomisation E�ort Randomisation & coverage probability Extra information Extra information - depth Detectability matters! Modelling requirements Plot sampling Sperm whales Example data Recap Example data How many animals are there? (500!) Block Island, Rhode Black bears in Alaska Island Heterogeneous spatial 1. Animals are distributed independent of lines H-T equation above assumes even coverage Area of each segment, 2 covariate "levels" in detection function Probability of sampling every point in the study area is Effort is area of each segment Need to "link" data Surveyed 5 lines (each area 1 2 0.025) Model counts or estimated abundance Two options: Account for effort Generally "nicer" to adjust effort We've assumed certain detection so far distribution First offshore wind in the Using the package Distance Once we have how do we get ? 𝑂 ̂ ℙ (detection | animal at distance 𝑦 ) 𝐵 𝑘 ∗ ∗ Don't want to be Hang out near canyons, Have transects equal 𝑞 ̂ USA adjust areas to account for effective effort "Observer"/"observation" -- change within segment Total covered area (or you can estimate) 5 1 (2 0.025) = 0.25 ✅ Distance data/detection function use 2. On the line, detection is certain Estimate H-T abundance per segment This rarely happens in the field Flexible/interpretable effects The effort is accounted for differently Keep response (counts) close to what was observed "Integrate out distance" == "area under curve" == Function ds() does most of the work Rescale the (flat) density and extrapolate restricted to predict on eat squid 𝑏 = ∗ ∗ ∗ 𝐵 𝑘 𝑞 ̂ 𝑞 ̂ 𝑘 Variation in counts and Is this true? Sometimes. Spatial impact segments use Horvitz-Thompson estimates as response "Segment" -- change between segments � Segment data Unless you want observation-level covariates Probability of detection Distance to the object is important Flexible models are good Predictions over an arbitrary area 0.546 Many different forms, depending on the data 3. Distances are recorded correctly More on this in the practical! Surveys in 2004, US east covars along them assessment 💮 effective strip width ( ) 𝑞 ̂ = If (and only if) the design is randomised 𝑡 𝑗 Predict within survey coast 𝜈 ̂ = 𝑥 𝑞 ̂ 𝑜 Incorporate detectability "Count model" only lets us use segment-level covariates Include detectability Detectability should decrease with increasing distance � Observation data (segments 🔘 detections) Saw 76 animals Lecture 1: distance sampling & density surface Lecture 1: distance sampling & density surface All share some characteristics 𝑜 ̂ = study area 𝑡 𝑗 Want a sample unit w/ 𝑘 4. Animals don't move before detection Response is counts per segment area 𝑂 ̂ ∑ 𝑜 = 𝑞 ̂ = Back to regular distance sampling Back to regular distance sampling Why model abundance spatially? Why model abundance spatially? Flexible, interpretable e�ects Flexible, interpretable e�ects Spatial decision making Spatial decision making We should model that! We should model that! Detection information Detection information Accounting for e�ort Accounting for e�ort Data requirements Data requirements Example data Example data Predictions Predictions Maps Maps library (Distance) 𝑗 Thanks to Debi Palka minimal variation 𝑗 covered area ∑ 2 tables + detection function needed Inflate to "Estimated abundance" lets us use either 139.198 𝑞 ̂ df_hn <- ds(distdata, truncation=6000) models models 𝑗 "Adjusting for effort" 𝑗 =1 Extrapolate outside (with (NOAA NEFSC), Lance (where the observations are in segment ) 𝑜 / = 𝑞 ̂ More info on course website. "Segments": chunks of 𝑗 caution) Garrison (NOAA SEFSC) 𝑘 are group/cluster sizes Estimated density 556.8 effort 𝑜 / 𝑞 ̂ ̂ for data. Jason Roberts 𝑡 𝑗 𝐸 = = 𝑏 Working on a grid of cells is the detection probability (from detection function) (Duke University) for data Total area 𝑞 ̂ 𝑗 prep. 𝐵 = 1 Estimated abundance 556.8 𝑂 ̂ ̂ = 𝐸 𝐵 = Credit Scott and Mary Flanders Physeter catodon by Noah Schlottman 45 / 52 44 / 52 52 / 52 51 / 52 50 / 52 49 / 52 47 / 52 48 / 52 48 / 52 11 / 52 45 / 52 10 / 52 46 / 52 13 / 52 12 / 52 29 / 52 14 / 52 34 / 52 36 / 52 35 / 52 15 / 52 30 / 52 21 / 52 34 / 52 33 / 52 26 / 52 22 / 52 32 / 52 23 / 52 24 / 52 25 / 52 31 / 52 27 / 52 37 / 52 37 / 52 19 / 52 43 / 52 16 / 52 42 / 52 28 / 52 41 / 52 17 / 52 18 / 52 31 / 52 38 / 52 28 / 52 40 / 52 20 / 52 39 / 52 39 / 52 2 / 52 2 / 52 1 / 52 5 / 52 3 / 52 3 / 52 4 / 52 5 / 52 6 / 52 7 / 52 7 / 52 8 / 52 9 / 52 1 / 52
Why model abundance spatially? Why model abundance spatially? 2 / 52 2 / 52
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 7 / 52 7 / 52
How many animals are there? (500!) 8 / 52
Plot sampling 9 / 52
Strip transect 10 / 52
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 12 / 52
Line transect 13 / 52
Line transects - distances 14 / 52
Distance sampling animation 15 / 52
Detection function 16 / 52
Distance sampling estimate Surveyed 5 lines (each area 1 2 0.025) ∗ ∗ Total covered area 5 1 (2 0.025) = 0.25 𝑏 = ∗ ∗ ∗ Probability of detection 0.546 𝑞 ̂ = Saw 76 animals 𝑜 = Inflate to 139.198 𝑜 / = 𝑞 ̂ Estimated density 556.8 𝑜 / 𝑞 ̂ ̂ 𝐸 = = 𝑏 Total area 𝐵 = 1 Estimated abundance 556.8 𝑂 ̂ ̂ = 𝐸 𝐵 = 17 / 52
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 18 / 52
What are detection functions? ℙ (detection | animal at distance 𝑦 ) "Integrate out distance" == "area under curve" == 𝑞 ̂ Many different forms, depending on the data All share some characteristics 19 / 52
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) 20 / 52
Horvitz-Thompson-like estimators Once we have how do we get ? 𝑂 ̂ 𝑞 ̂ Rescale the (flat) density and extrapolate 𝑜 study area 𝑡 𝑗 𝑂 ̂ = covered area ∑ 𝑞 ̂ 𝑗 𝑗 =1 are group/cluster sizes 𝑡 𝑗 is the detection probability (from detection function) 𝑞 ̂ 𝑗 21 / 52
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 23 / 52
Randomisation & coverage probability H-T equation above assumes even coverage (or you can estimate) 24 / 52
Extra information 25 / 52
Extra information - depth 26 / 52
Extra information - SST 27 / 52
We should model that! We should model that! 28 / 52 28 / 52
DSM �ow diagram 29 / 52
Modelling requirements Account for effort Flexible/interpretable effects Predictions over an arbitrary area Include detectability 30 / 52
Accounting for e�ort Accounting for e�ort 31 / 52 31 / 52
E�ort Have transects Variation in counts and covars along them Want a sample unit w/ minimal variation "Segments": chunks of effort 32 / 52
Chopping up transects Physeter catodon by Noah Schlottman 33 / 52
Flexible, interpretable e�ects Flexible, interpretable e�ects 34 / 52 34 / 52
Smooth response 35 / 52
Explicit spatial e�ects 36 / 52
Predictions Predictions 37 / 52 37 / 52
Predictions over an arbitrary area Don't want to be restricted to predict on segments Predict within survey area Extrapolate outside (with caution) Working on a grid of cells 38 / 52
Detection information Detection information 39 / 52 39 / 52
Recommend
More recommend
