This website supplements the paper:
- Farnsworth1,4, G.L., K.H. Pollock2, J.D. Nichols3, T.R. Simons1, J.E. Hines3 and J.R. Sauer3. 2002. A Removal Model For Estimating Detection Probabilities From Point Count Surveys, Auk 119:414-425.
2Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695;
3U.S. Geological Survey, Biological Resources Division, Patuxent Wildlife Research Center, Laurel, Maryland, 20708.
4current address: Department of Natural Sciences, University of Houston-Downtown, One Main Street, Houston, TX 77002-1014. email: FarnsworthG%40uhd.edu
Abstract.- We adapted a removal model to estimate detection probability during point count surveys. The model assumes that singing frequency is a major factor influencing the probability of detection when birds are surveyed using point counts. This may be appropriate for surveys of forest songbirds, when most detections are by sound. The model requires counts to be divided into several time intervals. Point counts are often conducted for ten minutes, where the number of birds recorded is divided into those first observed in the first three minutes, the subsequent two minutes, and the last five minutes. We developed a maximum-likelihood estimator for the detectability of birds recorded during counts divided into these intervals. This technique can easily be adapted to point counts divided into intervals of any length. We applied this method to unlimited-radius counts conducted in Great Smoky Mountains National Park. We used model selection criteria to identify whether detection probabilities varied among species, throughout the morning, throughout the season, and among different observers. We found differences in detection probability among species. Species that sing frequently such as Winter Wren (Troglodytes troglodytes) and Acadian Flycatcher (Empidonax virescens) had high detection probabilities (about 90%) and species that call infrequently such as Pileated Woodpecker (Dryocopus pileatus) had low detection probability (36%). We also found detection probabilities varied with the time of day for some species (e.g. thrushes) and between observers for other species. We used the same approach to estimate detection probability and density for a subset of the observations with limited-radius point counts. This method offers a promising new approach to using point counts to address questions of detectability, abundance, and density.
Estimating Ovenbird detectability and density using limited-radius counts and first visit to 155 count locations in 1994 (see paper for details). The total number of Ovenbirds counted was x.=209. Of these, x1=141 were detected within the first 3-minutes, x2=29 were first detected within the following 2-minute interval, and x3=39 were first detected within the last interval of 5-minutes.
Online analysis using R code (new):Download R source file here
Online analysis using SURVIV code:For all the following examples of SURVIV code, copy the text and paste it into the textbox on this website:
Use following code to choose between models Mc & M
PROC TITLE 'Model selection: Mc or M'; PROC MODEL NPAR=2; INLINE q=S(1); INLINE c=S(2); COHORT=209; 141:(1.-c*q*q*q)/(1.-c*q*q*q*q*q*q*q*q*q*q); 29:c*q*q*q*(1.-q*q)/(1.-c*q*q*q*q*q*q*q*q*q*q); 39:c*q*q*q*q*q*(1.-q*q*q*q*q)/(1.-c*q*q*q*q*q*q*q*q*q*q); LABELS; S(1)=q; S(2)=c; PROC ESTIMATE NSIG=6 MAXFN=32000 NAME=M_sub_c; INITIAL; S(1)=.5; S(2)=.5; PROC ESTIMATE NOVAR NSIG=6 MAXFN=32000 NAME=Model_M; CONSTRAINTS; S(2)=1; INITIAL; S(1)=.5; PROC TEST; PROC STOP;
Second step is estimation of p-hat:
Use following code to estimate p-hat using model M (appropriate when model_M has minimum AIC value from above analysis):
PROC TITLE '10-minute detection prob (p-hat) using Model M'; PROC MODEL NPAR=1; INLINE q=(1.-S(1))**(1./10.); INLINE c=1.; COHORT=209; 141:(1.-c*q*q*q)/(1.-c*q*q*q*q*q*q*q*q*q*q); 29:c*q*q*q*(1.-q*q)/(1.-c*q*q*q*q*q*q*q*q*q*q); 39:c*q*q*q*q*q*(1.-q*q*q*q*q)/(1.-c*q*q*q*q*q*q*q*q*q*q); LABELS; S(1)=p-hat; PROC ESTIMATE NOVAR NSIG=6 MAXFN=32000 NAME=Model_M; INITIAL; S(1)=.7; PROC STOP;
Use following code to estimate p-hat using model Mc (appropriate when model M_sub_c has minimum AIC value):
PROC TITLE '10-minute detection prob (p-hat) using Model Mc'; PROC MODEL NPAR=2; INLINE q=(S(1))**(1./10.); INLINE c=(1.-S(2))/(q*q*q*q*q*q*q*q*q*q); COHORT=209; 141:(1.-c*q*q*q)/(1.-c*q*q*q*q*q*q*q*q*q*q); 29:c*q*q*q*(1.-q*q)/(1.-c*q*q*q*q*q*q*q*q*q*q); 39:c*q*q*q*q*q*(1.-q*q*q*q*q)/(1.-c*q*q*q*q*q*q*q*q*q*q); LABELS; S(1)=ignore; S(2)=p-hat; PROC ESTIMATE NSIG=6 MAXFN=32000 NAME=M_sub_c; INITIAL; S(1)=.3; S(2)=.8; PROC STOP;
In the above example with Ovenbirds, the appropriate model was Model Mc.
Using the estimated p-hat from this model, we can estimate density and it's associated variance for these 155 points as follows:
^ 2 ^ ^ ^ ^ x. ^ N ^ (x.) VAR(p) (x.)(1-p) N = ----- D = ---- VAR(D) = ----------- + ---------- ^ A ^ ^ p A2 p4 A2 p2where A is the total area sampled. In this example,
p-hat from low-aic model: SE(p-hat):
A = 155 x π(50)2 = 1,217,000m2 = 121HaThe resulting estimates for density and its standard error are:
D-hat = 1.93 singing birds per hectare (SE(D-hat)=0.16)
The resulting estimates for population size and its standard error are:
N-hat = 234.48 singing birds per hectare (SE(N-hat) =19.07)
For more details, see the paper.