1Distance Estimation of Abundance:Assumptions and Possible Sources of BiasGeneral Approach• Density is homogeneous within the survey area• Some individuals go undetected• Probability of detection is related to distance from the observer• If we can assume all individuals at distance = 0 are detected, we can estimate the proportion that go undetectedDistance Sampling: Point Counts• Homogeneous density– Number in each ring increases due to increased area– Density is the same in each ring2Distance Sampling: Line Transects05101520250 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Distance from observerNumber of individualsDensity Estimation:Perfect Detection#2CountedwL05101520250 1 2 3 4 5 6 7 8 9 10Distance from observerNumber of individualsActualCountedwLine transect#2Abund CountedwL=Point count2#Abund Countedwπ=Abundance Estimation: Imperfect Detection#( )CountedAbundProportionDetected PD=05101520250 1 2 3 4 5 6 7 8 9 10Dis ta nce fr om obs er verNumber of individualsActu alCo un ted00[ ( )][ ( )]wwActual g xPDPerfect g x=∫∫00.20.40.60.810 2 4 6 8 10Distance from observerProbability of detection = g(x)Perfect[g(x)]Actual[g(x)]3Abundance Estimation: Imperfect Detection00[ ( )][ ( )] 1wwActual g x fittedPDPerfect g x w=== ×∫∫0.0000.2000.4000.6000.8001.0000 2 4 6 8 10Distance from observerProbability of detection = g(x)IF Actual[g(0)] = 1 Effects of Behavioral Changes• What if proportion detected changes from year to year?• Under what conditions will estimates be biased?• How does the assumption thatActual[g(0)] = 1 fit in?Hawaiian Akepa00.511.521985 1990 1995 2000 2005 2010YearDensity (Camp et al. in prep.)• Freed et al. suggested increased detectabilityof stressed individuals• Could bias high recent estimates of density405101520250 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Distance from observerActual number of individualsw• Abund = 20 * 11 = 220• No change in true abundance between 2 surveysLine transect#2Abund CountedwL=Assumptions for Detectability ScenariosScenario 1• Increased detection– more singing/calling• Result– more detections within a maximum distance2200.43194Survey 22200.27160Survey 1AbundPDg(0)# counted05101520250 1 2 3 4 5 6 7 8 9 10DistanceNumber countedSurvey 1Survey 29460Scenario 2• Increased detection– more movement– more singing• Result– more detections at further distances2200.501109Survey 22200.27160Survey 1AbundPDg(0)# counted05101520250 1 2 3 4 5 6 7 8 9 10DistanceNumber countedSurvey 1Survey 2109605Scenario 3• Increased detection– more singing/calling• Result– more detections within a maximum distance– increased detection at distance = 005101520250 1 2 3 4 5 6 7 8 9 10DistanceNumber countedSurvey 1Survey 26042Results Scenario 32200.27160Survey 21540.27142Survey 1AbundPDg(0)# countedAssumed2200.27160Survey 22200.190.742Survey 1AbundPDg(0)# countedActualScenario 4• Increased detection– more singing/calling– more movement• Result– more detections– increased detection at distance = 005101520250 1 2 3 4 5 6 7 8 9 10DistanceNumber countedSurvey 1Survey 285426Results Scenario 42200.39185Survey 21540.27142Survey 1AbundPDg(0)# countedAssumed2200.39185Survey 22200.190.742Survey 1AbundPDg(0)# countedActualResults Summary• Estimates are unbiased due to increased detectability IF Actual[g(0)] = 1 for both surveys• Estimates are biased low IF Actual[g(0)] < 1What Does This Mean for Trend Analysis• IF Actual[g(0)] < 1– If probability-of-detection at close distances is constant through time…– If varies but around a constant ‘mean’…– If there is a systematic bias over time…Valid indexValid indexInvalidates trend analyses and must be accounted for7Correcting the Bias• There is a relationship between the true number and the biased estimate IF Actual[g(0)] is KNOWNTrueAbund = EstAbund * 1/ Actual[g(0)] Estimating Actual[g(0)]• Paired observer methods (Kissling and Garton 2006)• Model the probability of detection at close distances based on environmental covariatesKissling, M. L. and E. O. Garton. 2006. Estimating detection probability and densityFrom point-count surveys: a combination of distance and double-observer sampling.The Auk
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