Alldredge et al Multiple Species Anal of Point Counts 07 J App Ecol

Journal of Applied Ecology

2007

44

281ndash290

copy 2007 The Authors Journal compilation copy 2007 British Ecological Society

Blackwell Publishing Ltd

Multiple-species analysis of point count data a more parsimonious modelling framework

MATHEW W ALLDREDGEdagger KENNETH H POLLOCKdagger THEODORE R SIMONSdagger and SUSAN A SHRINERDagger

USGS NC Cooperative Fish and Wildlife Research Unit

dagger

Department of Zoology North Carolina State University Raleigh NC 27695 USA and

Dagger

Department of Fish Wildlife and Conservation Biology Colorado State University Fort Collins CO 80523 USA

Summary

1

Although population surveys often provide information on multiple species thesedata are rarely analysed within a multiple-species framework despite the potential formore efficient estimation of population parameters

2

We have developed a multiple-species modelling framework that uses similarities incapturedetection processes among species to model multiple species data more par-simoniously We present examples of this approach applied to distance time of detectionand multiple observer sampling for avian point count data

3

Models that included species as a covariate and individual species effects weregenerally selected as the best models for distance sampling but group models withoutspecies effects performed best for the time of detection and multiple observer methodsPopulation estimates were more precise for no-species-effect models than for species-effectmodels demonstrating the benefits of exploiting speciesrsquo similarities when modellingmultiple species data Partial species-effect models and additive models were also usefulbecause they modelled similarities among species while allowing for species differences

4

Synthesis and applications

We recommend the adoption of multiple-species modellingbecause of its potential for improved population estimates This framework will beparticularly beneficial for modelling count data from rare species because informationon the detection process can be lsquoborrowedrsquo from more common species The multiple-species modelling framework presented here is applicable to a wide range of samplingtechniques and taxa

Key-words

abundance capturendashrecapture multiple-species modelling point countsurveys population surveys


(2007)

44

281ndash290doi 101111j1365-2664200601271x

Introduction

Most animal sampling methods are not species specificMethods such as small mammal trapping (Webb 1965Schwartz amp Whitson 1986 Mengak amp Guynn 1987)mist netting birds (Nur Jones amp Geupel 1999) electrofish-ing (Meador McIntyre amp Pollock 2003) and avianpoint counts (Canterbury

et al

2000 Thompson 2002)all provide information on multiple species Neverthe-less analyses of these types of data aimed at estimatingpopulation parameters are frequently performed at the

individual species level Because the capturedetectionprocess may be very similar among species betterestimates of precision and more parsimonious modelsare possible through analyses that exploit speciesrsquosimilarities Parsimonious models prioritize simplicityand represent a balance between squared bias andvariance (Burnham amp Anderson 2002) We demon-strate the use of multiple-species modelling for single-species parameter estimation with analyses of avian pointcount surveys as an example of a widely applicablemodelling framework

The methods implemented in this paper can also beused to obtain estimates of community abundance inorder to monitor biodiversity In order to carry out suchanalyses the method must be robust to species pooling

Correspondence Mathew W Alldredge Colorado Division ofWildlife 317 W Prospect Fort Collins Colorado 80526 USA(fax 970 472 4457 e-mail matalldredgestatecous)

282

M W Alldredge

et al



44

281ndash290

to avoid bias as a result of differences in detectionprobabilities among species (Buckland

et al

2004)However our focus is on improving single-speciesparameter estimation by lsquosharingrsquo information on thedetection process across species and not community-level parameters

The point count survey method is a general samplingapproach used to estimate relative abundance anddensity of bird populations (Ralph Sauer amp Droege 1995Thompson 2002) Several recent papers have emphasizedthe necessity of understanding the detection processand the limitations of using counts as indexes ofabundance (Nichols

et al

2000 Farnsworth

et al

2002 Rosenstock

et al

2002) This focus on modellingdetectability has resulted in a greater application ofsampling methods that directly estimate detection pro-babilities Currently three distinct methods are availablefor estimating abundance and modelling the detectionprocess from unrepeated point count surveys Firstdistance or point transect methods model the prob-ability of detection as a function of distance from theobserver and estimate the density of populations (Ramseyamp Scott 1979 Reynolds Scott amp Nussbaum 1980Buckland

et al

2001) Secondly multiple-observermethods estimate the probability of detection by eachobserver using a removal (primaryndashsecondary observer)(Nichols

et al

2000) or capturendashrecapture (independentobservers) (Alldredge Pollock amp Simons 2006)modelling framework Distance and multiple-observermethods assume all individuals in a sample area areavailable for detection Thirdly the time of detectionmethod estimates the probability of detection overmultiple time intervals using a first-detection removal(Farnsworth

et al

2002) or a multiple-detection capturendashrecapture framework (Alldredge

et al

2007) Thismethod estimates the combined probability thatan individual is available for detection and that it isdetected given that it is available

The detection process modelled by all three methodsinvolves a bird making itself available for detection andthe ability of observers to detect an available birdIn open habitats such as grasslands detection maybe primarily visual such that availability depends on abird being present and not hidden from view In heavilyvegetated habitats such as forests detections areprimarily auditory (Scott Ramsey amp Kepler 1981) andavailability depends on both a birdrsquos presence and theprobability that the bird sings or calls during a count(Farnsworth

et al

2002) Standard approaches toanalysing these data generally estimate the detectionfunction for each species separately ignoring similaritiesamong species (Ralph Sauer amp Droege 1995) Modelsof the detection process using standard single-speciesapproaches are overparameterized when similaritiesin the detection process exist among species Multiple-species models have fewer model parameters becausethey exploit similarities among species

We present a multiple-species modelling frameworkfor estimating single-species population parameters for

three methods of analysing point count data distancesampling time of detection and multiple observermethods Distance sampling uses recorded distancesfrom the observer to detected individuals to estimatea detection function that describes the probability ofdetecting an individual as a function of distance fromthe observer Time of detection sampling uses a capturendashrecapture approach in which a count is divided intoseveral intervals and observers record whether or notan individual is detected in each interval of the countThe resulting detection history is used to estimate theprobability of detecting an individual in a given timeinterval The multiple observer method also uses acapturendashrecapture framework by using the observationsof independent observers to develop a detection historyfor each individual in the count

We used point count data from primarily forestedhabitats in the Great Smoky Mountains National ParkUSA to classify 19 bird species into six groups based ontruncated maximum detection distance and similaritiesin singing rates If multiple-species models are supportedthey are likely to offer a significant advantage inpopulation studies if more precise population estimatescan be computed For each of the three methods ofanalysing point count data described above we com-pared the number of parameters precision and bias ofmultiple-species and individual-species models

Our approach to incorporating information frommultiple species into models of the detection processinvolved developing species groups based on assumedsimilarities in the detection process among species Oneof the challenges of multiple-species modelling is develop-ing a reasonable set of candidate models particularlywhen the number of species detected or captured is largeModelling all possible combinations of species is notrealistic Our approach is to define biologically reason-able groups of species and examine differences andsimilarities in the detection process within groupsSpecies should be grouped based on similarities in charac-teristics that affect the capture or detection processUnfortunately little is known on how various factorsaffect detection of birds from auditory cues

When birds are detected by ear important componentsof the detection process that can be used to group speciesare sound intensity (energy content of a song) soundpitch (frequency of a song) sound modulation (variationin either sound pitch or intensity Richards 1981) singingrate (Wilson amp Bart 1985 McShea amp Rappole 1997)and typical perching height (eg ground shrub orcanopy) Detection distance may serve as a surrogatefor characteristics that directly affect the distance atwhich a sound can be heard

Methods

Time-of-detection point transects of breeding songbirdswere conducted in the Great Smoky Mountains National

283

Modelling multiple-species count data



44

281ndash290

Park during May and June from 1996 to 1999 (Shriner2001) Survey points were located along low-use hikingtrails with a minimum of 250 m between points Vegeta-tion was closed-canopy deciduous hardwood forestconsequently detections were primarily aural (morethan 95)

All counts were conducted between dawn and 1015in the morning on days with good weather (no rainor excessive wind) Observers were trained and testedin identification and distance estimation prior to con-ducting point counts Counts were conducted for 10-min intervals divided into three observation intervalsthe first 3 min the next two min and the final five min ofthe count The time of initial detection and detectionsin subsequent intervals were recorded Detectiondistance was estimated for all observations and laserrange finders were used to calibrate and verify distanceestimates at each point

Data were limited to observations collected by a singleobserver in 1998 to eliminate temporal and observereffects in the models resulting in a data set of 323survey points We omitted species with fewer than 50observations from the analyses While these surveysallowed for both time of detection and distance analysesthe two data sets were not comparable because the timeof detection analyses were based on observations fromall three time intervals while distance analyses were basedonly on observations from the first 3-min intervalFurther distance sampling does not account for theportion of the population that is not available

Multiple independent observer data were also collectedin the Great Smoky Mountains National Park How-ever these data were collected independently in June1999 and were not comparable with the other datasets Four independent observers participated in eachmultiple observer point count Observers were highlytrained and had been conducting point counts for 6weeks prior to the survey Three minute counts wereconducted at 70 points and followed a protocol similarto that described previously mapping the location ofeach bird detected at a point Each bird was trackedduring the point count to avoid double counting and tosimplify matching observations among observersFollowing each count observers compared their obser-vations to determine the total number of birds detectedand to identify birds detected in common

We used maximum detection distance following 10truncation of the observations at the largest distancesas the first criterion for defining species groups Becausemany characteristics (sound intensity pitch modula-tion etc) can affect maximum detection distance wedefined three general groups (i) species with maximumdetection distance

le

100 m (ii) species with maximumdetection distance gt 100 m and

le

150 m and (iii) specieswith maximum detection distance gt 150 m Within thesegroups species were further grouped based on singing

rate rankings obtained from seven experts familiarwith the species and habitats used for our analysesRanks were based on a scale from one to five with oneindicating the smallest value (presumed lowest pro-bability of detection) and five indicating the highestvalue (presumed highest probability of detection)These ranks were averaged across the seven expertsExperts also ranked sound intensity sound pitch andsound modulation

Model selection was based on Akaikersquos informationcriterion corrected for small sample size (AIC

c

)(Burnham amp Anderson 2002) We report

∆

AICc valueswhich reflect the difference between the AICc value ofa particular model and the model with the lowest AICcvalue The model with a

∆

AICc of zero is the mostparsimonious (best) model and competing models withsubstantial empirical support are generally consideredto be those with

∆

AICc lt 2 (Burnham amp Anderson2002) We also present AIC

c

weights which describethe weight of evidence in favour of a given modelrelative to the set of candidate models (Burnham ampAnderson 2002)

We used the program

(Thomas

et al

20022005) to analyse the distance data with species identi-fication entered as an observation-level variable Thisscheme allowed for two multiple-species analyticalapproaches post stratification by species (Marques

et al

2001 Rosenstock

et al

2002) and the use ofspecies as model covariates (Marques amp Buckland 20032004) We limited these analyses to observations fromthe first 3-min interval truncating the data at 10 ofthe largest observed distances for all analyses asrecommended by Buckland

et al

(2001)We modelled the detection process within species

groups using three candidate models (i) a commondetection function for all species within a group (no specieseffect) (ii) different detection functions for each specieswithin a group (species effect) based on post-stratifyingon species and (iii) a detection function with a commonshape parameter for all species but using species as acovariate to model the scale parameter We tested thefollowing key functions and adjustments for detec-tion functions for the models with and without specieseffects for each species group comparison uniform keyfunction simple polynomial adjustment half-normalkey function cosine adjustment hazard rate key func-tion cosine adjustment

For the covariate models we used both the half-normal and hazard rate key functions with the multiplecovariate distance sampling (MCDS) analysis engineof program

(Thomas

et al

2005) The appro-priate key function and adjustment models were selected

284

M W Alldredge

et al



44

281ndash290

using AIC

c

AIC

c

was subsequently used to choosebetween the species-effect no-species-effect andcovariate models We compared the precision of modelswith and without a species effect using the effectivedetection radii (EDR) and density estimates (D) fromthe distance analysis

Single-species time of detection models are equivalentto closed-population capturendashrecapture models (Otis

et al

1978) that account for variation in detectionprobabilities associated with the length of the samplinginterval differences in the probability of first andsubsequent detections and differences in the detectionprobabilities of individual birds (Alldredge

et al

2007)Zeros in the capture history for this method can repre-sent either a bird that did not sing in a given interval ora bird that sang but was not detected by the observerwhich is why the method models both availability anddetectability We used two-point finite mixture modelsof heterogeneity (Norris amp Pollock 1996 Pledger 2000)to account for individual differences in detection pro-babilities (Alldredge

et al

2007) Finite mixture modelsgroup the surveyed population into a finite number ofgroups based on differences in detection probabilitiesFor example a population may consist of two groupsof birds one group that is easily detected and has highdetection probabilities and another group that is hardto detect and has low detection probabilities These modelsrequire estimation of the proportion of individuals ineach group (

λ

) and the detection probabilities for eachgroup (

p

T

) We used the constrained form of the modelin which detection probabilities for one of the mixturesis equal to one (Farnsworth

et al

2002 Alldredge

et al

2007) While this is a strong assumption and violationmay lead to bias in abundance comparisons across timeor space data sets with only three time intervals areinsufficient to estimate all parameters for an uncon-strained model We recommend future studies usefour or more time intervals to allow estimation of a fulltwo-point mixture model (Alldredge

et al

2007) Thesemodels can take one of three forms heterogeneity onlyheterogeneity and differences between first and sub-sequent detections or heterogeneity and time intervaleffects

There are seven single-species candidate models forthe time of detection method (see Appendix S1 in thesupplementary material) which include models thatincorporate time behaviour and heterogeneity effectsThe multiple-species time of detection method includes20 candidate models based on the seven single-speciesmodels (Alldredge

et al

2007) with or without a specieseffect (see Appendix S1 in the supplementary material)Models with time and species effects can be parame-terized in two ways an interaction effect between timeand species (model ) or an additive effect betweentime and species (model ) The interaction effectmodel is equivalent to a single-species approach with

an equivalent number of parameters The additive modelexploits similarities among species and only requires asingle parameter for each additional species

We also present partial heterogeneity models (models) These models assume detec-

tion probabilities are the same for all species in a groupbut the probability of being in one of the heterogeneitymixtures is not the same for all species within the groupIn other words

p

T

is the same for all species in the groupbut

λ

differs We assume that the biological mechanismunderpinning these models involves a process in whichthe probability of detection is similar among speciesat the same breeding stage but varies among breedingstages Alldredge (2004) describes these models andAppendix S1 (see the supplementary material) lists allthe models and the associated number of parameters

We used the program

(White 1983) to estimatethe detection parameters and two-point mixture heter-ogeneity parameters for the time of detection dataWe assumed an instantaneous rates formulation fordetection probabilities This approach was necessary toparameterize models with no time effect because datawere based on unequal time interval counts (Alldredge

et al

2007) All candidate models were run initially butmodels with both time effects and differences betweenprobabilities of first and subsequent detections wereomitted from further analysis because not allparameters were identifiable

Population estimates and standard errors were derivedfrom the estimated detection probabilities and hetero-geneity parameters (Alldredge

et al

2007) We reportthe probability of detecting an individual at least onceduring a count (

π

T

) the heterogeneity parameter (

7

)and the population estimates (

N

) for the selectedmodel For groups in which a species-effect model wasselected we also report parameters for the alternativeno-species-effect model

Independent observer data were analysed using the fullset of multiple observer models presented in AlldredgePollock amp Simons (2006) because data were collectedusing four observers allowing for full parameter estima-tion Single-species independent observer modelsare equivalent to closed-population capturendashrecapturemodels (Otis

et al

1978) and account for observerdifferences as well as differences in detectability forindividual birds (individual heterogeneity) Followingthis approach a zero in the capture history represents abird that was missed by a given observer but was detectedby at least one other observer In the absence of modelcovariates the independent observer method includesfour single-species candidate models (Alldredge Pollockamp Simons 2006) We used two-point finite mixture models(Norris amp Pollock 1996 Pledger 2000) to model heter-ogeneity in detection probabilities among individualbirds The parameters for this finite-mixture closed-population capturendashrecapture model are the detection

Mtspp

Mtspp+

M M Mhpart

bhpart

thpart and

285




44

281ndash290

probability for each observer (i) and

λ

the proportionof the population in one of the detection probabilitygroup Again the groups represent birds that havedifferent detection probabilities such as high and lowdetection probabilities

Excluding covariate models we obtained 12 candidatemodels for the multiple-species independent observerapproach by adding a species effect to the four single-species candidate models Observer and species effectswere modelled as either an interaction effect (model

) or an additive effect (model ) As abovethe interaction effect model was equivalent to thesingle-species approach The additive effect model usedthe similarities among species as a single parameter foreach species added to the group We also present a partialindividual heterogeneity effect similar to that usedin the time of detection models that allowed detectionprobabilities to remain constant among species but theprobability of being in any particular mixture to varyamong species Alldredge (2004) describes these modelsand Appendix S1 (see the supplementary material) liststhe complete set of models and associated number ofparameters

We used program

(White amp Burnham 1999)with the lsquoHuggins Closed Capturesrsquo and lsquoHuggins FullHeterogeneityrsquo data types to analyse the four-independentobserver count data We report the individual heter-ogeneity parameter estimate (

7

) the observer-specificdetection probabilities and the population estimate(

N

) for the selected model

Results

Nineteen species from the time of detectiondistancedata sets were selected for analysis Three groups weredefined in the

le

100 m category (groups A B and C)two groups in the 100ndash150 m category (groups D and E)and one group in the over 150 m category (group F)based on similarities in singing rates (see Appendix S2in the supplementary material) Group sizes rangedfrom two to four species

Because fewer points were sampled using the multipleobserver method sample sizes were sufficient for onlyeight species Therefore no analysis was done for groupA black-throated blue warbler

Dendroica caerulescens

was omitted from group B and indigo bunting

Passerinacyanea

was omitted from group C Scarlet tanager

Piranga olivacea

(group D) ovenbird

Seiurus aurocapillus

(group E) and tufted titmouse

Baeolophus bicolor

(group F) were combined into a single group DEF

Species-covariate models were selected as the best modelfor three of the six groups (B C and F) and alwayshad some support from the data (AIC

c

weights

ge

0middot12)(Table 1) indicating similarities in the underlying detec-

tion process across species within these groups andthe utility of multiple-species modelling A hazard ratedetection function was selected for groups B and C anda half-normal detection function with a cosine adjust-ment term was selected for group F Species-effect models(equivalent to a single-species approach) were selectedas the best model for two of the groups (A and E) andhad some support from the data (AIC

c

weights

ge

0middot17)for all but group F Uniform detection functions withsimple polynomial adjustment terms were selectedfor both groups A and E The no-species-effect modelwas selected as the best model for group D but had littlesupport from the data (AIC

c

weights

le

0middot03) for all othergroups A uniform detection function with a simplepolynomial adjustment term was selected for group D

Effective detection radii varied within groups exceptgroup D for which the no-species-effect model wasselected (Table 2) Differences in effective detectionradii among species were gt 10 m for all other groupsEstimates of effective detection radii were similarbetween the species-effect and species-covariatemodels but were generally larger for the species-covariate models No assessment of distance measure-ment error was made but measurement errors couldhave been substantial because most detections ofbirds were based on auditory cues with no visualreference

Density estimates for group D were identical for species-effect and no-species-effect models but the standarderrors were smaller for the no-species-effect model(Table 2) The increase in precision was particularlyobvious for the veery

Catharus fuscesens

(0middot018 for thespecies-effect model and 0middot009 for the no-species-effectmodel) which had a smaller observed count Whilespecies with relatively few observations are likely to beassociated with larger gains in precision we emphasizethe need for careful a priori grouping because thesespecies are also at greater risk of undetected biasDensity estimates were similar between the species-covariate models and species-effect models but estimateswere more precise for the species-covariate models

Models accounting for individual heterogeneity indetection probabilities were selected as the most parsi-monious models for all six species groups (Table 3)

Mobsspp Mobs

spp+

Table 1 ∆AICc and AICc weights (in parentheses) for distancemodels using the first 3-min interval of the time of detection data

Species group

No species effect

Species effect

Species covariate

A 6middot01 (0middot03) 0middot00 (0middot64) 1middot32 (0middot33)B 13middot60 (0middot00) 3middot20 (0middot17) 0middot00 (0middot83)C 7middot38 (0middot02) 1middot16 (0middot35) 0middot00 (0middot63)D 0middot00 (0middot62) 1middot76 (0middot26) 3middot29 (0middot12)E 9middot12 (0middot01) 0middot00 (0middot66) 1middot37 (0middot33)F 16middot64 (0middot00) 11middot08 (0middot00) 0middot00 (1middot00)

286

M W Alldredge

et al



44

281ndash290

Time effects were included in models selected for groupsB C E and F Models with differences in detectionprobabilities between first and subsequent detectionswere never selected All models including time effects

and differences between first and subsequent detectionsdid not give realistic estimates of detection probabilities(probabilities gt 1) The global model fit the observeddata and no extra-binomial variation was detected soa variance inflation factor (Burnham

et al

1987) of onewas used for all models

Models with no species effect were selected as themost parsimonious models for groups A and C Partialspecies-effect models were selected for groups D and FTherefore more parsimonious models were obtainedfor the multiple-species approach for groups A C Dand F indicating gains in estimate precision wheninformation on the detection process was sharedacross species The most general model accounting forindividual differences in detection probabilities witha time and species interaction effect was selected forboth groups B and E indicating that species effectswere important for these groups or that our groupingcriteria were not appropriate for these species (modelsequivalent to a single-species approach)

Estimates of the probability that an individual of agiven species or species group (depending on the modelselected) was detected at least once during the 10-minthree-interval count ranged from 0middot81 (group F) to0middot92 (group E) (Table 4) The estimated heterogeneityparameter (probability of being in the first heterogeneitygroup) ranged from 0middot15 to 0middot79 with both estimatesoccurring for species in group F Models that usedcommon parameters among species in a group showedincreased precision for all parameter estimates Thiswas most clearly seen in the increased precision forthe abundance estimates particularly for species withsmaller observed counts (eg the indigo bunting ingroup C) Note that abundance estimates apply only tothe area sampled

Table 2

Distance analysis results for species-effect models and for the selected model based on AIC

c

The observed count is after 10 truncation of thelargest detection distances EDR is the effective detection radius and density is individuals per hectare Standard errors are in parentheses

Group Species ModelObserved count

Species effect Selected model

EDR Density EDR Density

A Acadian flycatcher

Empidonax virescens

Species effect 58 53middot9 (6middot86) 0middot20 (0middot041)Black-and-white warbler

Mniotilta varia

90 43middot5 (1middot63) 0middot47 (0middot072)Golden-crowned kinglet

Regulus satrapa

64 47middot1 (2middot34) 0middot29 (0middot061)Worm-eating warbler

Helmitheros vermivorus

56 46middot9 (3middot14) 0middot25 (0middot056)B Black-throated blue warbler


Species covariate 145 59middot9 (2middot16) 0middot40 (0middot060) 56middot6 (1middot96) 0middot45 (0middot066)Dark-eyed junco

Junco hyemalis

109 49middot2 (2middot75) 0middot44 (0middot080) 58middot4 (2middot30) 0middot31 (0middot051)Hooded warbler

Wilsonia citrina

192 64middot5 (4middot41) 0middot46 (0middot078) 68middot4 (1middot82) 0middot40 (0middot046)Blue-headed vireo

Vireo solitarius

98 52middot8 (4middot88) 0middot35 (0middot079) 58middot7 (2middot44) 0middot28 (0middot044)C Black-throated green warbler

Dendroica virens

Species covariate 273 77middot6 (2middot98) 0middot45 (0middot049) 78middot0 (1middot49) 0middot44 (0middot038)Indigo bunting

Passerina cyanea

40 54middot5 (2middot03) 0middot13 (0middot027) 58middot5 (3middot85) 0middot12 (0middot027)Red-eyed vireo

Vireo olivaceus

270 78middot8 (6middot11) 0middot43 (0middot075) 78middot8 (1middot49) 0middot43 (0middot038)D Scarlet tanager

Piranga olivacea

No species effect 114 70middot6 (1middot85) 0middot23 (0middot029) 70middot1 (1middot51) 0middot23 (0middot025)Veery

Catharus fuscescens

39 69middot0 (2middot54) 0middot08 (0middot018) 0middot08 (0middot009)E Ovenbird Seiurus aurocapillus Species effect 328 72middot3 (1middot69) 0middot62 (0middot061)

Eastern towhee Pipilo erythrophthalmus 54 54middot5 (1middot75) 0middot18 (0middot037)F Red-breasted nuthatch Sitta canadensis Species covariate 30 104middot9 (15middot86) 0middot03 (0middot011) 129middot2 (9middot32) 0middot02 (0middot005)

Tufted titmouse Baeolophus bicolor 79 100middot7 (9middot11) 0middot08 (0middot018) 120middot8 (5middot51) 0middot05 (0middot009)Winter wren Troglodytes troglodytes 80 105middot7 (7middot58) 0middot07 (0middot014) 120middot6 (5middot46) 0middot05 (0middot009)Wood thrush Hylocichla mustelina 135 73middot6 (10middot84) 0middot25 (0middot077) 104middot9 (3middot88) 0middot12 (0middot017)

Table 3 ∆AICc and ∆AICc weights (in parentheses) for time of detection multiple-speciesmodels for unlimited radius plots with 10 truncation of the largest detection distancesSmaller values of ∆AICc indicate more parsimonious models Larger weights indicatemore support for a given model Models with weights ge 0middot20 are in bold for each speciesgroup indicating competing models Models with unrealistic parameter estimates wereomitted (blanks)

Model

Groups

A B C D E F

55middot5 (0middot00) 145 (0middot00) 124 (0middot00) 41middot1 (0middot00) 72middot1 (0middot00) 180 (0middot00)

58middot3 (0middot00) 123 (0middot00) 127 (0middot00) 36middot9 (0middot00) 73middot4 (0middot00) 84middot0 (0middot00)


36middot2 (0middot00) 79middot3 (0middot00) 48middot4 (0middot00) 36middot4 (0middot00) 52middot3 (0middot00) 44middot4 (0middot00)














M00

M spp0

Mt0

Mtspp+

Mtspp

Mb

0

Mbspp

Mtb0

Mtbspp+

Mtbspp

Mh

0

Mhpart

Mhspp

Mbh0

Mbhpart

Mbhspp

Mth0

Mthpart

Mthspp+

Mthspp

287Modelling multiple-species count data

copy 2007 The Authors Journal compilation copy 2007 British Ecological Society Journal of Applied Ecology 44 281ndash290

Heterogeneity models explained the information inthe independent observer data in a more parsimoniousmanner for all three species groups than models notincorporating heterogeneity (Table 5) indicating thatindividuals within a species could be placed in either ahigh- or low-detection probability group The hetero-geneity model with no observer or species effects was

selected for group B and was a reasonable alternativemodel for the other two groups (∆AICc weights ge 0middot22)The heterogeneity model with no observer or specieseffects on probabilities of detection and a partial specieseffect on the heterogeneity parameter was selectedfor group DEF and was also a reasonable alternativemodel for groups B and C (∆AICc weight ge 0middot25) Anindividual heterogeneity model with an observer effecton the probability of detection and no species effectwas selected for group C Again the multiple-speciesapproach provided gains in estimate precision bysharing information across species As with the time ofdetection models a variance inflation factor (Burnhamet al 1987) of one was used for all models because theglobal model fit the observed data with no indicationsof extrabinomial variation

The heterogeneity parameter ranged from 0middot34 to0middot58 for the independent observer model estimates Thedetection probability was generally gt 0middot90 for one ofthe mixtures in the heterogeneity models for all speciesgroups The detection probabilities for the othermixtures were le 0middot36 for all species groups (Table 6)Comparisons of the abundance estimates for the selectedmodel to the abundance estimates for the lsquobestrsquo species-effect model showed very similar estimates but consid-erably smaller standard errors for the selected modelswith no or partial species effects

Discussion

Application of multiple-species models to popula-tion survey data offers a promising approach whenmore than one species occurs in the sample We havedemonstrated that grouping species with similar detec-

Table 5 ∆AICc for the four independent observer multiple-species models for unlimited radius plots with 10 truncationof the largest detection distances ∆AICc weights are inparentheses Models with weights ge 0middot20 are in bold for eachspecies group indicating competing models

Models

Groups

B C DEF

56middot33 (0middot00) 103middot52 (0middot00) 114middot68 (0middot00)










17middot42 (0middot00) 6middot39 (0middot02)


Models did not give realistic estimates Standard errors for detection probabilities were much larger than one

M00

M spp0

Mobs0

Mobsspp+

Mobsspp

Mh0

Mhpart

Mhspp

Mobs h0

Mobs hpart

Mobs hspp

+

Mobs hspp

Table 4 Parameter estimates for the time of detection method for each species The probability that an individual is detected at least once during the countπT the probability of being in the first heterogeneity group 7 and the estimated abundance N are given for the best model and for the best single-speciesmodel The instantaneous rates formulation was used to estimate detection probabilities Standard errors are given in parentheses

Group SpeciesObserved count

Selected model Alternative single-species model

πT 7 N πT 7 N

A Acadian flycatcher 87 0middot89 (0middot049) 0middot58 0middot047) 98 (6middot4) 0middot91 (0middot172) 0middot51 (0middot115) 95 (18middot2)Black-and-white warbler 137 0middot89 (0middot049) 0middot58 (0middot047) 154 (9middot5) 0middot86 (0middot113) 0middot58 (0middot078) 160 (21middot7)Golden-crowned kinglet 82 0middot89 (0middot049) 0middot58 (0middot047) 92 (6middot1) 0middot92 (0middot089) 0middot67 (0middot155) 89 (9middot0)Worm-eating warbler 96 0middot89 (0middot049) 0middot58 (0middot047) 108 (6middot9) 0middot92 (0middot249) 0middot54 (0middot098) 104 (28middot5)

B Black-throated blue warbler 197 0middot90 (0middot094) 0middot48 (0middot081) 220 (23middot6) Same modelDark-eyed junco 189 0middot83 (0middot092) 0middot72 (0middot058) 227 (26middot0)Hooded warbler 274 0middot84 (0middot062) 0middot65 (0middot057) 326 (25middot4)Solitary vireo 148 0middot91 (0middot440) 0middot42 (0middot060) 163 (79middot1)

C Black-throated green warbler 377 0middot89 (0middot053) 0middot53 (0middot035) 424 (26middot2) 0middot9 (0middot066) 0middot55 (0middot057) 419 (31middot5)Indigo bunting 64 0middot89 (0middot053) 0middot53 (0middot035) 72 (5middot2) 0middot93 (0middot505) 0middot55 (0middot092) 69 (37middot6)Red-eyed vireo 397 0middot89 (0middot053) 0middot53 (0middot035) 446 (27middot5) 0middot87 (0middot086) 0middot51 (0middot048) 454 (45middot6)

D Scarlet tanager 161 0middot85 (0middot067) 0middot52 (0middot062) 189 (16middot0) 0middot86 (0middot085) 0middot53 (0middot068) 186 (19middot0)Veery 67 0middot85 (0middot067) 0middot75 (0middot088) 79 (7middot2) 0middot82 (0middot111) 0middot74 (0middot093) 82 (11middot9)

E Ovenbird 444 0middot92 (0middot053) 0middot51 (0middot062) 483 (28middot6) Same modelEastern towhee 79 0middot89 (0middot277) 0middot50 (0middot078) 89 (28middot1)

F Red-breasted nuthatch 54 0middot81 (0middot062) 0middot79 (0middot087) 67 (6middot4) 0middot79 (0middot139) 0middot80 (0middot099) 68 (12middot7)Tufted titmouse 104 0middot81 (0middot062) 0middot78 (0middot068) 128 (11middot2) 0middot77 (0middot093) 0middot78 (0middot068) 135 (17middot4)Winter wren 106 0middot81 (0middot062) 0middot50 (0middot069) 131 (11middot4) 0middot87 (0middot102) 0middot56 (0middot107) 121 (14middot8)Wood thrush 153 0middot81 (0middot062) 0middot15 (0middot047) 188 (15middot9) 0middot85 (0middot331) 0middot13 (0middot047) 180 (70middot4)

288M W Alldredge et al


tion processes results in more parsimonious models andmore precise estimates Evidence from the analysespresented here clearly indicates that in many casessingle-species models are overparameterized and amore efficient use of data is achieved using multiple-species models Estimates from models that lsquosharedrsquoinformation across similar species showed very littlebias relative to single-species models but were generallymuch more precise

Multiple-species analyses allow for direct comparisonsbetween models with and without species effects todetermine whether group-based parameter estimatesare warranted Another approach to multiple-speciesanalyses simply assumes similarities among speciesand analyses similar species as a group This approachhas been used for less common species when observedcounts are not sufficient for a single-species approach(Nichols et al 2000) Our approach actually evaluatessimilarities in detection probability among species andcan provide a justification for this type of analysis

We used both quantitative and qualitative informa-tion to define species groups In general the approachused to define species groups should consider speciesrsquocharacteristics that influence the detection processIn our study the use of maximum detection distanceworked well to categorize species into broad groupsbut it did not allow complete classification of speciesgroups Singing rate information provided a usefulframework for defining species groups within distancecategories Although not used in these analyses classi-fications based on behaviour may also be helpful inassigning a priori species groupings For example inforested habitats it may be appropriate to group birdspecies based on typical singing heights by separatingcanopy species from those that sing closer to the groundMovement behaviour is another potential groupingfactor While each of the methods presented here assumesbirds do not move during the recording period groupingspecies with considerably different movement charac-teristics may cause bias particularly for surveys withlonger recording times

For surveys based on visual observations factors suchas visibility activity patterns size and social behaviourmight be appropriate classification characteristicsDirect measures of characteristics such as singing ratesand song frequencies used to define species groups aredesirable whenever possible

Current knowledge of the detection process andthe effects of various factors is very limited The speciesgroups used in this paper were used to demonstratepossible approaches to grouping species and our know-ledge of factors that may influence detection probabilitiesFuture implementation of the multiple-species approachshould include research to determine which factorsare most important in the detection process andpossibly quantitative measures of these factorsThe limited information available on which charac-teristics affect the detection process led us to usingmaximum detection distance and rankings fromexperts on other characteristics Inappropriategrouping could produce bias in model estimates andreduce the benefits of the multiple-species modellingapproach In situations where detailed informationis not available grouping based on expert knowledgeis a viable approach and worked well for our exampleanalyses

A sequential approach to multiple-species modellingcould also be used where the within-group structure isexamined first and then the between-group structure isanalysed to determine whether groups could be com-bined to improve estimate precision without introduc-ing substantial bias The gains in precision are relativeto the number of individuals in the survey for eachspecies In our examples the number of species in agroup was relatively small because there were severalcommon species with large sample sizes If a surveyconsisted of several species with small sample sizesthen species groups would need to consist of morespecies to obtain similar gains in precision

Models based on distance sampling data generallydid not show as much improvement from sharing infor-mation for multiple species data as observed for the

Table 6 Independent observer results based on the selected model for group B C and DEF The probability of being in the low or high detectability groups is given by 7 and the probability of detection by one of the four observers is given by π1 π2 π3 and π4 The abundance estimate N is given for the selected model and for the selected species-effect model

Group Species Count

Group probability and observer detection probabilities

Nselected Nspecies7 π1 π2 π3 π4

B Dark-eyed junco 36 0middot24 (0middot083) 41 (2middot9) 44 (5middot7)Hooded warbler 38 0middot34 (0middot065) 0middot90 (0middot027) 43 (3middot0) 40 (2middot0)Solitary vireo 51 57 (3middot7) 59 (5middot9)

C Black-throatedGreen warbler 47 0middot40 (0middot057) 0middot20 (0middot091) 0middot13 (0middot070) 0middot19 (0middot072) 0middot11 (0middot051) 59 (5middot4) 60 (7middot2)Red-eyed vireo 72 0middot99 (0middot016) 0middot95 (0middot030) 0middot85 (0middot054) 0middot91 (0middot050) 90 (7middot6) 88 (7middot9)

DEF Ovenbird 90 0middot36 (0middot066) 0middot36 (0middot062) 96 (3middot3) 96 (3middot7)Scarlet Tanager 61 0middot58 (0middot094)

0middot96 (0middot021)68 (3middot6) 70 (5middot6)

Tufted Titmouse 44 0middot44 (0middot097) 48 (2middot4) 48 (3middot3)



other methods Increased precision was demonstratedwhen no-species-effect or species-covariate models wereselected Distance models have few parameters tobegin with so little reduction in the number of param-eters is achieved with the multiple-species approachMultiple-species covariate models (Marques amp Buckland2004) showed slight improvements over no-species-effectmodels Covariate distance models require that the shapeof the detection function is similar among speciesModels with no species effects require similarity inboth the shape and the scale of the detection functionamong species

While our results did not provide as much supportfor multiple-species modelling for distance samplingthis lack of support may be related to the a priori speciesgroupings used for these analyses It is possible thatdifferent characteristics of the detection process areimportant in distance sampling and could prove usefulwhen using a multiple-species approach The distancedata used here were primarily from auditory detectionsof birds which probably has a large distance estima-tion error (M Alldredge et al unpublished data) Thesubstantial error associated with these data may obscurethe benefits of the approach In situations where dis-tances can be estimated accurately the multiple-speciesapproach is likely to provide better gains in precisionover a single-species approach

The multiple-species approach provided more preciseestimates of abundance for both time of detectionand multiple observer methods These methods exploitsimilarities among species in song structure andsinging behaviour and are not as sensitive to differencesin detection distance As these models are closed-population capturendashrecapture models similar benefitsare likely to be realized for capturendashrecapture experi-ments of other taxa

Many sources of variation can cause individualdifferences in animal surveys (Burnham 1981 JohnsonBurnham amp Nichols 1986) Temporal variation in sing-ing rates (Wasserman 1977 Lein 1981) is one potentialsource of these differences Habitat local abundance andproximity to observers have all been shown to affectsinging rates of breeding songbirds (McShea ampRappole 1997) Models incorporating individual dif-ferences among birds were always selected as the mostparsimonious models for our data Further investiga-tion is needed to determine the effect of singing rate ondetection probability and to identify and account forother sources of variation in detection probabilities

The analyses presented were based on surveys wheredetections of birds were auditory and thus our group-ings were based on auditory characteristics likely toaffect the detection process Survey data where animalsare detected visually (open habitat point counts aerialsurveys etc) or are physically captured (mist-nettingsmall mammal trapping electrofishing etc) could alsobe analysed within this multiple-species frameworkGrouping of species for these situations would dependon characteristics directly related to the sampling

methods Groups for visual surveys would be basedon factors affecting visibility such as size colour andactivity Factors affecting the probability of physicalcapture are related to the selectivity of the capturemethods being used

Multiple-species modelling approaches provide moreefficient analyses of multiple species data Becausetwo of the methods presented here are based on closed-population capturendashrecapture models application tosimilar approaches such as CormackndashJolly Seber (Seber1982 Williams Nichols amp Conroy 2002) and tag returnmodels (Brownie et al 1985 Williams Nichols ampConroy 2002) should be similarly beneficial Althoughthe additive models were not selected in the analysespresented here in some cases they were reasonablealternative models Application of additive and partialeffect models for multiple-species analysis should beinvestigated further as they do not require similarityin the detection process among species The use ofcovariates such as detection distance as additive effectsin multiple-species models may also prove useful inexplaining speciesrsquo differences This will be particularlytrue for rare species when sample sizes are limiting Amultiple-species approach allows more precise modelsof rare species because information for parameterestimation can be lsquoborrowedrsquo from similar but morecommon species

Acknowledgements

This project was funded by the US Geological Surveyand the National Park Service Comments from J NicholsC Brownie L Bailey J Gilliam and L Thomas on earlierdrafts were particularly helpful

References

Alldredge MW (2004) Avian point count surveys estimatingcomponents of the detection process PhD DissertationNorth Carolina State University Raleigh NC

Alldredge MW Pollock KH amp Simons TR (2006)Estimating detection probabilities from multiple observerpoint counts Auk 123 1172ndash1182

Alldredge MW Pollock KH Simons TR Collazo JAamp Shriner SA (2007) Time of detection method for esti-mating abundance from point count surveys Auk 124 inpress

American Ornithologistsrsquo Union (1998) Checklist of NorthAmerican Birds 7th ed American Ornithologistsrsquo UnionWashington DC

Brownie C Anderson DR Burnham KP amp Robson DR(1985) Statistical Inference from Band Recovery Data AHandbook 2nd edn Resource Publication 156 US Fishand Wildlife Service Washington DC

Buckland ST Anderson DR Burnham KP Laake JLBorchers DL amp Thomas L (2001) Introduction to DistanceSampling Oxford University Press Oxford UK

Buckland ST Anderson DR Burnham KP Laake JLBorchers DL amp Thomas L (2004) Advanced DistanceSampling Oxford University Press Oxford UK

290

M W Alldredge

et al



44

281ndash290

Burnham KP (1981) Summarizing remarks environmentalinfluences

Estimating Numbers of Terrestrial Birds

(edsCJ Ralph amp JM Scott) pp 324ndash325 Studies in AvianBiology No 6

Burnham KP amp Anderson DR (2002)

Model Selection andMultimodel Inference A Practical Information-TheoreticApproach

Springer-Verlag New York NYBurnham KP Anderson DR White GC Brownie C amp

Pollock KH (1987) Design and analysis methods for fishsurvival experiments based on releasendashrecapture

AmericanFisheries Society Monograph

5

1ndash437Canterbury GE Martin TE Petit DR Petit LJ amp

Bradford DF (2000) Bird communities and habitat asecological indicators of forest condition in regional monitor-ing

Conservation Biology

14

544ndash558Farnsworth GL Pollock KH Nichols JD Simons TR

Hines JE amp Sauer JR (2002) A removal model for estimat-ing detection probabilities from point-count surveys

Auk

119

414ndash425Johnson DH Burnham KP amp Nichols JD (1986) The role

of heterogeneity in animal population dynamics

Proceedingsof the International Biometrics Conference

13

1ndash15Lein MR (1981) Display behavior of ovenbirds (

Seiurusaurocapillus

) II Song variation and singing behavior

Wilson Bulletin

93

21ndash41McShea WJ amp Rappole JH (1997) Variable song rates in

three species of passerines and implications for estimatingbird populations

Journal of Field Ornithology

68

367ndash375Marques FFC amp Buckland ST (2003) Incorporating

covariates into standard line transect analyses

Biometrics

59

924ndash935Marques FFC amp Buckland ST (2004) Covariate models

for the detection function

Advanced Distance Sampling

(eds ST Buckland DR Anderson KP Burnham JLLaake DL Borchers amp L Thomas) pp 31ndash47 OxfordUniversity Press London UK

Marques FFC Buckland ST Goffin D Dixon CEBorchers DL Mayle BA amp Peace AJ (2001) Estimatingdeer abundance from line transect surveys of dung Sika deerin southern Scotland


38

349ndash363Meador MR McIntyre JP amp Pollock KH (2003) Assess-

ing the efficacy of single-pass backpack electrofishing tocharacterize fish community structure

Transactions of theAmerican Fisheries Society

132

39ndash46Mengak MT amp Guynn DC Jr (1987) Pitfalls and snap

traps for sampling small mammals and herpetofauna

American Midland Naturalist

118

284ndash288Nichols JD Hines JE Sauer JR Fallon FW Fallon JE

amp Heglund PJ (2000) A double-observer approach forestimating detection probability and abundance from pointcounts

Auk

117

393ndash408Norris JL amp Pollock KH (1996) Nonparametric MLE under

two closed capturendashrecapture models with heterogeneity

Biometrics

52

639ndash649Nur N Jones SL amp Geupel GR (1999)

A Statistical Guideto Data Analysis of Avian Monitoring Programs

BTP-R6001-1999 US Fish and Wildlife Service Washington DC

Otis DL Burnham KP White GC amp Anderson DR(1978)

Statistical Inference from Capture Data on ClosedAnimal Populations

Wildlife Monographs No 62Pledger S (2000) Unified maximum likelihood estimates for

closed capturendashrecapture models using mixtures

Biometrics

56

434ndash442Ralph JC Sauer JR amp Droege S (1995)

Monitoring BirdPopulations by Point Counts

PSW-GTR-149 US ForestService General Technical Report Albany CA

Ramsey FL amp Scott JM (1979) Estimating populationdensities from variable circular plot surveys

SamplingBiological Population

(eds RM Cormack GP Patil amp

DS Robson) pp 155ndash181 International CooperativePublishing House Fairland MD

Reynolds RT Scott JM amp Nussbaum RA (1980) Avariable circular-plot method for estimating bird numbers

Condor

82

309ndash313Richards DG (1981) Environmental acoustics and censuses

of singing birds

Studies in Avian Biology

6

297ndash300Rosenstock SS Anderson DR Giesen KM Leukering

T amp Carter MF (2002) Landbird counting techniquescurrent practices and an alternative

Auk

119

46ndash53Schwartz OA amp Whitson PD (1986) A 12-year study of

vegetation and mammal succession on a reconstructedtallgrass prairie in Iowa


117

240ndash249

Scott JM Ramsey FL amp Kepler CB (1981) Distanceestimation as a variable in estimating bird numbers fromvocalizations


6

334ndash340Seber GAF (1982)

The Estimation of Animal Abundance andRelated Parameters

2nd edn Edward Arnold London UKShriner SA (2001)

Distribution of breeding birds in GreatSmoky Mountains National Park

PhD Dissertation NorthCarolina State University Raleigh NC

Thomas L Laake JL Strindberg S Marques FFCBuckland ST Borchers DL Anderson DR Burnham KPHedley SL amp Pollard JH (2002)

Distance 4middot0 Release 2Research Unit for Wildlife Population Assessment

Universityof St Andrews St Andrews UK httpwwwruwpast-andacukdistance accessed 3 August 2002

Thomas L Laake JL Strindberg S Marques FFCBuckland ST Borchers DL Anderson DR Burnham KPHedley SL Pollard JH Bishop JRB amp Marques TA(2005)

Distance 5middot0 Release BETA 3 Research Unit forWildlife Population Assessment

University of St AndrewsSt Andrews UK httpwwwruwpast-andacukdistanceaccessed 2 June 2005

Thompson WL (2002) Towards reliable bird surveys accountingfor individuals present but not detected

Auk

119

18ndash25Wasserman FE (1977) Mate attraction function of song in

the white-throated sparrow

Condor

79

125ndash127Webb WL (1965) Small mammal populations on islands

Ecology

46

479ndash488White GC (1983) Numerical estimation of survival rates

from band-recovery and biotelemetry data

Journal of WildlifeManagement

47

716ndash728White GC amp Burnham KP (1999) Program MARK

survival estimation from populations of marked animals

Bird Study

46

S120ndashS139Williams BK Nichols JD amp Conroy MJ (2002)

Analysisand Management of Animal Populations

Academic PressSan Diego CA

Wilson DM amp Bart J (1985) Reliability of singing birdsurveys effects of song phenology during the breedingseason

Condor

87

69ndash73

Received 18 November 2005 final copy received 22 November 2006Editor Jack Lennon

Supplementary material

The following supplementary material is availableas part of the online article (full text) from httpwwwblackwell-synergycom

Appendix S1

Models for the time of detection andmultiple observer methods

Appendix S2

Number of parameters in candidatemodel for the multiple observer method

282

M W Alldredge

et al



44

281ndash290

to avoid bias as a result of differences in detectionprobabilities among species (Buckland

et al

2004)However our focus is on improving single-speciesparameter estimation by lsquosharingrsquo information on thedetection process across species and not community-level parameters

The point count survey method is a general samplingapproach used to estimate relative abundance anddensity of bird populations (Ralph Sauer amp Droege 1995Thompson 2002) Several recent papers have emphasizedthe necessity of understanding the detection processand the limitations of using counts as indexes ofabundance (Nichols

et al

2000 Farnsworth

et al

2002 Rosenstock

et al

2002) This focus on modellingdetectability has resulted in a greater application ofsampling methods that directly estimate detection pro-babilities Currently three distinct methods are availablefor estimating abundance and modelling the detectionprocess from unrepeated point count surveys Firstdistance or point transect methods model the prob-ability of detection as a function of distance from theobserver and estimate the density of populations (Ramseyamp Scott 1979 Reynolds Scott amp Nussbaum 1980Buckland

et al

2001) Secondly multiple-observermethods estimate the probability of detection by eachobserver using a removal (primaryndashsecondary observer)(Nichols

et al

2000) or capturendashrecapture (independentobservers) (Alldredge Pollock amp Simons 2006)modelling framework Distance and multiple-observermethods assume all individuals in a sample area areavailable for detection Thirdly the time of detectionmethod estimates the probability of detection overmultiple time intervals using a first-detection removal(Farnsworth

et al

2002) or a multiple-detection capturendashrecapture framework (Alldredge

et al

2007) Thismethod estimates the combined probability thatan individual is available for detection and that it isdetected given that it is available

The detection process modelled by all three methodsinvolves a bird making itself available for detection andthe ability of observers to detect an available birdIn open habitats such as grasslands detection maybe primarily visual such that availability depends on abird being present and not hidden from view In heavilyvegetated habitats such as forests detections areprimarily auditory (Scott Ramsey amp Kepler 1981) andavailability depends on both a birdrsquos presence and theprobability that the bird sings or calls during a count(Farnsworth

et al

2002) Standard approaches toanalysing these data generally estimate the detectionfunction for each species separately ignoring similaritiesamong species (Ralph Sauer amp Droege 1995) Modelsof the detection process using standard single-speciesapproaches are overparameterized when similaritiesin the detection process exist among species Multiple-species models have fewer model parameters becausethey exploit similarities among species

We present a multiple-species modelling frameworkfor estimating single-species population parameters for

three methods of analysing point count data distancesampling time of detection and multiple observermethods Distance sampling uses recorded distancesfrom the observer to detected individuals to estimatea detection function that describes the probability ofdetecting an individual as a function of distance fromthe observer Time of detection sampling uses a capturendashrecapture approach in which a count is divided intoseveral intervals and observers record whether or notan individual is detected in each interval of the countThe resulting detection history is used to estimate theprobability of detecting an individual in a given timeinterval The multiple observer method also uses acapturendashrecapture framework by using the observationsof independent observers to develop a detection historyfor each individual in the count

We used point count data from primarily forestedhabitats in the Great Smoky Mountains National ParkUSA to classify 19 bird species into six groups based ontruncated maximum detection distance and similaritiesin singing rates If multiple-species models are supportedthey are likely to offer a significant advantage inpopulation studies if more precise population estimatescan be computed For each of the three methods ofanalysing point count data described above we com-pared the number of parameters precision and bias ofmultiple-species and individual-species models

Our approach to incorporating information frommultiple species into models of the detection processinvolved developing species groups based on assumedsimilarities in the detection process among species Oneof the challenges of multiple-species modelling is develop-ing a reasonable set of candidate models particularlywhen the number of species detected or captured is largeModelling all possible combinations of species is notrealistic Our approach is to define biologically reason-able groups of species and examine differences andsimilarities in the detection process within groupsSpecies should be grouped based on similarities in charac-teristics that affect the capture or detection processUnfortunately little is known on how various factorsaffect detection of birds from auditory cues

When birds are detected by ear important componentsof the detection process that can be used to group speciesare sound intensity (energy content of a song) soundpitch (frequency of a song) sound modulation (variationin either sound pitch or intensity Richards 1981) singingrate (Wilson amp Bart 1985 McShea amp Rappole 1997)and typical perching height (eg ground shrub orcanopy) Detection distance may serve as a surrogatefor characteristics that directly affect the distance atwhich a sound can be heard

Methods

Time-of-detection point transects of breeding songbirdswere conducted in the Great Smoky Mountains National

283




44

281ndash290






le


le




c


∆


∆


∆


c


We used the program

(Thomas

et al


et al

2001 Rosenstock

et al


et al




(Thomas

et al


284

M W Alldredge

et al



44

281ndash290

using AIC

c

AIC

c



et al


et al


et al


λ


p

T


et al

2002 Alldredge

et al


et al



et al





p

T


λ


We used the program


et al



et al


π

T


7


N



et al


Mtspp

Mtspp+

M M Mhpart

bhpart

thpart and

285




44

281ndash290


λ




We used program


7


N


Results


le





Passerinacyanea


Piranga olivacea

(group D) ovenbird



Baeolophus bicolor



c

weights

ge



c

weights

ge


c

weights

le




Catharus fuscesens



Mobsspp Mobs

spp+


Species group

No species effect

Species effect

Species covariate


286

M W Alldredge

et al



44

281ndash290



et al




Table 2


c






Empidonax virescens


Mniotilta varia


Regulus satrapa






Junco hyemalis


Wilsonia citrina


Vireo solitarius


Dendroica virens


Passerina cyanea


Vireo olivaceus


Piranga olivacea


Catharus fuscescens





Model

Groups

A B C D E F


















M00

M spp0

Mt0

Mtspp+

Mtspp

Mb

0

Mbspp

Mtb0

Mtbspp+

Mtbspp

Mh

0

Mhpart

Mhspp

Mbh0

Mbhpart

Mbhspp

Mth0

Mthpart

Mthspp+

Mthspp






Discussion



Models

Groups

B C DEF














M00

M spp0

Mobs0

Mobsspp+

Mobsspp

Mh0

Mhpart

Mhspp

Mobs h0

Mobs hpart

Mobs hspp

+

Mobs hspp




πT 7 N πT 7 N

















Group Species Count

















Acknowledgements


References








290

M W Alldredge

et al



44

281ndash290









5




14



Auk

119




13


Seiurusaurocapillus


Wilson Bulletin

93




68



Biometrics

59







38




132




118



Auk

117



Biometrics

52








Biometrics

56









Condor

82


of singing birds


6



Auk

119




117

240ndash249



6













Auk

119



Condor

79


Ecology

46




47



Bird Study

46





Condor

87

69ndash73




Appendix S1


Appendix S2


283




44

281ndash290






le


le




c


∆


∆


∆


c


We used the program

(Thomas

et al


et al

2001 Rosenstock

et al


et al




(Thomas

et al


284

M W Alldredge

et al



44

281ndash290

using AIC

c

AIC

c



et al


et al


et al


λ


p

T


et al

2002 Alldredge

et al


et al



et al





p

T


λ


We used the program


et al



et al


π

T


7


N



et al


Mtspp

Mtspp+

M M Mhpart

bhpart

thpart and

285




44

281ndash290


λ




We used program


7


N


Results


le





Passerinacyanea


Piranga olivacea

(group D) ovenbird



Baeolophus bicolor



c

weights

ge



c

weights

ge


c

weights

le




Catharus fuscesens



Mobsspp Mobs

spp+


Species group

No species effect

Species effect

Species covariate


286

M W Alldredge

et al



44

281ndash290



et al




Table 2


c






Empidonax virescens


Mniotilta varia


Regulus satrapa






Junco hyemalis


Wilsonia citrina


Vireo solitarius


Dendroica virens


Passerina cyanea


Vireo olivaceus


Piranga olivacea


Catharus fuscescens





Model

Groups

A B C D E F


















M00

M spp0

Mt0

Mtspp+

Mtspp

Mb

0

Mbspp

Mtb0

Mtbspp+

Mtbspp

Mh

0

Mhpart

Mhspp

Mbh0

Mbhpart

Mbhspp

Mth0

Mthpart

Mthspp+

Mthspp






Discussion



Models

Groups

B C DEF














M00

M spp0

Mobs0

Mobsspp+

Mobsspp

Mh0

Mhpart

Mhspp

Mobs h0

Mobs hpart

Mobs hspp

+

Mobs hspp




πT 7 N πT 7 N

















Group Species Count

















Acknowledgements


References








290

M W Alldredge

et al



44

281ndash290









5




14



Auk

119




13


Seiurusaurocapillus


Wilson Bulletin

93




68



Biometrics

59







38




132




118



Auk

117



Biometrics

52








Biometrics

56









Condor

82


of singing birds


6



Auk

119




117

240ndash249



6













Auk

119



Condor

79


Ecology

46




47



Bird Study

46





Condor

87

69ndash73




Appendix S1


Appendix S2


284

M W Alldredge

et al



44

281ndash290

using AIC

c

AIC

c



et al


et al


et al


λ


p

T


et al

2002 Alldredge

et al


et al



et al





p

T


λ


We used the program


et al



et al


π

T


7


N



et al


Mtspp

Mtspp+

M M Mhpart

bhpart

thpart and

285




44

281ndash290


λ




We used program


7


N


Results


le





Passerinacyanea


Piranga olivacea

(group D) ovenbird



Baeolophus bicolor



c

weights

ge



c

weights

ge


c

weights

le




Catharus fuscesens



Mobsspp Mobs

spp+


Species group

No species effect

Species effect

Species covariate


286

M W Alldredge

et al



44

281ndash290



et al




Table 2


c






Empidonax virescens


Mniotilta varia


Regulus satrapa






Junco hyemalis


Wilsonia citrina


Vireo solitarius


Dendroica virens


Passerina cyanea


Vireo olivaceus


Piranga olivacea


Catharus fuscescens





Model

Groups

A B C D E F


















M00

M spp0

Mt0

Mtspp+

Mtspp

Mb

0

Mbspp

Mtb0

Mtbspp+

Mtbspp

Mh

0

Mhpart

Mhspp

Mbh0

Mbhpart

Mbhspp

Mth0

Mthpart

Mthspp+

Mthspp






Discussion



Models

Groups

B C DEF














M00

M spp0

Mobs0

Mobsspp+

Mobsspp

Mh0

Mhpart

Mhspp

Mobs h0

Mobs hpart

Mobs hspp

+

Mobs hspp




πT 7 N πT 7 N

















Group Species Count

















Acknowledgements


References








290

M W Alldredge

et al



44

281ndash290









5




14



Auk

119




13


Seiurusaurocapillus


Wilson Bulletin

93




68



Biometrics

59







38




132




118



Auk

117



Biometrics

52








Biometrics

56









Condor

82


of singing birds


6



Auk

119




117

240ndash249



6













Auk

119



Condor

79


Ecology

46




47



Bird Study

46





Condor

87

69ndash73




Appendix S1


Appendix S2


285




44

281ndash290


λ




We used program


7


N


Results


le





Passerinacyanea


Piranga olivacea

(group D) ovenbird



Baeolophus bicolor



c

weights

ge



c

weights

ge


c

weights

le




Catharus fuscesens



Mobsspp Mobs

spp+


Species group

No species effect

Species effect

Species covariate


286

M W Alldredge

et al



44

281ndash290



et al




Table 2


c






Empidonax virescens


Mniotilta varia


Regulus satrapa






Junco hyemalis


Wilsonia citrina


Vireo solitarius


Dendroica virens


Passerina cyanea


Vireo olivaceus


Piranga olivacea


Catharus fuscescens





Model

Groups

A B C D E F


















M00

M spp0

Mt0

Mtspp+

Mtspp

Mb

0

Mbspp

Mtb0

Mtbspp+

Mtbspp

Mh

0

Mhpart

Mhspp

Mbh0

Mbhpart

Mbhspp

Mth0

Mthpart

Mthspp+

Mthspp






Discussion



Models

Groups

B C DEF














M00

M spp0

Mobs0

Mobsspp+

Mobsspp

Mh0

Mhpart

Mhspp

Mobs h0

Mobs hpart

Mobs hspp

+

Mobs hspp




πT 7 N πT 7 N

















Group Species Count

















Acknowledgements


References








290

M W Alldredge

et al



44

281ndash290









5




14



Auk

119




13


Seiurusaurocapillus


Wilson Bulletin

93




68



Biometrics

59







38




132




118



Auk

117



Biometrics

52








Biometrics

56









Condor

82


of singing birds


6



Auk

119




117

240ndash249



6













Auk

119



Condor

79


Ecology

46




47



Bird Study

46





Condor

87

69ndash73




Appendix S1


Appendix S2


286

M W Alldredge

et al



44

281ndash290



et al




Table 2


c






Empidonax virescens


Mniotilta varia


Regulus satrapa






Junco hyemalis


Wilsonia citrina


Vireo solitarius


Dendroica virens


Passerina cyanea


Vireo olivaceus


Piranga olivacea


Catharus fuscescens





Model

Groups

A B C D E F


















M00

M spp0

Mt0

Mtspp+

Mtspp

Mb

0

Mbspp

Mtb0

Mtbspp+

Mtbspp

Mh

0

Mhpart

Mhspp

Mbh0

Mbhpart

Mbhspp

Mth0

Mthpart

Mthspp+

Mthspp






Discussion



Models

Groups

B C DEF














M00

M spp0

Mobs0

Mobsspp+

Mobsspp

Mh0

Mhpart

Mhspp

Mobs h0

Mobs hpart

Mobs hspp

+

Mobs hspp




πT 7 N πT 7 N

















Group Species Count

















Acknowledgements


References








290

M W Alldredge

et al



44

281ndash290









5




14



Auk

119




13


Seiurusaurocapillus


Wilson Bulletin

93




68



Biometrics

59







38




132




118



Auk

117



Biometrics

52








Biometrics

56









Condor

82


of singing birds


6



Auk

119




117

240ndash249



6













Auk

119



Condor

79


Ecology

46




47



Bird Study

46





Condor

87

69ndash73




Appendix S1


Appendix S2







Discussion



Models

Groups

B C DEF














M00

M spp0

Mobs0

Mobsspp+

Mobsspp

Mh0

Mhpart

Mhspp

Mobs h0

Mobs hpart

Mobs hspp

+

Mobs hspp




πT 7 N πT 7 N

















Group Species Count

















Acknowledgements


References








290

M W Alldredge

et al



44

281ndash290









5




14



Auk

119




13


Seiurusaurocapillus


Wilson Bulletin

93




68



Biometrics

59







38




132




118



Auk

117



Biometrics

52








Biometrics

56









Condor

82


of singing birds


6



Auk

119




117

240ndash249



6













Auk

119



Condor

79


Ecology

46




47



Bird Study

46





Condor

87

69ndash73




Appendix S1


Appendix S2












Group Species Count

















Acknowledgements


References








290

M W Alldredge

et al



44

281ndash290









5




14



Auk

119




13


Seiurusaurocapillus


Wilson Bulletin

93




68



Biometrics

59







38




132




118



Auk

117



Biometrics

52








Biometrics

56









Condor

82


of singing birds


6



Auk

119




117

240ndash249



6













Auk

119



Condor

79


Ecology

46




47



Bird Study

46





Condor

87

69ndash73




Appendix S1


Appendix S2











Acknowledgements


References








290

M W Alldredge

et al



44

281ndash290









5




14



Auk

119




13


Seiurusaurocapillus


Wilson Bulletin

93




68



Biometrics

59







38




132




118



Auk

117



Biometrics

52








Biometrics

56









Condor

82


of singing birds


6



Auk

119




117

240ndash249



6













Auk

119



Condor

79


Ecology

46




47



Bird Study

46





Condor

87

69ndash73




Appendix S1


Appendix S2


290

M W Alldredge

et al



44

281ndash290









5




14



Auk

119




13


Seiurusaurocapillus


Wilson Bulletin

93




68



Biometrics

59







38




132




118



Auk

117



Biometrics

52








Biometrics

56









Condor

82


of singing birds


6



Auk

119




117

240ndash249



6













Auk

119



Condor

79


Ecology

46




47



Bird Study

46





Condor

87

69ndash73




Appendix S1


Appendix S2


Documents

Alldredge et al Multiple Species Anal of Point Counts 07 J App Ecol