THE SOUTHWESTERN NATURALIST 50(2):223–229 JUNE 2005

TRACK COUNT CALIBRATION TO ESTIMATE DENSITY OFWHITE-TAILED DEER (ODOCOILEUS VIRGINIANUS) IN MEXICAN DRY

TROPICAL FOREST

SALVADOR MANDUJANO*

Departamento de Biodiversidad y Ecologıa Animal, Instituto de Ecologıa A. C., Km 2.5 Carretera Ant. a Coatepec No.351 Congregacion del Haya, Xalapa 91070, Veracruz, Mexico

*Correspondent: mandujan@ecologia.edu.mx

ABSTRACT Track counting is a quick, easy, cost-effective technique to estimate the populationdensity of white-tailed deer (Odocoileus virginianus). By employing the double-count procedure, Igenerated 2 models in which track counts were calibrated to estimate the density of deer in drytropical forest in Chamela on the Mexican Pacific Coast. For both models, I calibrated a trackindex using density obtained from the line-transect method as a reference. The first model wasbased on simple linear regression and the second on the strip-transect method. I discuss theusefulness of these models for monitoring local populations as well as possible applications inother regions.

RESUMEN Contar huellas es una tecnica facil, rapida, y poco costosa para estimar la densidadpoblacional del venado cola blanca (Odocoileus virginianus). Empleando el procedimiento del do-ble conteo, genere 2 modelos en los que se calibra el conteo de huellas para estimar la densidadde venado en el bosque tropical seco de Chamela, en la costa Pacıfica de Mexico. En ambosmodelos, calibre el conteo de huellas usando como referencia la densidad obtenida con el metodode conteo en transectos de lınea. El primer modelo se baso en una regresion lineal simple, y elsegundo en el metodo de transecto de franja. Discuto la utilidad de estos modelos para monitorearpoblaciones locales ası como la posibilidad de aplicaciones en otras regiones.

The double-sampling procedure has beenused to estimate the population density ofmany taxa (Caughley, 1974; Pollock and Ken-dall, 1987; Hone, 1988a). It has, for example,been applied to crocodiles (Bayliss et al.,1986), emu (Caughley and Grice, 1982), andmammals as diverse as kangaroos (Coulsonand Raines, 1985; Barnes et al., 1986; Shortand Hone, 1988), weasels (Graham, 2002),lynx (Andren et al., 2002), feral pigs (Hone,1988b), pronghorn (Firchow et al., 1990), anddeer (Floyd et al., 1979; Bobek et al., 1986; Es-cos and Alados, 1988; White et al., 1989; Fuller,1991; Potvin et al., 2002). Double samplingconsists of 2 phases (Eberhardt and Simmons,1987). During the first phase, 2 independentmethods are applied simultaneously; the den-sity estimate obtained with the first model isconsidered more accurate but costlier to applyin the field, whereas the second yields less re-liable results but is easy and inexpensive. Dur-ing the second phase, the estimate obtained

with the less precise method is fitted to that ofthe more reliable method. If there are paireddata between an abundance index and density,the index can be calibrated with a linear re-gression fit (McCaffery, 1976; Eberhardt, 1978;Hone, 1986; Parer and Price, 1987; Menkes etal., 1990).

It is not easy to select a method of determin-ing density of populations in tropical foreststhat is accurate, easily applied in the field, andinexpensive (Duckworth, 1998; Caro, 1999). Inthe case of white-tailed deer (Odocoileus virgi-nianus), methods used elsewhere ( Jeter, 1965;Jenkins and Marchinton, 1969; Mooty, 1980)are not appropriate, because they are based onassumptions developed with information gen-erated in temperate zones (Mandujano andGallina, 1995). Furthermore, it is difficult tosee deer in tropical forests due to limited visi-bility and to frequent harassment by people.Therefore, the track count might be the bestway to estimate density of deer in tropical for-

224 vol. 50, no. 2The Southwestern Naturalist

ests (Fritzen et al., 1995). Along dirt roads,track counts correlate well with other indicesof population abundance (Mooty et al., 1984).The track count is inexpensive and easy to ap-ply on a large scale ( Jenkins and Marchinton,1969) and can detect up to 20% of variationsin population size (Downing et al., 1965). Oth-er researchers have correlated the number oftracks with the amount of excrement (Mootyet al., 1984), number of deer (Tyson, 1959;Daniel and Frels, 1971; Bobek et al., 1986),and paths made by deer (McCaffery, 1976).The development of a density estimator usingtrack counts requires modeling the relation-ship between the number of animals in thearea, spatial distribution, and the abundanceof tracks (Caughley, 1977). Tyson (1959) andDaniel and Frels (1971) developed models thatconvert track counts to population density.

In a tropical forest, Mandujano and Gallina(1995) compared estimated densities of white-tailed deer obtained with transect-line meth-ods using the Fourier Model to those obtainedwith track counts using the Tyson (1959) Mod-el. The assumptions of the Tyson Model, whichwas developed for temperate habitats wheredeer move more widely than in tropical habi-tats (Sanchez-Rojas et al., 1995), are not satis-fied in tropical forest. Consequently, estimatesderived from the Tyson Model are biased asmuch as 85% more than estimates based onthe Fourier Model (Mandujano and Gallina,1995). Despite the drawback to the Tyson Mod-el, it is an attractive method for estimating den-sity due to the ease with which tracks, as op-posed to the deer themselves, can be countedin the study area. The purpose of this study isto present 2 models for estimating density ofdeer in tropical forests using the track index.Both models were calibrated using the double-sampling procedure. I considered the densityobtained through the line-transect method asmore accurate but also more costly in terms ofsampling effort, and track counts as less accu-rate but easier to apply in the field. I also dis-cuss the possible application of both models inother regions.

METHODS Study Area This research was conduct-ed at the Chamela Biology Station of the Universi-dad Nacional Autonoma de Mexico (UNAM), onthe coast of Jalisco, Mexico (198309N, 1058009W; Fig.1). The Station covers 3,600 ha at an elevation of 30

to 580 m. The mean annual temperature is 258C; thewarmest months are May through September (Bull-ock, 1986). Mean annual rainfall for 1977 through1997 was 748 mm (SD 5 119 mm). The rainy seasonruns from July to October, when 80% of annual rain-fall occurs. The dominant vegetation is dry tropicalforest, located on shallow-soiled slopes. The arborealstratum varies from 4 to 15 m and has a well-devel-oped understory. Numerous species of trees andshrubs lose leaves in the dry season (Lott et al.,1987). Tropical semi-deciduous forest occurs indeep soils of protected areas along major streams,where the arboreal stratum ranges from 10 to 25 m.

Direct Deer Count Method From 5 to 8 permanenttransects were established on dirt roads (Fig. 1) andvaried from 6 to 11 km in length. I walked along theroads (1 to 2 km/h) between 0700 and 1200 h and1600 and 1900 h 2 or 3 times per month. All obser-vations were grouped into 4 classes of perpendiculardistance: 0 to 10 m, 11 to 20 m, 21 to 30 m, and 31to 40 m. I estimated monthly density (D, individu-als/km2) as D 5 nf(0)/2L, where n is the number ofanimals detected, f(0) is the probabilistic functionof density at a perpendicular distance of 0 m, and Lis total transect length (km). To estimate f(0) andthe standard error, I employed the DISTANCE Re-lease 2 program (Thomas et al., 2003). I sampledduring the rainy seasons ( July to November) of 1989and 1990 and during the dry seasons (December toJune) of 1990 and 1991.

Track Count Method I established 12 strip tran-sects 500 3 0.90 m on dirt roads (Fig. 1). No tran-sects were placed in heavy traffic or rocky areas, norwhere 2 roads were close together. One day beforethe track count took place, I swept transects cleanof litter, removing loose dirt to erase old tracks andto permit a clearer impression. After 20 to 24 h, Iobserved the transects between 0700 and 1200 h,repeating the procedure twice during each samplingmonth. When I found tracks, I recorded the follow-ing data: track length and width, distance or stridebetween tracks, and the direction and number ofanimals when .1 series of tracks were found neareach other. To calculate density, I used the TysonModel, modified to metric units: D 5 (n/((t 3 0.5)/1.6))/(2.56), where D is deer density/km2, n the to-tal number of tracks counted, and t the total numberof transects on the 500-m transect. I estimated pop-ulation density for each sampling period. In the fol-lowing 2 models, n/t was used as a track index (IT)to derive a density estimate. Nevertheless, the meth-od of estimating density varied with each model.

Model I This model is based on the equation ob-tained from the simple linear regression model, us-ing the track index as an independent variable andthe density obtained with the line-transect methodas the dependent variable. I paired data obtainedfrom the 4 sampling periods. The linear-regression

June 2005 225Mandujano—Track count calibration estimate

FIG. 1 Location of study area, detailed map of roads used as transects for direct counting, and approx-imate location of 500-m 3 0.90-m transects for track counting (the thick black line on road maps) for white-tailed deer (Odocoileus virginianus) in Jalisco, Mexico. From http://www.ibiologia.unam.mx/ebchamela/HIST2.html.

226 vol. 50, no. 2The Southwestern Naturalist

FIG. 2 Relationship between track index (tracknumber/500 m) and population density (deer/km2)of white-tailed deer (Odocoileus virginianus) in Jalis-co, Mexico, obtained with the line-transect method.Each point on the graph represents a season (rainyor dry) during the 2 years of the study period. Dot-ted lines represent confidence intervals to 95%.

slope was tested using an analysis of variance to as-certain the functional relationship between track in-dex and density. I also estimated confidence inter-vals for the regression coefficient.

Model II Finding fresh deer tracks on the roadimplies that, at a particular time, I had the oppor-tunity to see the animal leaving them. Such a sight-ing could have been from a perpendicular distanceof 0 to 40 m. This strip includes the maximum widthat which I saw deer on line transects. Therefore, forthis model, assuming that I determine the averagenumber of times that an individual crossed the roadover 24 h, the track index can be transformed intopopulation density. This is the model proposed:

n 21 21 2t 3D 5 3 100 (1)

1,000 3 2 3 W1 210,000

where n/t is the track index (IT), 2 to obtain thenumber of tracks/kilometer, and 3 the number oftimes that, on average, a deer crosses the road (Dan-iel and Frels, 1971). The denominator is the surfaceof the strip transect (2Lw, expressed in hectares),where W is transect width. Thus, Equation 1 can beresolved as follows:

333.5D 5 I 3 (2)T W

To estimate density using the track index with thismodel, it is necessary to define the appropriate W.To do this, I substituted various widths (10, 20, 30,and 40 m) into Equation 2 and used a one-way anal-ysis of variance to compare the densities obtained.To determine the appropriate width, I used pairedt-Student tests to compare the estimates obtained us-ing each width against that obtained with the line-transect method. The width at which there was nostatistical difference between Model II and the linetransect was substituted as the calibration factor inEquation 2.

Finally, I applied a one-way analysis of variance todetermine differences in the density estimates ob-tained from the 4 models (transect line, Tyson, Mod-el I, and Model II) and used the Student-Newman-Keuls Test for comparison of means (Zar, 1985).

RESULTS I counted 226 tracks on 82 km(164 transects) and 177 deer on 418 km of linetransects. The track index was 1.32 6 0.25 (SD)tracks/500 m, while the direct index was 0.436 0.07 deer/km. Both indices increased si-multaneously, although the correlation was notsignificant (r2 5 0.87, df 5 3, P 5 0.07). Onthe contrary, there was a correlation betweentrack index (IT) and the density estimated with

line transects (Fig. 2; r2 5 0.90, F 5 18.2, df 51, 2, P 5 0.05). Thus, the regression equationfor Model I that predicted density on the basisof track index was:

D 5 6.0 1 4.5 3 IT (3)

and the standard error of the slope was 1.41 (t5 4.2, n 5 4, P 5 0.05).

The substitution of different widths in Mod-el II resulted in significant differences betweendensity estimates (F 5 34.4, df 5 3, 15, P 50.0001). With an increase in transect width, es-timated density decreased (Table 1, SNK test,P , 0.05). Comparison of these estimates andthe density obtained with line transect showedthat when transect widths of 10 and 20 m wereused, significant differences resulted (t 5 27.5,df 5 6, P 5 0.0003, and t 5 24.6, df 5 6, P 50.004, respectively); in contrast, use of 30-mand 40-m widths produced no differences (t 521.8, df 5 6, P 5 0.12, and t 5 0.75, df 5 6, P5 0.48, respectively). In consequence, when astrip-transect width of 40 m was employed, thedensity estimate was similar to that obtainedwith the line-transect method. Thus, by substi-tuting W 5 40 m in Equation 2, the expressionis reduced as follows:

D 5 8.338 3 IT (4)

Finally, the density obtained with the TysonModel produced the lowest estimate of allmodels (Table 1, F 5 48.4, df 5 6, 27, P 50.00001).

DISCUSSION With the track-count method,6.4 times more deer tracks were recorded per

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TABLE 1—Estimations of population density (D, deer/km2) of white-tailed deer (Odocoileus virginianus) indry tropical forest in Chamela, Mexico, obtained with the line-transect method (DTL), the track-count meth-od using the Tyson Model (DTyson), Model I (DModel I) using linear regression, and Model II (DModel II) basedon the strip-transect method with varying widths (w). P values on the last line indicate the comparison ofdensity as estimated with each model against that estimated with the line-transect method.

Season/year

Methods

DTL DTyson DModel I

DModel II*

w 5 10 m w 5 20 m w 5 30 m w 5 40 m

Rainy/1989Dry/1990Rainy/1990Dry/1991

11.313.310.612.5

1.42.01.31.7

11.913.110.412.6

40.955.635.644.1

20.527.817.822.1

13.618.511.914.7

10.213.98.9

11.0MeanSEP

12.00.6

1.60.2

,0.0001

12.00.60.99

44.14.20.0003

22.12.10.004

14.71.40.12

11.01.10.48

* In Model II, different values of the transect width (w) were substituted in Equation 2.

km than the number of animals observed di-rectly; moreover, the sampling effort was 5times lower with track counting. As reportedby others (such as Daniel and Frels, 1971),track counts had the advantages of minimallydisturbing the population and of obtaining arelatively large sample size. Furthermore, thenumber of tracks was correlated with the esti-mated density obtained with the line-transectmethod, as previously reported by Tyson(1959), Daniel and Frels (1971), McCaffery(1976), Mooty et al. (1984), and Bobek et al.(1986). In addition to supplying data on thenumber of animals, the track-count methodpermits the detection of differences in trackcharacteristics that can indicate age group(fawn or adult) and probably gender (Mc-Cullough, 1965). Tracks can be monitoredduring the rainy season, when soil conditionsyield clearer tracks. For these reasons, thetrack count is an appealing and easily appliedmethod for estimating density of deer in drytropical forest.

The main limitation of the track-count meth-od was that, in this habitat, dirt roads were notlocated randomly. Human activity can causedisturbance that keeps deer away from roads,or, on the contrary, deer can be attracted toroads as foraging sites during certain times ofyear (Harlow and Downing, 1967; Sage et al.,1983; Mooty et al., 1984). Ideally, transectsshould be established randomly for trackcounting, but in tropical forest, this is neithersimple nor economical due to abrupt topo-

graphic changes and dense vegetation. If hu-mans cause little disturbance to deer, anotheroption might be to establish a certain transectlength, divide roads into equal segments, andselect randomly certain segments as transects,as I did in this study. During the rainy season,deer can be seen foraging alongside roads inthis region. However, preliminary data on deerequipped with radiotransmitters (Sanchez-Ro-jas et al., 1997) suggested that activities are notnear roads during all seasons. For this reason,using roads as transects for track counts shouldbe limited as much as possible; it is only advis-able to use forest paths when there is evidencethat doing so does not disturb deer.

Both models derived in this study (Equa-tions 3 and 4) served to monitor populationsof white-tailed deer in the tropical forest ofChamela. Extrapolation to other sites should,however, be considered with caution. To ob-tain the regression equation for other regionswith Model I, it would be necessary first to pairtrack data with a density estimate obtainedwith the line-transect method, and then to cal-ibrate the track count using a robust regressionmodel. Model II (Equation 2) is more widelyapplicable to other tropical dry forests and dif-ferent habitat types because of the use of astrip transect with a defined width. The densityestimate will depend on an adequate defini-tion of transect width; width can be deter-mined using the farthest perpendicular dis-tance at which deer have been observed at thesite in question. Thus, by substituting this

228 vol. 50, no. 2The Southwestern Naturalist

width into Equation 2, the track count can becalibrated to estimate density.

With the double-sampling procedure, 2equations were obtained that resulted fromcalibrating track counts on the basis of thedensity obtained with the line-transect method.Because the density obtained with the line-transect method is not free from possible bias(Mandujano and Gallina, 1995), the applica-tion of any of the models proposed in thisstudy should be done cautiously and not ex-trapolated to other regions indiscriminately. Itwould be interesting to calibrate track countsor fecal group counts, a method widely usedin Mexico to estimate the density of deer(Ezcurra and Gallina, 1981), with estimates ofdensity obtained with more direct methods,such as the identification of individualsthrough DNA (e.g., Kohn et al., 1999; Taberletand Luikart, 1999). One alternative might beto recalibrate the Tyson Model with accuratedata on home range size and daily distancetraveled by deer in tropical zones (Fritzen etal., 1995). It is important to develop and im-prove methods that accurately estimate popu-lation size in tropical regions where deer com-monly are hunted. The double-sampling pro-cedure is appropriate; using 2 methods allowscalibration for extensive monitoring of animalpopulations.

I thank L. E. Martinez-Romero, who aided me insampling, and J. M. Aranda for discussions aboutideas. I also thank S. Gallina and E. Naranjo for sug-gestions about the manuscript. The Station of Biol-ogy ‘‘Chamela’’ of the UNAM granted me all thefacilities to carry out the study. The National Coun-cil of Science and Technology supported the projectfinancially.

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Submitted 4 June 2003. Accepted 23 October 2004.Associate Editor was Cheri A. Jones.