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Karner Blue Butterfly

A guide to the use of distance sampling to estimate abundance


by Ralph Grundel, U.S. Geological Survey, Great Lakes Science Center, Porter, Indiana


Below are the first 8 pages of the Guide. Click here for the complete 30-page Guide (PDF).


This guide is intended to describe the use of distance sampling as a method for evaluating the abundance of Karner blue butterflies at a location.  Other methods for evaluating abundance exist, including mark-release-recapture and index counts derived from Pollard-Yates surveys, for example.  Although this guide is not intended to be a detailed comparison of the pros and cons of each type of method, there are important preliminary considerations to think about before selecting any method for evaluating the abundance of Karner blue butterflies.  These include:


(1) How will monitoring data be used to make management decisions?

  • For the Karner blue butterfly, methods for monitoring adults that yield an absolute population estimate, rather than an index, can help managers assess the risk of Karner blue extinction at a site because the actual population density or abundance is being estimated.  Distance sampling produces an absolute density estimate on a given day and therefore may be useful in this regard.
  • Theoretically, distance sampling, mark-release-recapture, or index methods can be used to assess population trends through time, and these trends can be examined to assess the relationships among habitat change, climate, and population change. However, the ratio of the absolute population size, such as can be estimated by distance sampling, to a population index can vary from day to day.  An index represents an unknown fraction of the total population and this fraction may be different on different days.  Thus, it is not correct to assume that distance sampling and index counts are producing the same results concerning population trends. 
  • The Karner blue butterfly produces two broods of adults between May and August.  Occasionally, adults from the end of the first brood may survive until the start of the second brood but generally little overlap between broods occurs.  Analysis of population trends through time are probably best based on estimates of the total number of butterflies present throughout a single brood, rather than population estimates from one or two days within a brood.  Aaron Ellingson (personal communication) has shown for the Uncompaghre Fritillary that peak numbers are not consistent predictors of brood size.  Nowicki et al. (2005) found the same for several species of European butterflies and concluded, “Taking everything into account it appears that the assumption of a constant proportion of individuals occurring at peak population is unlikely to be ever met in butterfly populations.”
  • Because large confidence intervals can exist around brood estimates, and because Karner blue brood sizes can vary substantially from year to year, it is important to determine before embarking on a monitoring program whether population trend in time can be separated from within-year variation in estimation and between-year variability in actual population size.  This is one reason why it is important to consult with a statistician when establishing a monitoring program and during the course of the program.  Given some preliminary or typical data, a statistician can perform a power analysis that will help address issues such as whether you are likely to be able to discern population trends given background variation.

(2) Are we monitoring the correct thing? 

  • The relative importance of different life stages in determining Karner blue population size is not well established at present.  However, recent work by Steve Fuller may significantly improve our assessment of how production and survival of different life stages (eggs, larvae, pupae) contribute to the overall adult population size (Fuller 2008).  One should ask whether monitoring adults, as is typically done with distance sampling, will meet the objectives of your program.  For instance, should one be monitoring egg or larval density and survivorship instead?
  • Are the habitat monitoring units going to meet your program’s needs?  Rich King (2003), for example, has pointed out that the ability of monitoring data to comment on the effectiveness of habitat management is often compromised by the lack of proper experimental design comparing populations before and after management actions while maintaining proper control sites in which the management action does not occur.

Objectives of a distance sampling program

  • If monitoring adults meets your program’s needs, distance sampling can yield more reliable estimates of population abundance than typical index methods (Brown and Boyce 1998).  Both distance sampling and index methods count butterflies along transects.  Distance sampling adjusts these counts for differences in detectability of butterflies at different distances from the transect line while index methods make no such adjustment.  Because of this adjustment, the end product of a distance sampling survey is an estimate of the actual density of butterflies along the transects.  The end product of the index survey is a count that is assumed to be proportional to the butterfly abundance present in the surveyed area.  However, we rarely know what that proportion is and whether that proportion remains nearly constant from day to day, year to year, and observer to observer.  Therefore, if your monitoring program meets the assumptions of distance sampling, distance sampling can produce an estimate of actual butterfly density rather than an index whose relationship to actual abundance is not well defined. 

Challenges in implementing a distance sampling program include the following.

  • How does a distance sampling program proceed?  A distance sampling program for the Karner blue butterfly might proceed by (1) delimiting the site for which you want to estimate abundance, (2) establishing line transects through the site, (3) walking the transects and recording distances from the transect line to observed Karner blues, (4) using program Distance (Buckland et al. 2001, Thomas et al. 2004) to convert the recorded distances to an estimate of density in the site, and (5) multiplying the density estimate by the area of the site to yield an estimate of the population across the site for the day of the survey. 
  • Ensuring that assumptions of distance sampling are met.  These assumptions include observing all butterflies that occur directly on the transect line and accurately measuring distances from the transect line to butterflies observed away from the line.  Accurately determining which distance category an observed butterfly occurs in relative to the transect line (e.g., a butterfly was observed within 0.5 to 1.0 m from the transect line) is generally sufficient for producing a reliable estimate of density using the distance sampling protocol.
  • Many factors can affect the proportion of the population observed during a survey.  For example, time of day or temperature at the time of survey can affect results (Harker and Shreeve 2008) and should be standardized to the extent possible.
  • Survey design is a challenge for any type of population assessment survey.  A distance sampling program for the Karner blue butterfly might proceed by first delimiting the site for which you want to estimate abundance, as noted above.  Often a tradeoff occurs in defining your site. In scenario 1, the border of a site is drawn, and transects are randomly placed throughout the site, without regard to the suitability of areas for the Karner blue.  For example, you might be interested in knowing how many Karner blues occur in your entire park and you could then simply define the boundary of your survey site as the boundary of your park.  Areas of non-habitat, wetlands, or parking lots, for example, may be surveyed and the number of Karner blues observed per hour might be relatively low.  However, the area of the site is accurately known when it comes time to multiplying area by density to yield Karner blue abundance across the entire site.  In scenario 2, one identifies “good” habitat and places transects only within the “good” habitat and estimates density only for “good” habitat.  More butterflies are likely to be observed per hour surveying.  However, this method assumes that one can accurately identify and map “good’ habitat.  When we multiply density by area to estimate total abundance, we are really estimating total abundance within “good” habitat.  If the Karner blue only occurs in “good” habitat then this estimate will be of the entire population.  If the Karner blue occurs in marginal habitat as well as “good” habitat, the total abundance estimate will be off but the error might be small enough that the added efficiency, and increased Karner blue observations, resulting from surveying from just the “good” habitat, might make this a worthwhile tradeoff.  The tradeoffs between scenario 1 & 2, and within scenario 2, are indicative of difficulties in defining sites and effectively placing transects.  You might consider using a stratified sampling design, where transects would be placed in low, medium, and high quality habitats to obtain a more comprehensive population count.  Different distance sampling analyses might be carried out for each habitat type and the population estimates from each habitat type summed for the total estimate across the entire location.  Good statistical advice is very important at this stage.  Strategic placement of transects can help to reduce the sampling effort.  Information a statistician will need to help you effectively layout transects may include (1) accurate maps of possible survey sites that include information on habitat variation across the sites, (2) preliminary survey results that might inform the statistician of where butterflies occur, (3) a rough estimate of how many butterflies you might expect to encounter along a given survey route, and (4) an explanation of what you hope to accomplish from your surveys. 
  • Distance sampling produces a population or density estimate for a single day but we are often interested in estimating the total number of butterflies present in an entire brood.  Therefore, we will often repeat the distance sampling survey on several days during a brood to produce population estimates for several days within the brood.  
    • If total brood abundance is desired, these daily abundances must be converted into an estimate of total abundance for the brood.  This conversion must take into account the fact that some of the butterflies present on a given day will be adults that newly emerged on that day, some will have survived from a previous day, and some butterflies present on the previous day will not have survived to the current day.  Therefore, if you simply add abundances from two days, you will be double counting some adults.  While methods for estimating total population size are readily available for vertebrate populations in which the entire population is often present on a given day, determining total size of butterfly populations is more challenging when using methods, such as distance sampling, in which individual butterflies are not marked.  This is because butterflies like the Karner blue have short life spans, so the entire brood is not present at a given moment in time and the population estimate on a single day will not equal the total number of butterflies present in a brood.  While methods for estimating butterfly brood size using mark-release-recapture are available (Gall 1985), a standard method for converting daily abundances from distance sampling, or similar methods, into a brood estimate with associated error has not yet been published.  However, some possible approaches have been published or suggested.  If a method is developed, it will likely apply information about survivorship to the data on daily abundances.  Survivorship will allow us to estimate how many butterflies present on a given day were present on a previous day.  Estimates of daily survivorship have been made at several Karner blue locations from mark-release-recapture studies.  Although it is preferable to establish survivorship at each specific location, if this is not feasible, the estimates from these other locations can be used as an approximation, if survivorship rates are to be applied in the brood estimation process.  Another, currently available method for converting daily abundance estimates into brood estimates is through use of INCA (Insect Count Analyzer) software (http://www.urbanwildlands.org/INCA/) (Longcore et al. 2003).  At other sites (e.g., Necedah NWR), abundances from surveys separated by seven days are added together to produce a brood estimate.  Data are likely available for comparisons of these different methods for estimating brood size for the Karner blue.  However, the comparisons have not yet been done.
  • Advantages and disadvantages of distance sampling.  Density estimation using distance sampling helps overcome biases in detection that are not accounted for by typical index methods.  Nonetheless, distance sampling does not avoid all biases in density estimation.  Bart et al. (2004) noted that distance sampling can have problems with incomplete coverage of an area (e.g., butterflies might be hidden by a hill), butterflies fleeing from the observer, inaccurate distance measurement, sampling unrepresentative habitats, insufficient butterfly detections to accurately estimate density, and observer-to-observer variation in detection of butterflies.  In fact, these sources of error might be more problematic when applied to birds than relatively weak fliers such as the Karner blue that are measured within short distances of transects. 
  • Seek statistical advice in setting up a sampling program.  Good statistical advice is especially important in survey design (i.e. where should we place transects, how many transects do we need to achieve a given level of confidence in the population estimate).  It also is useful for the actual density calculations and when considering how to convert daily population estimates to brood size estimates.  Brian Underwood, of the US Geological Survey, has recently developed a model, implemented through an Excel spreadsheet, for estimating the length of transects likely necessary for achieving a given level of error (amount of variation) around a daily population estimate when using distance sampling.  The greater the length of transects surveyed at a site, the more accurate the density estimation is likely to be.  Brian Underwood’s model can help you understand the tradeoff between survey effort and estimation error.
  • Can results from distance sampling surveys be applied to different sites?  The distance sampling calculation involves estimating an “effective strip width” (esw).  Knowing the esw for a transect allows one to convert counts from that transect to an estimated density.  Buckland et al. (2001. p. 53) define esw as follows, “ The parameter μ is often termed the effective strip width, or more strictly, the effective strip half-width; if all objects were detected out to a distance μ on either side of the transect, and none beyond, then the expected number of objects detected would be the same as for the actual survey”.  Although collecting the information on distances from transects to butterflies and then doing the distance calculations adds relatively little time to the process of counting butterflies and processing the results, there is still a question of whether a “universal” esw might exist for the Karner blue, obviating the need to estimate esw for particular sites.  Here is a summary of esw at several Karner blue monitoring sites across its range.  (N.B. These data belong to their respective researchers, so please do not disseminate without their approval).  From these studies, there is about a 6-fold range of estimated esw, suggesting that producing an esw estimate specific to your site is a good idea and that obtaining new esw in each survey year or brood might also be warranted.


The following is a guide to setting up a distance sampling program written for Indiana Dunes National Lakeshore. Some of this information will be specific to Indiana Dunes – survey design, for example, and will need to be modified for other sites. This guide describes data entry using palmtop computers. You may chose to use paper forms or other computer systems and data forms in the field.

At Indiana Dunes, adult Karner blue butterflies (Lycaeides melissa samuelis) were sampled along twenty-five 100-m-long transects. For each butterfly observed, the perpendicular distance to the transect line was recorded. An index of nectar plant abundance was also recorded for each transect line. Note again that the specifics of transect placement, transect length, and transect numbers will likely be different at your particular site. Click here for the complete 30-page Guide (PDF).


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Last updated: April 1, 2014