Estimation of Population Size and Probabilities of Survival and Detection in Mead's Milkweed

Ecology, 84(3), 2003, pp. 791±797 q 2003 by the Ecological Society of America ESTIMATION OF POPULATION SIZE AND PROBABILITIES OF SURVIVAL AND DETECTION IN MEAD'S MILKWEED NORMAN A. SLADE,1,2,4 HELEN M. ALEXANDER,2 AND W. D EAN KETTLE3 1Natural History Museum, 1345 Jayhawk Blvd., University of Kansas, Lawrence, Kansas 66045-7561 USA 2Department of Ecology & Evolutionary Biology, University of Kansas, Lawrence, Kansas 66045-7534 USA 3Kansas Biological Survey, University of Kansas, Lawrence, Kansas 66047-2906 USA Abstract. Statistical similarities exist between estimating numbers of cryptic animals and of inconspicuous plants. Without ¯owers, Mead's milkweed (Asclepias meadii)isan unobtrusive prairie plant, and most plants ¯ower irregularly. We used maximum likelihood to estimate probabilities of survival and detection for milkweeds in annual censuses during 1992±1999. Initially, we assumed no recruitment and ®t models to all data and to ¯owering plants only. Because plants were marked when located, probabilities of resighting exceeded those of initial discovery. Plants were most likely to ¯ower and be detected in years when the prairie was burned. We marked 177 plants in eight years but estimated the 1992 population to be 337 or 191 plants with 166 or 121 surviving to 1999, depending on the data set. Thus, estimated population size exceeded number of plants seen. Estimated annual survival probability was generally $0.95, but aggregate survival over eight years predicted rapid extinction without recruitment. When we included recruitment, estimates of survival changed little, and estimated population size varied between 118 and 147 individuals. Discovery of new plants in two additional years (2000 and 2001) appeared to be consistent with required recruitment, but simple counts of these plants did not track population trends. Key words: Asclepias meadii; capture±recapture; census; estimation of population size; maximum likelihood; Mead's milkweed; probability of detection; survival. INTRODUCTION tures (Shefferson et al. 2001); other examples are dis- cussed in Lesica and Steele (1994). Similarly, the focus Counting or estimating the numbers of individuals of this study, Mead's milkweed (Asclepias meadii Torr. is one of the central tasks of population ecologists. For ex A. Gray), may be undetected in some years either many groups of animals, complete counts are impos- because it does not produce aboveground structures or sible or impractical, and total numbers must be inferred it can exist only as small, non¯owering stems embed- from the number of individuals that are actually seen ded in dense tallgrass prairies (Alexander et al. 1997). or captured over a series of censuses. If the proportion of surviving individuals that have been captured, Recently, ecologists have used capture±recapture anal- marked, and subsequently resighted or recaptured is yses, developed for animals, to estimate population size low (i.e., low detection probability), the estimated pop- and survival rates for such cryptic plants (Alexander ulation size will be much larger than the count at any et al. 1997, Shefferson et al. 2001). single census. A number of methods have been devel- In our previous work (Alexander et al. 1997), we oped to estimate population size based on various sta- used mark±recapture methodology to estimate popu- tistical models and assumptions regarding population lation size for a population of Mead's milkweed in a processes (Pollock et al. 1990). We can treat popula- 4.5-ha area using data from 1992 through 1995. With tions as closed, with no births or deaths occurring; our four-year data set, an assumption of a closed pop- alternatively, they can be open to recruitment and loss. ulation seemed reasonable, because plants had quite Individuals may all be equally likely to be encountered, high rates of survival (96.3% per annum) and low rates or probabilities of detection may vary with time or of reproduction. That paper reported that the estimated among individuals. population size was $50% greater than the total num- Plants have been assumed easier to count than ani- ber of plants that had been marked in four annual cen- mals because plants are stationary. However, many suses. We speculated that, if recruitment were truly plants are dif®cult to detect for a variety of reasons. negligible, continued censuses should reveal more For instance, the small yellow lady's slipper orchid plants but that the total number of marked plants would (Cypripedium calceolus spp. parvi¯orum) may undergo reach an asymptote through time. Our study has con- periods of dormancy when it has no aboveground struc- tinued, making the assumption of no mortality more tenuous. In this paper, we include data from an additional four years (total span of eight years, 1992±1999) Manuscript received 2 January 2002; revised 29 July 2002; accepted 2 August 2002. Corresponding Editor: E. S. Menges. and estimate initial population size (e.g., in the year 4 E-mail: [email protected] 1992) and subsequent rates of decrease using a model 791 792 NORMAN A. SLADE ET AL. Ecology, Vol. 84, No. 3 of variable rates of survival and detection that depend reseeded prairie. The prairie has been mowed and on management treatment. That is, we allow the pop- burned periodically since at least 1930. Most recently, ulation to be open and plants to be lost, but initially it has been burned in March or April of even numbered we retain the assumption of no recruitment to the pop- years, before the emergence of Mead's milkweeds, to ulation, based on low seed production (Kettle et al. discourage the growth and spread of woody plants 2000) and our inability to observe seedlings. We use (Kettle et al. 2000). this model to compare estimates of population size and survival with those from the ®rst four years of study Census (Alexander et al. 1997), and we examine the numbers Annual surveys for individual plants were conducted of newly detected plants for indications that we are from 1992 to the present (see Alexander et al. 1997 reaching an asymptote in total numbers of plants that and Kettle et al. 2000 for details). In early June, ®eld have been discovered. However, the assumption of no crews systematically searched the entire area. Plants recruitment overestimates survival if there actually is were marked with ¯ags when found, and locations were some recruitment. Therefore, we also estimate survival plotted using a preexisting coordinate system. Subse- based solely on the frequency of resightings, which is quent surveys involved intensive search at each loca- independent of estimates of recruitment or population tion where a plant had been found, as well as systematic size. We then estimate the level of recruitment needed search for new plants. Annual surveys were conducted to sustain the population and compare predictions with using consistent methods and sampling intensity; one the numbers of newly discovered plants in 2000 and of us (W. D. Kettle) oversaw all surveys, whereas G. 2001. Finally, we used a model of recruitment and mor- Pittman led the ®eld crews since 1994 and made de- tality to estimate survival and population size simul- cisions regarding identity of individual plants. Despite taneously. intensive search, plants were not seen in every year between their ®rst and last discovery. Hence each in- METHODS dividual plant generated a ``capture history''; that is, each plant was represented by a series of ones and zeros Study organism and site denoting whether it had been seen or not in a particular Mead's milkweed is a clonal perennial of tallgrass year (see the Appendix). prairies in the central United States. These milkweeds Annual survey data were explored in several ways. are long-lived; for example, plants have persisted for First, we examined a plot of cumulative number of decades in mowed hay meadows, where sexual repro- plants discovered over time for evidence of an asymp- duction is prevented by the mowing schedule (Bowles tote. Second, we plotted the total number of plants seen et al. 1998). Betz (1989) suggested that individual in each year, looking for evidence of population per- plants might live for a century or more. Further, there sistence or decline. Third, in our earlier paper (Alex- are low rates of seed production on our 4.5-ha study ander et al. 1997), we were intrigued by whether the area (Kettle et al. 2000). Over an eight-year span, very large number of newly discovered plants in 1994 ,20% of ¯owering plants produced seeds; and, for ®ve (an unusual year in which burning was preceded by of these years, fewer than ®ve follicles (seed pods) were extraordinarily heavy rainfall in 1993; Kettle et al. produced on the entire site. Seedlings may take 15 yr 2000) constituted a subclass of the population that to reach reproductive size (Bowles et al. 2001). Burning ¯owered infrequently. Thus, we compared the subse- seems to increase production of both ¯owers and fol- quent frequency of ¯owering of plants ®rst seen in 1994 licles. Mead's milkweed was once found throughout with those of plants seen in 1994 and before by using Midwestern prairies, but is now federally listed, due x2 and Kruskal-Wallis tests. in part to destruction of habitat (Betz 1989, Bowles et al. 1998). In this paper, we follow Alexander et al. Models (1997) and Kettle et al. (2000) in referring to clusters Because all living plants were not seen in each sur- of stems within 1.25 m as a single plant. At our site, vey, we used statistical methods, originally developed extensive clonal spread does not occur. The maximum for estimating survival and numbers from capture±re- span of a plant was less than 1.7 m, and plants were capture of animals (see Nichols [1992] for an over- usually separated by several meters.

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