Ecological Applications, 15(3), 2005, pp. 1036±1052 ᭧ 2005 by the Ecological Society of America

STOCHASTIC AND PRECIPITATION REGIMES AND THE POPULATION DYNAMICS OF A THREATENED FLOODPLAIN

MARIAN SMITH,1,4 HAL CASWELL,2 AND PAIGE METTLER-CHERRY3 1Department of Biological Sciences, Southern University, Edwardsville, Illinois 62026 USA 2Biology Department MS-34, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543 USA 3Department of Biological Sciences, Lindenwood University, St. Charles, 63301 USA

Abstract. decurrens is an endangered plant restricted to the Valley. Its complex life cycle has evolved in response to the dynamics of the historic ¯ood regime, which has changed dramatically in the last century due to the construction of navigation dams and agricultural . To explore the effects of these changes, we de- veloped deterministic and stochastic matrix population models of the demography of Bol- tonia. We used periodic matrix models to incorporate intra-annual seasonal variation. We estimated parameters as a function of the timing of spring ¯ood recession (early or late) and of growing season precipitation (high or low). Late ¯oods and/or low precipitation reduce population growth (␭). Early ¯oods and high precipitation lead to explosive pop- ulation growth. Elasticity analysis shows that changes in ¯oods and precipitation alter the life history pathways responsible for population growth, from annual to biennial and even- tually clonal pathways. We constructed and analyzed a stochastic model in which ¯ood timing and precipitation vary independently, and we computed the stochastic growth rate ␭ ␴2 (log s) and the variance growth rate ( ) as functions of the frequency of late ¯oods and low precipitation. Using historical data on ¯oods and rainfall over the last 100 years, we ␭ found that log s has declined as a result of hydrological changes accompanying the reg- ulation of the river. Stochastic elasticity analysis showed that over that time the contribution ␭ of annual life history pathways to log s has declined as the contributions of biennial and clonal pathways have increased. Over the same time period, ␴2 has increased, in agreement with observations of large ¯uctuations in local B. decurrens populations. Undoubtedly, many plant and animal species evolved in concert with dynamic habitats and are now threatened by anthropogenic changes in those dynamics. The data and analyses used in this study can be applied to management and development strategies to preserve other dynamic systems. Key words: Boltonia decurrens; conservation; elasticity; ¯oodplain; ¯ood regime; LTRE; matrix population model; periodic matrix model; stochastic elasticity; stochastic environment; stochastic matrix model; threatened species.

INTRODUCTION in large river systems are stochastic distur- bances on a massive scale. For example, the 1993 ¯ood All environments are subject to stochastic distur- in the upper system affected a third bances, some more so than others. Species adapt to this of the , lasted for 244 days, and caused stochasticity, often by modi®cations of the life cycle 52 deaths and $18 billion in damages (Changnon 1996). that synchronize biological processes with conditions Between 26 June and 14 September, 5.5 ϫ 107 metric favorable to these processes. These adaptations are not tons of sediment and 1.4 ϫ 1011 m3 of water (enough to a single condition, but to the statistical properties of to cover the states of Missouri and Illinois to a depth the stochastic environment (e.g., the frequency of ®res or ¯oods, the probability distribution of the severity of of 43 cm) passed St. Louis, Missouri (U.S. Army Corps hurricanes, etc.). Therefore, changes in those statistical of Engineers [USACE] 1994). In spite of the intensity properties can have dramatic impacts on populations. of such disturbances, a variety of ancient and endemic In extreme cases, a change in the statistics of a dis- species have evolved to take advantage of the natural turbance regime could render large areas uninhabitable cycle of ¯ooding and have thrived in the Illinois river± for a disturbance-adapted species, without any apparent ¯oodplain system (Sparks 1995, Sparks et al. 1998, change in the landscape. Smith and Mettler 2002). Human activities, however, have caused major changes in the timing and severity of ¯ooding of the Illinois River. In this paper, we use Manuscript received 4 March 2004; revised 29 August 2004; stochastic population models to explore the conse- accepted 13 September 2004; ®nal version received 6 October 2004. Corresponding Editor: C. Nilsson. quences of these changes for the population dynamics 4 E-mail: [email protected] of Boltonia decurrens (Torrey and Gray 1841) Wood 1036 June 2005 POPULATION DYNAMICS OF A FLOODPLAIN PLANT 1037

until the 1930s when the system of agricultural levees and navigation dams was completed (Yaeger 1949, Scarpino 1985, Thompson 1989). In 1988, the U.S. Fish and Wildlife Service placed B. decurrens on the federal list of threatened species; it is currently listed as a ``species of concern'' in Mis- souri (Missouri Department of Conservation 1999) and as threatened in Illinois (Herkert 1991). Although it is the consensus of federal, state, and private conservation agencies that alterations of the ¯ood regime have caused the threatened status of B. decurrens (USFWS 1990, Missouri Department of Conservation 1999, Smith and Mettler 2002), the inference has not been tested until the present study. The species and its habitat Although commonly classi®ed as a perennial, B. de- currens may complete its life cycle as a winter annual, or more rarely, as a facultative biennial (Smith and Mettler 2002; see Plate 1). ¯ower from August through October, and seeds, which mature from Sep- tember to November, exhibit conditional dormancy (Baskin and Baskin 2001). Some seeds germinate in the fall and overwinter as rosettes; others overwinter

PLATE 1. Cluster of ¯ower heads of Boltonia decurrens in a variety of stages of development (fully expanded disk and ray ¯owers, upper right; ray ¯owers senescing, upper left; and maturing seed head, center right). Each ¯ower head produces about 250 disk ¯owers and 50 ray ¯owers, which produce dimorphic seeds. Photo credit: Nancy Parker.

(), a threatened plant of the Illinois River valley. Populations of B. decurrens are restricted to a narrow band of ¯oodplain along the lower Illinois River (U.S. Fish and Wildlife Service [USFWS] 1990) (Fig. 1). The number of populations, which ¯uctuates annually, has declined over the past 100 years (Schwegman and Ny- boer 1985, USFWS 1990, Smith 1995, 2002). In the 19th and early 20th centuries B. decurrens was abun- dant in wet prairies, shallow marshes, and open shores of lakes of the Illinois River (Torrey and Gray 1841, Hus 1908, Turner 1934, 1936). Since the 1970s, it has been collected only from disturbed alluvial ground (Morgan 1980) and open, muddy edges of ¯oodplain forests (Kurz 1981, Schwegman and Nyboer 1985). Although settlers in the late 1800s changed the prairie landscape in Illinois by cultivating the fertile upland FIG. 1. Map of Illinois showing the historical distribution areas (Allen 1870, Nelson et al. 1994), the wetland of Boltonia decurrens (counties shaded in gray); and locks prairies that formed the habitat for B. decurrens were and dams on the Illinois and Mississippi Rivers that control safe from settlement, due to their frequent ¯ooding, the water levels at all B. decurrens sites (black rectangles). 1038 MARIAN SMITH ET AL. Ecological Applications Vol. 15, No. 3 as seeds and produce seedlings the following spring. Summer ¯owering plants may arise from spring-ger- minating seedlings or overwintering rosettes, with large differences in size and seed production. As seeds are forming, senescing plants produce basal rosettes that ¯ower the following season. Regardless of origin (rosette or seedling) or time of germination (fall or spring), all plants die during the season they ¯ower, leaving no overwintering root. Boltonia decurrens' life cycle is intimately linked to the annual regime of ¯ooding. It is a fugitive species (sensu Hutchinson 1951), depending on disturbance to create habitat suitable for colonization and population growth. As we will show, the key to the disturbance process is a ¯ood of appropriate timing early in the year followed by suf®cient rainfall during the growing season later in the year. After such disturbances, B. decurrens colonizes and grows rapidly, dominating the vegetation in the short term. Without subsequent dis- FIG. 2. Daily water-level hydrographs (meters above turbances, the population crashes within three to ®ve mean sea level) from 1880 to 1895 and from 1980 to 1995 years (Schwegman and Nyboer 1985, USFWS 1990, measured at a USACE gage station located in the La Grange Smith et al. 1998). navigation pool, 220.11 km above the con¯uence of the Il- The Illinois River has been modi®ed to control its linois and Mississippi Rivers. hydrology. A series of locks and dams on the Illinois River (Fig. 1) was completed by 1939 with the primary goal of keeping the river navigable for barge traf®c by within a single year (germination of seeds and growth maintaining a 2.7 m navigation channel (Waller 1972, and ¯owering of seedlings) as well as between years Tweet 1984). The locks and dams created a series of (overwintering of seeds and vegetative rosettes). To- navigation pools (the stretch of river impounded by gether, these within-year and between-year processes each navigation structure) in which water levels are determine population growth on a multi-year time manipulated by the U.S. Army Corps of Engineers scale. The periodic matrix model approach to annual (USACE) to maintain the necessary channel depth. A life cycles (Caswell 2001, Section 13.2) was developed network of 54 districts constructed during the for just such cases. early 1900s constricted the river channel, raising water We developed demographic models to explore the depth and increasing the velocity of ¯ow (Thompson interacting effects of two environmental factors: the 1989, Sparks et al. 1998). The combination of water timing of spring ¯ood recession and the amount of level manipulation and channelization has drastically precipitation during the growing season. When ¯ood- altered the historic hydrologic cycle, creating chaotic waters recede late, seed germination is delayed, the ¯ood conditions that shorten the summer growing sea- growing season is shortened, ¯owering plants are son for ¯oodplain plants (Fig. 2). In addition, many smaller, and seed production is reduced. When precip- areas that formerly provided habitat for B. decurrens itation during the growing season is low, the survival are now either isolated from the river, permanently in- and growth of seedlings and rosettes, and the produc- undated, or experience severe ¯ooding during the tion of seeds and rosettes, are reduced. growing season (Sparks 1995, Sparks et al. 1998, Smith As a ®rst approximation to an environment-depen- and Mettler 2002). dent model, we estimated population projection matri- ces for all four combinations of early and late ¯ood Demographic analysis recession and high and low growing season precipi- It is widely believed that the decline in range, num- tation. We refer to these as the condition-speci®c ma- ber of populations, and population size of B. decurrens trices. and other Illinois ¯oodplain species is primarily due With the condition-speci®c matrices, we projected to alteration of the river's hydrology (Schwegman and population growth under (hypothetical) constant en- Nyboer 1985, Nelson et al. 1996, Smith and Mettler vironmental conditions, and used life table response 2002). If this is true, the demography of the species experiment (LTRE) analysis to determine the contri- should vary in response to the characteristics of ¯oods bution of each of the vital rates to the effects of ¯ood and other environmental factors. Thus, we have de- timing and precipitation on population growth. veloped a demographic model for B. decurrens in a Such projections are hypothetical, because real en- dynamic ¯ood and precipitation environment. The life vironments are not constant, so we used the condition- cycle of B. decurrens includes processes operating speci®c matrices to build a stochastic model, charac- June 2005 POPULATION DYNAMICS OF A FLOODPLAIN PLANT 1039

FIG. 3. A seasonal life cycle graph for Bol- tonia decurrens. Each horizontal row represents a season of the year. Each circle represents a stage (SR ϭ small rosette, LR ϭ large rosette, SFP ϭ small ¯owering plant, LFP ϭ large ¯ow- ering plant). Small and large rosettes in the fall (f) may overwinter, and seeds may overwinter and germinate as seedlings in the spring (s). From spring to summer (u), small and large ro- settes may ¯ower, producing large ¯owering plants. Spring seedlings may remain vegetative as small rosettes or may ¯ower. Summer small rosettes, if they survive, remain as small rosettes in the fall. Flowering plants in the summer pro- duce seeds and basal rosettes (small or large) in the fall.

terizing the environment by the frequency of early and given by the left eigenvector v. The stable-stage dis- late ¯oods and high and low precipitation. The results tribution and reproductive value at other phases of the show how the stochastic properties of the environment cycle are given by the eigenvectors of the appropriate

affect the long-term growth rate of B. decurrens and cyclic permutations of the Bi; e.g., those at phase 2 its probability of quasi-extinction. Such stochastic would be obtained from models have been used before, particularly to explore A ϭ BB ´´´B . (2) the consequences of dynamic ®re regimes (Canales et 21p 2 al. 1994, Caswell and Kaye 2001, Satterthwaite et al. The life cycle 2002). We have been able to integrate historical chang- es in the ¯ood and precipitation regime into the sto- We used three phases: fall (the period when seeds chastic model, permitting us to evaluate the hypothesis are formed and vegetative rosettes are produced), that these environmental changes could be responsible spring (the period immediately following ¯ood reces- for the threatened status of B. decurrens. sion when seedlings emerge and fall rosettes resume growth), and summer (the time at which plants bolt and ADEMOGRAPHIC MODEL FOR B. DECURRENS begin ¯owering). We will begin with a seasonal life cycle graph, from At each phase, we classi®ed individuals as seeds, which we construct a periodic matrix model (Caswell seedlings, small rosettes, large rosettes, small ¯owering 2001, Section 13.2). The graph is constructed by choos- plants, or large ¯owering plants. Rosette size was based ing a set of time points, or phases, within the year on diameter at the widest point (small rosettes Ͻ15 cm, (spring, summer, and fall in our case). They need not large rosettes Ն15 cm); all our studies indicated that be evenly spaced. At each phase of the cycle, we choose rosette size is related to survival. size a set of stages into which to classify individuals. The was de®ned by height (small ¯owering plants, Ͻ46 cm; stages need not be the same at each phase. We represent large ¯owering plants, Ն46 cm); plant height is posi- the stages by circles on a horizontal row, one row for tively related to seed production. Boltonia decurrens each phase in the cycle (Fig. 3). The starting point of is a proli®c seed producer (Smith and Keevin 1998), the cycle has no effect on population growth rate, the and up to 15 vegetative ramets can originate from the seasonal cycles of stage distribution and reproductive base of each large senescing plant in the fall (Redmond value, or the sensitivity and elasticity of population 1993, Baker 1997). This reproductive potential, how- growth to the seasonal vital rates. A copy of the ®rst ever, is seldom realized. Seedling establishment is often phase is added at the bottom to complete the cycle. low or lacking entirely, particularly in established pop- Arrows between rows show how stages at one phase ulations (USFWS 1990, Moss 1997, Smith et al. 1998). contribute to the next. In general, the arrows from phase Vegetative rosettes are not produced in years when late ϩ h to phase h 1 de®ne a matrix Bh that projects the summer and fall precipitation is below normal (M. population from phase h to phase h ϩ 1. Smith, unpublished data) or when succession has been Population growth over an annual cycle of p phases, uninterrupted for several years (Schwegman and Ny- starting at phase 1, is given by a periodic product: boer 1985, USFWS 1990, Cochran 2002). Larger ro- settes, whether produced from seedlings or vegetative A ϭ B ´´´BB. (1) 1 p 21 ramets, produce taller plants, more in¯orescences and The population growth rate per cycle is given by the seeds, and suffer lower mortality (Redmond 1993, Bak- ␭ dominant eigenvalue of A1. The stable stage distri- er 1997, Tofari 2000). Although mortality in new seed- bution (at phase 1) is given by the corresponding right lings is signi®cantly higher than in vegetative ramets eigenvector w. The reproductive value distribution is (Baker 1997, Moss 1997), once rosettes have become 1040 MARIAN SMITH ET AL. Ecological Applications Vol. 15, No. 3 established (approximately 4 weeks after germination), tagged plants. Line transects were established by bury- mortality is independent of rosette type (Redmond ing a 46-cm length of metal conduit pipe at each end 1993, Tofari 2000, Cochran 2002). and marking the locations with 2.5-m metal poles cov- Seasonal and annual projections ered in plastic. Rosettes were marked using metal tags attached to 21-cm metal plant stakes, and sampling Seasonal projections are described by matrices Bf plots for seedlings were marked at two corners in the (from fall to spring), Bs (from spring to summer), and same manner. To minimize the loss of metal tags and Bu (from summer to fall). All three annual matrices stakes, tags were inserted level with the soil surface constructed from these seasonal matrices give the same and located using a metal detector. ϭ population growth rates, so we will focus on Af Rosette survival was monitored monthly, provided BuBsBf , which projects from fall in year t to fall in year the site was not ¯ooded, until the individual ¯owered ϩ t 1. and senesced. All seedlings were marked with 9-cm Parameter estimation plastic cocktail picks and survival was monitored Data used in the construction of the projection ma- monthly from germination through the end of the grow- trices were collected from two populations on the Il- ing season. Transects that lost their above ground metal linois River and two populations in the area of con¯u- poles were re-established by using a metal detector to ence with the Mississippi River (Fig. 1). These sites locate the buried conduit pipe. In some years (e.g., encompass approximately 60% of the historical range 1993, 1995, and 1997), ¯ooding was so severe that of B. decurrens (USFWS 1990). many tags and plots were swept away or buried under 1) Rice Lake, Fulton County, Illinois. Three 10-m thick layers of silt. If the plant population survived at transects were established in 1997; two additional tran- the site, transects and plots were re-established along sects were established in 1998; and two more were the original transect lines. When rosettes were plenti- established in 2000 to monitor rosette survival, plant ful, they were tagged following a random number sys- biomass, and in¯orescence production. From 1997 to tem, otherwise every rosette on each transect was 2000, nine 1-m2 plots randomly spaced along the three marked. As rosettes were tagged, the maximum di- original transects were established to monitor seedling ameter of each was measured and the rosette deter- survival. mined to be either a small rosette (SR) or a large rosette 2) Gilbert Lake, Jersey County, Illinois. In August, (LR). When possible, equal numbers of rosettes in each 1994, four 10-m transects were established and rosette size class were tagged at each site. At anthesis, plant survival was monitored through August 1996. In April height was measured and ¯owering plants were as- 1995, four 1-m2 plots were established on a fourth tran- signed to one of two groups: small ¯owering plants sect, and germination and seedling survival were mon- (SFP) or large ¯owering plants (LFP). itored from April through August in 1995 and 1996. We estimated seed production from in¯orescence Three 10-m transects were established in 1997 and ro- number. The number of in¯orescences increases with sette survival was monitored until 2000. From May plant height, but seed number per in¯orescence does through July 1996, nine 25 ϫ 25 cm plots were estab- not (Smith et al. 1993, Moss 1997, Cochran 2002); lished at regular intervals along three new 10-m tran- therefore, we used the average number of in¯ores- sects to monitor germination and seedling survival. cences for each size class, multiplied by seed produc- 3) Horseshoe Lake, Madison County, Illinois. In Au- tion per in¯orescence, to estimate seed production. The gust 1994, eight 1-m2 plots were established along four seed to seedling transition was calculated as the density 10-m transects and rosette survival, height, and in¯o- of seedlings established following ¯ood recession as a rescence production were monitored through August percentage of the estimated seed density in the pre- 1996. Three 10-m transects were established in 1997 ceding fall. and rosette survival, biomass, and in¯orescence pro- To evaluate the possibility of a seed bank, we mea- duction were monitored through 1999. Seed germina- sured germination of seeds from soil cores at two of tion and seedling survival were monitored on 30, 25 our sites. Although Baskin and Baskin (2002) reported ϫ 25 cm plots on three additional transects from No- that ϳ90% of the seeds of B. decurrens unearthed from vember 1998 through August 1999. potted soil in an unheated greenhouse germinated after 4) West Alton, St. Charles County, Missouri. Four- 88 months, we found germination rates of only 0±6% teen 20-m transects were established and monitored in seeds recovered from the soil cores (Redmond 1993; from 1990 to 1992 for rosette and seedling survival, M. Smith, unpublished data). It is not surprising that plant height, and in¯orescence and rosette production. B. decurrens lacks a signi®cant seed bank, even though Seed germination and seedling survival were moni- it lives in a disturbed environment. Light is required tored from March through November 2000 on 36 plots, for germination (Baskin and Baskin 1988, Smith and each 25 ϫ 25 cm, located at regular intervals on nine Keevin 1998) and the disturbance provided by ¯ooding 30-m transects. leaves a thick layer of sediment as ¯ood waters recede, Over the 10 years of this study (1990±2000), sur- rendering a seed bank useless. In addition, seeds of B. vival was followed on more than 5000 individually decurrens have a permeable seed coat and may have June 2005 POPULATION DYNAMICS OF A FLOODPLAIN PLANT 1041

TABLE 1. Values of deterministic population growth rate ␭ from condition-speci®c matrices.

Flood High Low condition precipitation precipitation Averaged Early ¯ood ␭(11) ϭ 5.0313 ␭(12) ϭ 0.240 ␭( j´) ϭ 2.6012 Late ¯ood ␭(21) ϭ 0.5345 ␭(22) ϭ 0.0264 ␭(2´) ϭ 0.2905 Averaged ␭(´i) ϭ 2.3288 ␭(´2) ϭ 0.1246 ␭(´´) ϭ 1.2174 Notes: Superscripts denote environmental conditions: (i, j ) denotes ¯ood condition i and precipitation condition j. Dots indicate growth rates calculated from seasonal matrices averaged over ¯ood or precipitation conditions. little protection against soil microbes. For these rea- whether rainfall during the growing season (June sons, a seed bank was not included in the model. through October) was greater or less than the 100-yr More information on the data utilized in the model average during that period at the nearest weather sta- can be found in a series of theses, papers and agency tion. Because we believe that low precipitation during reports, including the following: seed production of the growing season does not affect environmental con- small and large ¯owering plants (Smith and Keevin ditions during the subsequent winter, we used the same 1998, Tofari 2000, Cochran 2002); seed viability and fall matrix for both high and low precipitation years. germination (Redmond 1993, Moss 1997, Smith and The range of sites used in this study sometimes enabled Keevin 1998); seed dormancy and contribution of the us to collect data on plant survival under different ¯ood seed bank (Redmond 1993, Baskin and Baskin 2002); and precipitation regimes within a single year. transition of small and large rosettes to small and large ¯owering plants (Tofari 2000, Cochran 2002; J. BASIC DEMOGRAPHIC ANALYSES Brooks, unpublished data); seedling survival (Red- The condition-speci®c matrices characterize the re- mond 1993, Moss 1997, Mettler-Cherry 2004); and sur- sponse of B. decurrens to ¯ood and precipitation con- vival of small and large ¯owering plants and the num- ditions, following the standard logic of population pro- ber of basal rosettes produced by each (Redmond 1993, jection (Key®tz 1972, Caswell 2001). That is, analysis Baker 1997, Tofari 2000). of the matrix for, say, early ¯ood and high precipitation Following the fate of marked individuals is a stan- projects what would happen if early ¯ood and high dard technique in plant ecology, but in our case it was precipitation conditions occurred every year. Since challenging due to the sheer magnitude of ¯ood dis- they do not, this projection cannot forecast future turbances. In the 1993 ¯ood, levees were breached in growth; rather it is a way to characterize the effects of many areas, including our West Alton site. The re- the environment on B. decurrens. Such projections are sulting uncontrolled ¯ooding left scour holes 15±21 m essential for interpreting stochastic models that include deep and up to 0.8 km wide (USACE 1994). Tons of environmental variability. The seasonal matrices on sand and silt were deposited in areas beyond the broken which the analyses are based are available in the Ap- levee, covering tagged plants and seedling plots with pendix. layers up to 46 cm deep. Flooding on the upper Illinois Population growth rate and structure River was even more severe in 1995 and 1997 than in 1993, and many levees were breached or overtopped. We use superscripts to denote environmental con- To minimize our losses, we established transects and ditions, so that A(ij) is the projection matrix, and ␭(ij) sampling plots at several widely separated population the population growth rate, under ¯ood condition i and sites, and developed a system that allowed us to locate precipitation condition j. Table 1 shows the effects. stakes and tags under silt layers that obscured our mark- With early ¯oods and high precipitation, B. decurrens ers, but often left plants alive and well. would be capable of explosive population growth Despite these efforts, our data are not as well bal- (␭(11) ϭ 5.03) (Table 1). Under conditions of late ¯ood anced as they would have been in a more benign en- recession or low precipitation, the population would be vironment. However, we were able to obtain estimates unable to persist because ␭Ͻ1. of the major seasonal life cycle transitions under dif- Flood timing has a major impact on population struc- ferent environmental conditions. None of our conclu- ture, especially in the summer (Fig. 4a±d). Under early sions, we believe, would be changed by better luck ¯ood conditions, the summer population would even- with the ¯ooding of a major river. tually be dominated by small and large ¯owering plants. Under late ¯ood conditions, the summer pop- Condition-speci®c matrices ulation would be dominated by small rosettes, with a In constructing the condition-speci®c matrices, we few large ¯owering plants. de®ned ¯ood recession as early or late depending on whether ¯oodwaters receded before or after 1 June; we Sensitivity and elasticity analysis will refer to these as ``early ¯oods'' and ``late ¯oods.'' To evaluate the effect of changes in the vital rates, We de®ned precipitation as high or low depending on we computed the elasticities of ␭ to the entries of each 1042 MARIAN SMITH ET AL. Ecological Applications Vol. 15, No. 3

FIG. 4. Summer stable population structure for Boltonia decurrens under (a) early ¯ood and high precipitation, (b) early ¯ood and low precipitation, (c) late ¯ood and high precipitation, and (d) late ¯ood and low precipitation. Stable stage (ij)(ϭ ij)(ij)(ij) distributions calculated from the matrix Aff BBBus for the appropriate ¯ood and precipitation conditions.

FIG. 5. Elasticities of ␭ (population growth) to changes in the entries of the seasonal matrices in each environment: (a) early ¯ood and high precipitation, (b) early ¯ood and low precipitation, (c) late ¯ood and high precipitation, and (d) late ¯ood and low precipitation. Only elasticities Ն0.01 are shown. Bold arrows indicate pathways with elasticities Ն0.1. June 2005 POPULATION DYNAMICS OF A FLOODPLAIN PLANT 1043 of the seasonal matrices, using the approach of Lesnoff LTRE analysis et al. (2003). Let SA be the sensitivity matrix for A The effects of ¯ood timing and precipitation on ␭ ץ ␭ץ (i.e., the matrix whose (i, j) entry is / aij). In general, suppose that there are p matrices in a seasonal cycle, (Table 1) are mediated through effects on the vital rates ␭ at each season. We decomposed the contributions of B1, ..., Bp. To calculate the sensitivity of to the each seasonal rate to the overall effect on ␭ via a LTRE entries of the mth of these matrices, Bm, write A as analysis (Caswell 1989, see Caswell 2001 for a com- ϭ A FBGmmm (3) plete description). We used a 2 ϫ 2 factorial design, where with two levels of ¯oods and two levels of precipita- tion. We describe the main effects of these factors by B ´´´B ϩ m ± p F ϭ pm1 averaging the seasonal matrices and calculating all oth- m Ά ϭ I m p er quantities from them. For example, denoting means

B Ϫ ´´´B m ± 1 by dots, the matrix describing ¯ood condition i is ϭ m 11 Gm Ά (4) (i´)ϭ (i´) (i´) (i´)where (i´)ϭ 1/2⌺ 2 (ij) , etc. We I m ϭ 1. ABBBffffus B jϭ1 B write a linear model for ␭(ij) as

The sensitivity matrixSBm whose entries are the sen- ␭ (m) ␭ϭ␭ϩ␣ϩ␤ϩ␣␤(ij) (´´) (i)(j)(ij) (7) sitivities of tob ij is ϭ TT where ␣(i) is the main effect of level i of ¯ooding, ␤( j) SBm FSGm A m. (5) is the main effect of level j of precipitation, and ␣␤(ij) The elasticity matrixE is Bm is the interaction effect. We found the interaction ef- 1 fects to be negligible, and report only the main effects (E ϭ B ؠ S (6 Bmm␭ m B here. The main effects can be written, to ®rst order, as a -where``ؠ'' denotes the Hadamard, or element-by-ele sum of contributions from each of the vital rates at ment, matrix product. each season. To keep track of matrix elements, envi- The elasticitiese (m) sum to 1 within each season, so ij ronmental conditions, and seasons, letb (ij,f ) be the they can be interpreted as proportional contributions kl (m) (k, l) element of the matrix Bf in the (ij) treatment of the seasonal vital ratesb ij to population growth. The elasticities of the condition-speci®c matrices thus combination, and similarly for the other seasons. Then, show the life cycle pathways responsible for population growth under a given set of ¯ood and precipitation conditions. The results reveal dramatic shifts in the seasonal life cycle pathways responsible for population growth un- der the four different environmental conditions: 1 and 2) Early ¯oods, high or low precipitation (Fig. 5a and b). Over 95% of ␭ is accounted for by an annual life history pathway, from seeds in year t to seedlings to large ¯owering plants to seeds in year t ϩ 1. Al- though many other transitions occur in the life cycle, this pathway accounts for almost all population growth. 3) Late ¯oods, high precipitation (Fig. 5c). When the growing season is shortened by late ¯ood recession, over 90% of ␭ is accounted for by a biennial life history pathway. Seeds in year t produce seedlings and small rosettes in year t ϩ 1, which overwinter to form large ¯owering plants in year t ϩ 2. 4) Late ¯oods, low precipitation (Fig. 5d). This com- bination of conditions leads to precipitous population decline (␭ϭ0.0264), and the meager rate of population growth is accounted for by a very different pathway involving clonal reproduction. Large rosettes overwin- ter and ¯ower the next summer, but their only contri- bution to population growth comes from the vegetative production of large rosettes. Only a seasonal model coupled with elasticity anal- ysis could detect these shifts in life history pathways within the year. The extent to which similar shifts occur Because there are only two levels of each treatment, in other species is an interesting question. we present the results in terms of the effect of late 1044 MARIAN SMITH ET AL. Ecological Applications Vol. 15, No. 3

The accuracy of the linear approximations in Eqs. 8 and 9 can be judged by comparing the sum of all the contributions (Ϫ2.360 for the late-¯ood effect; Fig. 6a; Ϫ2.200 for the low-precipitation effect; Fig. 6b) with the observed effects of late ¯oods and low precipitation on ␭ (Ϫ2.311 and Ϫ2.204, respectively; Table 1). The LTRE contributions capture the effect of late ¯oods to within 2.1% and the effect of low precipitation to with- in 0.2%, so the approximation, using only the main effects, is excellent.

BOLTONIA DECURRENS IN A STOCHASTIC ENVIRONMENT Boltonia decurrens lives in a stochastic environment, in which ¯ood timing and precipitation vary from year to year. To explore the consequences of that variation, we require a model in which we can vary the stochastic properties of the environment and obtain their conse- quences for population growth, ¯uctuation, and poten- tial extinction. A stochastic model for the environment A stochastic population model begins with a model for the environment. Here, we used the simplest pos- sible description of the ¯ood and precipitation regime. We assume that the late and early ¯oods occur inde- pendently from year to year, with probabilities p and 1 Ϫ p, respectively. Low and high precipitation years occur independently from year to year with probabil- ities q and 1 Ϫ q, respectively. We assume no temporal

FIG. 6. LTRE (life table response experiment) analysis of autocorrelation in the ¯ood and precipitation regimes, (a) late ¯ood effects on ␭ and (b) low precipitation effects and no cross-correlation between ¯ooding and precip- on ␭. The numbers on each arrow show the contribution of itation (remember that the model describes precipita- differences in that vital rate to the effect on ␭. Only contri- tion after ¯oods have receded). butions greater than 0.01 in absolute magnitude are shown. In both (a) and (b) the seasonal totals and the overall total Stochastic population growth contributions are shown. At each year t, a population projection matrix At is chosen at random from one of the four condition spe- ci®c matrices A(ij) using the probabilities p and q. The relative to early ¯oods (␣(2) Ϫ␣(1)) and of low relative population grows according to to high precipitation (␤(2) Ϫ␤(1)). ϩ ϭ The values of ␭ calculated from the various average n(t 1) Atn(t). (10) matrices are shown in Table 1. Fig. 6a and b show the Two facts about stochastic demography are relevant contributions of each of the seasonal vital rates to these here. First, with probability 1, the population eventu- effects. Late ¯oods reduce ␭ mainly by reducing the ally grows at the stochastic growth rate given by probability that spring seedlings will grow to large ␭ϭ 1 ࿣ ࿣ ¯owering plants in the summer; this re¯ects the short- log s lim log ATϪ10´´´An(0) (11) ened growing season. There is also a small contribution T→ϱ T from reduced seed germination due to the longer period (Cohen 1976, Tuljapurkar and Orzack 1980). The sto- of ¯ood coverage. Low precipitation also reduces ␭ by chastic growth rate is the relevant measure of popu- reducing the growth of spring seedlings to large ¯ow- lation growth. It is the eventual long-term growth rate ering plants and the vegetative production of large ro- of any population experiencing the speci®ed environ- settes in the fall. Thus, the combination of a late ¯ood mental probabilities. It is the relevant measure of ®tness and low precipitation delivers a double insult to the in a stochastic environment, and it helps to determine transition from spring seedlings to summer large ¯ow- the probability of quasi-extinction. ering plants. The seasonal totals of the contributions Second, if N(t) is the total population size, then log effects show that late ¯oods and low precipitation affect N(t) is asymptotically normally distributed with a mean ␭ ␭ almost exclusively through processes operating from that grows at the rate log s and a variance that grows spring to summer (Fig. 6a and b). at a rate ␴2 (Tuljapurkar and Orzack 1980). The mean June 2005 POPULATION DYNAMICS OF A FLOODPLAIN PLANT 1045

of N(t) grows at a rate log ␮, which, for the independent  ␭ Յ 1 log s 0 and identically distributed environment model used ␪ ϭ  2 log ␭ log ␪ Pq( )  s ␭Ͼ (16) exp΂΃ log s 0. here, is given by the log of the dominant eigenvalue  ␴ 2 of the average matrix, ␪ ␭ All else being equal, Pq( ) is higher the smaller log s Å ϭ Ϫ Ϫ (11)ϩ Ϫ (12) A (1 p)(1 q)A (1 p)qA and the larger the variance. ␪ ϩ p(1 Ϫ q)A(21)ϩ pqA (22). (12) Fig. 8a shows Pq( ) as a function of late ¯ood fre- quency, for reductions to 10%, 50%, and 90% of cur- ␴2 The variance growth rate can then be estimated by rent population size (i.e., ␪ϭ0.1, 0.5, 0.9), for a ®xed probability of low precipitation q ϭ 0.1. The quasi- ␴ϭ2 ␮Ϫ ␭ extinction probabilities are quite high, as a result of 2(log log s). (13) the high variance exhibited by B. decurrens. For ex- The quantity ␴2 shows how fast uncertainty increases ample, when p ϭ 0.3 the population is still able to grow ␭ ϭ when projecting population growth in the face of en- rapidly (log s 0.47, an average growth rate of over vironmental ¯uctuations. 60% per year). But there is a 23% chance that it will ␭ Fig. 7a shows log s as a function of the frequency decline to 10% of its initial size, a 64% chance of of late ¯oods and low precipitation. In the lower left shrinking to 50% of its initial size and a 93% chance corner, the environment is constant with early ¯oods of declining to 90% of its current population size. ␪ and high precipitation, and Pq( ) gives the asymptotic probability of quasi-ex- tinction as t → ϱ, but the results are still relevant for log ␭ϭlog ␭ϭ(11) log 5.03 ϭ 1.62. s (14) short-term calculations. Fig. 8b shows the conditional In the upper right corner, the environment is constant probability distribution of the time to quasi-extinction with late ¯oods and low precipitation, and (calculated from Eq. 14.143 of Caswell 1989), for ␪ϭ 0.1. Most of the quasi-extinction events happen within ␭ϭ ␭ϭ(22) ϭϪ log s log log 0.026 3.63. (15) 20, or even 10 years. ␭ Between these limits, log s declines as the frequency Historical trends in ¯oods and precipitation of either late ¯oods or low precipitation increases. The ␭ ϭ Water levels on the Illinois River are measured daily contour where log s 0 de®nes critical combinations of late ¯ood and low precipitation frequency beyond at a network of gage stations maintained by the USA- CE. We analyzed daily gage readings for the period of which the population cannot persist. 1877±2000 at the gage station at Copperas Creek (Ban- In most of the region of parameter space within ner, Illinois) located at river mile 136.8 on the Illinois which log ␭ Ͼ 0, the variance growth rate ␴2 is in the s River (34Њ40Ј28Љ N, 18Њ89Ј53Љ W). We classi®ed each range of 0.5±2.0 (Fig. 7b). These are very high values; year as early or late depending on whether ¯oods re- for comparison, an analysis of the prairie perennial ceded before or after 1 June. ␴2 plant Lomatium bradshawii found values less than We obtained precipitation data for the months of about 0.07 (Caswell and Kaye 2001) and a hypothetical June±October from 1895±2000 from the U.S. National example of the desert tortoise (Gopherus agassizii) Climatic Data Center, Illinois Region 6. Since we are yielded values on the order of 0.01 (Caswell 2001). As interested in precipitation during the growing season, we will see, the high value of ␴2 for B. decurrens has we classi®ed an early ¯ood year as having high or low implications for the precision of population projections precipitation depending on whether rainfall was above and the risk of population decline. or below average between 1 June and 31 October. Late ¯ood years were classi®ed in the same way based on Quasi-extinction rainfall during the period 1 July±31 December. We used a Gaussian kernel smoother (a moving av- ␭ Յ If log s 0, the population will eventually become erage in which the data surrounding each point are ␭ Ͼ extinct with probability 1. Even if log s 0, however, weighted by a Gaussian distribution with speci®ed the population may ¯uctuate to low values. Quasi-ex- standard deviation; see Copas 1983) to calculate and tinction is de®ned as a decline to a fraction ␪ of the plot the frequencies of late-¯ood years and low-pre- initial population size (Ginzburg et al. 1982). The qua- cipitation years (Fig. 9a). The data show a clear in- si-extinction threshold ␪ can be chosen either as rep- crease in the frequency of late ¯oods over the last cen- resenting a risk of genuine extinction, or as a reduction tury. The frequency of low precipitation years has os- that is a management concern. cillated between about 0.3 and 0.5, without any ap- The probability of quasi-extinction with a threshold parent trend. ␪ is calculated using the following diffusion approxi- This historical trajectory of ¯ood and precipitation ␭ mation to the stochastic matrix model (Tuljapurkar and frequency is indicated on the contour plot of log s and Orzack 1980, Lande and Orzack 1988, Dennis et al. ␴2 (Fig. 7). That trajectory has carried B. decurrens 1991): from a regime supporting positive stochastic growth to 1046 MARIAN SMITH ET AL. Ecological Applications Vol. 15, No. 3

␭ FIG. 7. (a) The stochastic growth rate log s as a function of the frequency of late ¯oods and low precipitation. The ␭ ϭ contour identi®es frequencies of late ¯oods and low precipitation leading to log s 0. The arrow shows the observed historical trajectory of late ¯ood and low precipitation frequencies between 1895 and 2000, from Fig. 9a. (b) The growth rate ␴2 of the variance in log population size as a function of the frequency of late ¯oods and of low precipitation.

␭ one in which log s is negative, implying that the pop- jectory of late ¯ood frequency (holding the frequency ulation cannot maintain itself. The same trajectory has of low precipitation at its 1895 value, which is also also increased ␴2, from about 1.8 to about 2.6. In Fig. approximately the mean value), of the trajectory of low ␭ 9b, we plot log s as a function of the historical tra- precipitation frequency (holding the frequency of late June 2005 POPULATION DYNAMICS OF A FLOODPLAIN PLANT 1047

࿣Aw(t)࿣ R ϭ t . (18) t ࿣w(t)࿣ Starting with an arbitrary ®nal vector v(T), with ࿣v(T)࿣ ϭ 1, we generate a sequence of reproductive value vectors v T(t)A v T(t Ϫ 1) ϭ t t ϭ T, ...,1. (19) ࿣ T ࿣ v (t)At ϭ ϭ Then, writing At A FmBmGm as in Eq. 3, the elas- ␭ ticity of s to the entries of Bm is given by (log ␭ 1 TϪ1 b(m)(t)v T(t) f (t)g (t)w(t ץ s ϭ lim͸ ij ´ij´ (20) m) T ϩ ϩ) ץ log bTRij T→ϱ tϭ0 tv (t 1)w(t 1)

where f´i (t) and gj´(t) are column i and row j of Ft and

Gt , respectively. In place of the in®nite limit in Eq. 20, we used T ϭ 10 000. As in the deterministic seasonal model, these sto- chastic elasticities sum to 1 within each season and can be interpreted as the proportional contributions of the matrix entries to stochastic population growth. The contributions have changed dramatically over the last

␪ FIG. 8. (a) The quasi-extinction probability Pq( )asa function of the threshold ␪ and the frequency of late ¯oods, with the frequency of low precipitation ®xed at 0.1. (b) The probability density of the time to quasi-extinction.

¯oods at its 1895 value) and of both trajectories. The ␭ decline in log s is due primarily to the historical chang- es in the frequency of late ¯oods. The changes in pre- cipitation impose oscillations on the downward trend ␭ in log s, but by themselves would not have produced any trend in population growth rate.

Elasticity of the stochastic growth rate ␭ We calculated the elasticity of s to the entries of each of the seasonal matrices using an extension of Tuljapurkar's (1990) perturbation analysis to seasonal models (Caswell 2005). We use the stochastic envi- ronment model to generate a sequence of projection

matrices A0, A1,...,ATϪ1 for some large value of T. FIG. 9. (a) Frequencies of late ¯oods and of low precip- Then, starting with an arbitrary initial vector w(0), with itation calculated from historical data on the Illinois River. ࿣w(0)࿣ ϭ 1, we generate a stochastic sequence of stage Binary data were smoothed with a Gaussian kernel smoother with a standard deviation of 9 yr. (b) The stochastic growth distribution vectors ␭ rate log s calculated from the observed historical frequencies of late ¯oods and of low precipitation from 1895 to 2000. Aw(t) w(t ϩ 1) ϭ t t ϭ 0,...,T Ϫ 1 (17) Curves show the result of the ¯ood trend with the frequency ࿣ ࿣ of low precipitation ®xed at its 1895 value, the result of the Awt (t) precipitation trend with the frequency of late ¯oods ®xed at and one-step growth rates its 1895 value, and the result of both trends. 1048 MARIAN SMITH ET AL. Ecological Applications Vol. 15, No. 3

annual pathway has declined, while the contributions of the biennial and clonal pathways have increased. The contribution of vegetative reproduction re¯ects the oscillations in precipitation conditions from 1940 to 2000.

DISCUSSION Habitat destruction threatens more species in the United States than overharvesting, invasive species, or diseases (National Research Council 1995). Discus- sions of habitat loss often focus on land use (e.g., drain- ing marshes or converting prairie to farmland), but hab- itat loss is also caused by interruption or modi®cation of natural stochastic environmental ¯uctuations. The change in the ¯ood regime over the last century may not have ``destroyed'' habitat in the usual sense of the word; Illinois River ¯oodplain still exists, and still ex- periences both early and late ¯oods, but for B. decur- rens the habitat has deteriorated dramatically. Because of the economic and societal value of river- ¯oodplain ecosystems, their natural hydrologic regimes have been altered by human activities (Johnson et al. 1995). Before alteration, these ecosystems were char- acterized by seasonal ¯oods that provided pulses so dependable that plants and animals evolved life his- tories adapted to the disturbance regime (Junk et al. 1989, Bayley 1995, Middleton 2002). A systemic change to the ¯ood regime results in the loss of all suitable habitat throughout the system for any species adapted to the historic ¯ood patterns. From this per- spective, more damage has been done by the combi- nation of changing hydrology and land use than by changing land use alone. Some intact river±¯oodplain ecosystems remain in the developing world, but they are rapidly diminishing FIG. 10. (a, b) The elasticity of the stochastic growth rate, as land use intensi®es and as countries follow the west- log ␭ , to the entries of the seasonal matrices for the fre- s ern model of economic development (Welcomme 1985, quencies of late ¯oods and of low precipitation observed in 1895 and 2000. All elasticities Ն0.01 are shown; bold arrows Sparks 1992). It is often impossible to restore such indicate the major life history pathways (elasticity Ն0.1) re- ecosystems (Cairns 1991, Brookes and Shields 1996), sponsible for stochastic population growth. (c) The propor- and it is far more expensive to rehabilitate or recon- tional contribution of the annual, biennial, and clonal path- struct them (e.g., the ongoing effort to reconstruct the ways to stochastic population growth, as determined by the historical trajectories in late ¯ood and low precipitation fre- Kissimmee River in Florida; Toth et al. 2002) than it quencies. is to plan for their preservation. Thus, it is critical to assess the long-term biological impact of proposed al- terations in ¯ood regimes. Stochastic demographic century (Fig. 10). Unlike the changes in Fig. 5a±d, analysis can reveal the interactions by which environ- which re¯ect the effects of different ®xed environ- mental variation and life histories combine to deter- mental conditions, the changes in Fig. 10 are caused mine population growth. This approach becomes even by changes in the statistical properties of the ¯oodplain more powerful when the results are related to long- environment. In 1895, when the frequency of early term historical data. ¯oods was high, the stochastic growth rate was almost completely determined by the annual life history path- Elasticity patterns way (Fig. 10a). By 2000, when late ¯oods had become The environmental conditions encountered in our common, all three pathways contribute almost equally study produce dramatic shifts in the elasticity patterns, ␭ to s (Fig. 10b). Summing the contributions of each of interpretable in terms of annual, biennial, and clonal ␭ the three pathways to s (assuming that the biennial life cycles. Some of these patterns agree with other pathway displays the symmetry shown in Fig. 5c), comparative studies of elasticity patterns, although gives the results in Fig. 10c. The contribution of the those generalizations were not based on seasonal mod- June 2005 POPULATION DYNAMICS OF A FLOODPLAIN PLANT 1049 els and thus are not directly comparable. For example, Such extreme population ¯uctuations have indeed species in variable habitats sometimes have higher elas- been observed. For example, in Jersey County, Illinois, ticity values for the seed-to-seedling transition than do a population of fewer than 10 large ¯owering plants in populations in more stable habitats (van Groenendael September 1992 exploded into a population of 20 000 and Slim 1988). Boltonia decurrens lives in a highly ¯owering individuals in the fall of 1994, a year with variable habitat, and the seed-to-seedling transition has early ¯ood recession and high precipitation (Smith a high elasticity value. When ¯ood recession is late 1995). Conversely, in 2001, a late ¯ood and low pre- and precipitation is low, however, this transition has cipitation resulted in the decline of a population in virtually no effect on population growth. Silvertown et Fulton County, Illinois from 18 000 individuals to 125 al. (1996) reported that the contribution of fecundity ¯owering plants in 2002 (Smith and Mettler 2002). In to ␭ is higher during early stages of colonization than 2002, a GIS database for the Illinois River Valley en- later in the successional process. Boltonia decurrens is abled us to identify 26 populations (the most ever), but an early colonizer (Schwegman and Nyboer 1985, because of late ¯oods and low precipitation the total Smith et al. 1998), and the ¯ood regime under which number of plants declined from more than 1 000 000 it evolved favored the development of an annual life in 2001 to fewer than 300 000 in 2002 (Smith 2001, cycle in which fecundity and growth contribute heavily 2002). to population growth (Fig. 10a). Future model extensions Long-lived perennials sometimes have higher elas- ticity values associated with survival in the same class A basic principle of population modeling in conser- than do shorter-lived, faster growing species (Caswell vation is to begin with simple models and gradually 1986, Silva et al. 1991, Silvertown et al. 1993). While build up complexity (Caswell 2001, Section 18.4). Here B. decurrens is classi®ed as a perennial in the taxo- we have focused on the crucial factor of environmental nomic (Torrey and Gray 1841, Gleason and Cronquist stochasticity. Our analysis could be extended in several 1991) and conservation literature (Schwegman and Ny- directions. It would be possible, for example, to de- boer 1985, USFWS 1990), it is certainly not a long- scribe ¯oods in more detail than a binary choice be- lived one. The elasticity of ␭ to survival is low, es- tween early and late ¯ood recession, and to describe pecially under conditions favoring rapid growth. precipitation as a continuous, rather than a discrete These patterns refer to hypothetical projections of variable. To develop such models would require de- constant ¯ood and precipitation regimes, so it is sig- mographic parameter estimates under a wider array of ni®cant that the differences in elasticity patterns among environmental conditions. It is unlikely, however, that the deterministic matrices are mirrored in the historical such re®nements would signi®cantly change the pat- changes in the elasticity of the stochastic growth rate, terns reported here. documenting the shift from the importance of annual It would be interesting to explore the consequences to biennial and clonal life history pathways. This is the of correlation between ¯ood recession and precipita- ®rst time that such shifts have been documented in tion, and the autocorrelation patterns in each. A pos- variable environments using stochastic elasticities. itive correlation between late-receding ¯oods and high precipitation during the growing season would amelio- Uncertainty and population ¯uctuation rate some of the negative effects of changes in the ¯ood regime. There is no obvious sign of such a correlation Environmental stochasticity affects not only the (Fig. 9a), but we have not investigated the time series growth rate, but also the variability in population size. in detail. One consequence is the high probability of quasi-ex- Perhaps the most interesting extension will be to tinction (Fig. 8). Another is that projections of popu- include spatial structure. In recent years, GIS technol- lation size are very uncertain. The variance growth rate ogy has permitted a systematic survey of all potential ␴2 measures the rate at which the uncertainty in log B. decurrens habitat in the Illinois River Valley (Smith N(t) increases in the long run (and the short-run be- 2002). In the short term, populations continue to ap- havior is often predicted by ␴2 with only small errors; pear, disappear and shift annually, typical of a meta- see Runge and Moen 1998, Caswell 2001). Values of population. The B. decurrens metapopulation is largely ␴2 for B. decurrens are large (ϳ1.5±2.5). This creates con®ned to the narrow littoral zone along a 400-km extreme variability in short-term projections of popu- stretch of the Illinois River, and extinction of large lation growth. Since log N(t) is asymptotically nor- populations is common (Schwegman and Nyboer 1985, mally distributed with a variance equal to t␴2, the ratio Smith et al. 1998, Smith and Mettler 2002). The genesis of the upper to the lower 95% projection interval for of new populations is facilitated by the ability of the N(t) is exp(3.92͙t␴2 ). During the 20th century, this seeds to ¯oat for extended periods (Smith and Keevin interval of uncertainty surrounding a 10-yr population 1998), provided that suitable habitat exists in areas projection was between six and eight orders of mag- connected to the ebb and ¯ow of the river. The Illinois nitude. This means that it is essentially impossible to River ¯ows slowly and meets a hydrological barrier at predict population size even over short time scales. its con¯uence with the Mississippi River. When both 1050 MARIAN SMITH ET AL. Ecological Applications Vol. 15, No. 3 rivers are in ¯ood stage, this results in signi®cant back ground suitable for seed germination and seedling es- and lateral ¯ow (Cooley as cited in Kofoid 1903, Ak- tablishment may offer viable alternatives. One thing is anbi and Singh 1997), so dispersal was possible in any certain: to be successful, conservation strategies for direction. In addition, seed dispersal was historically this species must look beyond efforts to maintain static unimpeded by navigation structures. Today, however, ``protected'' populations and make strategic use of the the frequency of a favorable annual ¯ood regime has environmental variability to which B. decurrens is fallen to 30%, and genetic evidence (DeWoody 2002) adapted. indicates that population establishment depends upon seeds from a small number of source populations. ACKNOWLEDGMENTS In a metapopulation model, each location would ex- This work was supported by grants to M. Smith from NSF perience its own ¯ood timing and precipitation regime. (DEB 9509763, DED 9321517), USACE, Illinois Ground- water Consortium and USFWS, and an EPA STAR grant (U- An important parameter would be the degree of spatial 91578101-2) to P. Mettler. H. Caswell also received support autocorrelation between the ¯ood and precipitation re- from NSF grant OCE-9983976 and EPA grant R-82908901, gimes among sites. Current evidence suggests that and a Maclaurin Fellowship from the New Zealand Institute ¯ood timing and precipitation can vary substantially of Mathematics and its Applications. We thank a myriad of over very small spatial scales. A metapopulation model graduate and undergraduate students who worked on this proj- ect, including Scott Moss, Jason Chapman, Melissa Baker, incorporating dispersal and stochastic environmental Adrienne Estler, Teresa Cochran, Sarah Tofari, Anjela Red- variation would permit evaluation of the threat of ex- mond, Martin Stoecker, and Kelly Victory. We give a special tinction for B. decurrens, and the role of alterations to thanks to Dr. Tom Keevin of the USACE who has been a the ¯oodplain system in its decline. Preliminary results loyal supporter of all of our Boltonia work, Dr. Nancy Parker for help in proofreading and editing this manuscript, and Dr. (unpublished data) suggest that incorporating spatial Christine Hunter for helpful discussions. structure modi®es the details but does not change any of the conclusions of our study here. LITERATURE CITED Akanbi, A., and K. P. Singh. 1997. Managed ¯ood storage Implications for management option for selected levees along the lower Illinois River for Our study indicates that the threatened status of B. enhancing ¯ood protection, agriculture, wetlands, and rec- decurrens can be explained by historical changes in reation. Second report: validation of the UNET model for the lower Illinois River no. 608. Illinois State Water Survey, ¯ooding. One strategy for species recovery would be Hydrology Division, Champaign, Illinois, USA. to restore the river±¯oodplain system to pre-1900 con- Allen, J. A. 1870. The ¯ora of the prairies. American Nat- ditions; economic and political considerations make uralist 9:577±585. this unlikely (Sparks et al. 2000). Conservation efforts Baker, M. A. 1997. Effects of intra- and interspeci®c rosette competition on Boltonia decurrens. Thesis. Southern Illi- will necessarily focus on mitigating the effects of le- nois University at Edwardsville, Edwardsville, Illinois, vees and dams, whenever possible. The combination USA. of technological advances in managing navigation Baskin, C. C., and J. M. Baskin. 1988. Germination eco- pools (Busse 1998, Flowers et al. 1998) and a rising physiology of herbaceous plant species in a temperate re- concern about the effects of navigation structures on gion. American Journal of Botany 75:286±305. Baskin, C. C., and J. M. Baskin. 2001. Seeds: ecology, bio- ¯oodplain species (Sparks et al. 1998, 2000) has re- geography, and evolution of dormancy and germination. sulted in experimentation with a pool drawdown strat- Second edition. 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APPENDIX Condition-speci®c seasonal projection matrices for Boltonia decurrens are presented in ESA's Electronic Data Archive: Ecological Archives A015-028-A1.