rank order of the strategies. This uncertainty analysis Burning Prairie to indicated that the rank order of burning strategies is most sensitive to our confidence in rates of habitat change after a burn (number of “good” years after a Restore Butterfly fire and time for habitat to return to pre-burn condi- tions). Surprisingly, however, the rank order of strate- gies changes little over a wide range of butterfly de- Habitat: A Modeling mographic rates. Better knowledge of rates of habitat change after a burn would improve our ability to Approach to make management decisions substantially more than better knowledge of the butterfly’s vital rates. Management Tradeoffs Introduction for the Fender’s Blue nvasive weeds pose a significant threat to rare plants Iand in a wide range of terrestrial habitats Cheryl B. Schultz1 (Randall 1996). Fire is a powerful tool for destroying 1,2 weeds, but it often decimates the invertebrate fauna Elizabeth E. Crone (Miller 1979; Warren et al. 1987; Hastings & DiTomaso 1996). Habitat managers often aim to help rare species by eliminating problem weeds. But designing strategies Abstract to reduce weeds and save rare species may hinge on us- Designing strategies to manage rare species’ habitats ing methods that have negative short-term impacts in may involve tradeoffs that include negative short- order to attain positive long-term success. term impacts to achieve positive long-term success. In Grasslands around the world are a key ecological managing grasslands, fire is a powerful tool to control community that may benefit from the use of fire as a invasive weeds and stimulate native plant growth, management tool. Historically, many grasslands were but it may decimate the invertebrate fauna. To rank maintained by fire (Collins & Gibson 1990). In North potential burn strategies for icarioides fenderi America, fires ignited by lightning burned vast areas of (Fender’s blue butterfly) habitat, we present an empir- the tallgrass and shortgrass prairies of the Midwest, ically based mathematical model. Parameter estimates and fires set by Native Americans burned shortgrass are based on experiments conducted by Wilson and prairies in the Pacific Northwest (Anderson 1990; Agee Clark from 1994 to 1997. Potential strategies include 1996). Only in the last century, with “Smokey-the-Bear” combinations of times between burn (1, 2, 3, 4, or 5 fire prevention policies enforced in most natural areas years) and fractions of a habitat to burn in each fire (1/8, of the United States, have fires ceased to be a major 1/4, 1/3, or 1/2), as well as a strategy of never burning. force in structuring grassland communities. Today, grass- Burning one-third of the habitat every year maximizes lands have dramatically declined, and those that sur- the average annual population growth rate, but, based vive are threatened by a wide variety of weeds, includ- on maximum likelihood parameter estimates, 8 of 21 ing both nonnative plants and, in the absence of fire, strategies led to 95% of simulated butterfly popula- native woody plants (Randall 1996). In the Pacific North- tions persisting for 100 years. In simulations based on west, forests now cover many areas that were grass- the parameters’ lower confidence limits, however, lands 200 years ago, and the remaining grasslands are there were some cases in which no strategies led to being invaded by weedy shrubs such as native Toxico- populations persisting 100 years. In this uncertainty dendron diversiloba (poison oak) and nonnative Cytisus analysis—the effect of changes in parameters based scoparius (Scot’s broom; Agee 1996). on our confidence in them—we also investigated the Managing grasslands for native species will require both reintroducing historic fire disturbances and elimi- nating invasive plants that were not present when the 1 Department of Zoology, University of Washington, Box communities were historically burned. Biologists must 351800, Seattle, Washington 98195-1800, U.S.A. consider both factors because, for example, simply re- 2Current address: Ecology Division, Biological Sciences De- partment, University of Calgary, Calgary, Alberta T2N 1N4, storing a fire regime may not reduce problem weeds. Canada Therefore, to design conservation strategies for a native grassland, we need to combine what we know about © 1998 Society for Ecological Restoration the historic disturbance regime for the given commu-

244 Restoration Ecology Vol. 6 No. 3, pp. 244–252 SEPTEMBER 1998

Restoring Butterfly Habitat nity with strategies to remove key invasive weeds at of lupine leaves. The eggs hatch a few weeks later, and those sites. larvae eat lupine leaves until the plants begin senescing Icaricia icariodes fenderi (Fender’s blue butterfly) is a in late June or early July. The young larvae then drop to rare butterfly endemic to upland prairies in the Wil- the ground, crawl under nearby vegetation, and enter lamette Valley in Oregon. It depends on perennial lu- winter diapause. They remain in diapause until late pines for its larval foodplants. The butterfly’s habitat February or early March, when lupine begins emerging has dramatically declined over the last 150 years due to from the ground. The larvae crawl onto new lupines agriculture, urbanization, and the cessation of annual and eat the young lupine leaves for the next 6–8 weeks. autumn fires set by Native Americans (Ingersoll & Wil- Around the end of April the larvae pupate and emerge son 1991; Noss et al. 1995). Forests and weedy shrubs as butterflies in mid-May. now threaten to overrun the remnant prairies that re- Weeds degrade the habitat of every Fender’s blue main (Hammond & Wilson 1993). Fire reduces the site. Unfortunately, designing strategies to control one cover of woody shrubs and, in the years after a fire, but- problematic weed is not sufficient to manage its habitat. terfly reproduction dramatically rises (M. V. Wilson & At some sites problem shrubs include poison oak, Ru- D. L. Clark, personal communication). Fire kills Fender’s bus discolor (Himalayan blackberry), and Scot’s broom blue butterfly larvae, however. (Hammond & Wilson 1993). Fire is likely to reduce At Baskett Slough National Wildlife Refuge, weedy these weeds, but in dramatically different ways. Poison poison oak is a significant problem for Fender’s blue oak and blackberry resprout after a fire. Scot’s broom is butterflies. In this study, strategies for managing Fender’s killed by fire, but fire stimulates germination of the blues at this location were explored with respect to in- seed bank. At some sites problem weeds are grasses like formation from an experimental burning by Wilson Arrhenatherum elatius (tall oatgrass), Brachypodium syl- and Clark (personal communication). Models based on vaticum (false-brome grass), or Festuca arundinaceae (tall these data were used to ask (1) what combinations of fescue). The effect of fire on these grasses is unknown, burn frequency and burn size are best for the Fender’s but other strategies such as mowing are being investi- blue butterfly, and (2) how sensitive are our predic- gated (M. V. Wilson & D. L. Clark, personal communi- tions to limitations in the data? Our approach differs cation). In this study we consider the specific problem from traditional population viability methods. Instead of how to use fire to control poison oak at Baskett of seeking a single “best” management strategy, we Butte, which hosts the largest population of Fender’s identify a range of “acceptable” strategies. Then we blue butterflies. Although our methods do not explicitly investigate how our range of acceptable strategies consider other weeds or management approaches, the changes based on our confidence in our parameter esti- general approach of linking models to management ex- mates. periments is transferrable to such concerns.

Methods Experimental Data

Biology and Habitat of the Fender’s Blue Butterfly From 1994 to 1997, Wilson and Clark experimentally burned areas at Baskett Butte to reduce problem shrubs The Fender’s blue is a rare butterfly that survives in Or- (M. V. Wilson & D. L. Clark, personal communication). egon prairies that maintain at least one of its larval host- Poison oak is the most abundant shrub invading these plants, sulphureus kincaidii (Kincaid’s lupine) or grasslands. Although native to Oregon, poison oak was L. laxiflorus (spur lupine). Both the butterfly and the not common in the Willamette Valley in pre-settlement Kincaid’s lupine are extremely rare, and the butterfly is times, possibly due to burning by Native Americans a candidate for listing on the U.S. Endangered Species (Agee 1996). Other problem shrubs include blackberry, list (Anonymous 1996). Butterfly populations persist at Rosa eglanteria (rose), Amelanchier alnifolia (serviceberry), 13 of the 45 sites that harbor appropriate hostplants and Crataegus douglasii (hawthorn). In the analyses that (Kuykendall & Kaye 1993). Among these, seven sites follow, we assume that burning is necessary to main- have less than 100 butterflies, three sites have 100–300 tain prairie habitat at Baskett Butte; a discussion of al- butterflies, and three sites have more than 300 butter- ternative shrub-control methods (mowing and herbi- flies (Hammond & Wilson 1993; Hammond 1996; Schultz cide) will be presented later (M. V. Wilson & D. L. 1996). The largest population, 1000–1400 butterflies, is Clark, personal communication). on Baskett Butte at Baskett Slough National Wildlife In 1994, Wilson and Clark established five 400-m2 ex- Refuge in Benton County, Oregon. perimental blocks. Each block contained several treat- The Fender’s blue butterfly is a “spring” species, and ments, including one 120-m2 burn plot and one 40-m2 the adults can be seen in May and June. At that time, control plot (5 blocks ϫ 1 plot/treatment/block ϭ 5 butterflies mate and females oviposit on the underside plots/treatment). In the spring of 1994, Wilson and

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Restoring Butterfly Habitat

Clark assessed pretreatment conditions by estimating Model of Butterfly Dynamics in Response to Burning the percent cover of key native and nonnative plants. In To explore possible management strategies, we proceeded addition, one of us (Schultz) counted the numbers of in four steps. First, we built a model of butterfly popu- Fender’s blue eggs and larvae in each treatment. Burn- lation dynamics, including the effects of burning on ing was done in the autumn of 1994 and again in the au- egg-larva survivorship and oviposition rates. Second, tumn of 1996. In 1995, 1996, and 1997, Wilson, Clark, parameters from this model (and associated confidence and Schultz assessed the impact of their treatments by intervals) were fit to Wilson, Clark, and Schultz’s exper- assessing the same factors measured in the pretreat- imental data by standard maximum likelihood meth- ment year. Two of the control plots never contained ods. Third, the parameterized model was compared to host lupine or Fender’s blue eggs or larvae, so only the possible burning strategies (varying fraction of habitat remaining three plots are used in the analyses that fol- burned and number of years between burns). Finally, to low. (Wilson and Clark’s experiment was designed to address the limitations of the available data, predictions look at plant communities as a whole, not just lupine of models based on maximum likelihood parameter es- and Fender’s blue.) In addition, in each study year the timates were compared with models based on extreme number of adult butterflies in the experimental area confidence bounds for each parameter. and the number of butterflies in 10 other areas on Bas- kett Butte were assessed (Hammond 1997). Mathematical Model. To incorporate the effects of burning Wilson, Clark, and Schultz’s data show two clear on survivorship and fecundity, butterfly population patterns: (1) burning improves Fender’s blue butterfly growth was divided into three stages: (1) survivorship habitat (comparison of oviposition rates per female but- (s1) from eggs (et) to postdiapause larvae (lt): lt ϭ s1et; (2) terfly, likelihood ratio test of post-burn versus pretreat- survivorship (s2) from postdiapause larvae (lt) to adults ment and unburned plots, ␹2 ϭ 9.24, df ϭ 1, p ϭ 0.0024; (Nt): Nt ϭ s2lt; (3) per capita fecundity ( f) of surviving Fig. 1a), but (2) burning kills butterfly larvae (compari- adults: etϩ1 ϭ fNt. son of egg to postdiapause larval survivorship in post- Then it was assumed that both egg-larva survivor- burn year versus control plots and all other years in ship (s ) and fecundity ( f) are functions of years since 2 1 burned plots, likelihood ratio test, ␹ ϭ 44, df ϭ 1, p ϭ habitat was last burned (y): s ϭ s (y), f ϭ f(y). Survival, Ϫ11 1 1 2 ϫ 10 , Fig. 1b). In addition, the 1994 and 1996 burns growth, and timing of burns were then combined into a had the same magnitude of effect on both butterfly fe- model of population dynamics: cundity and egg-larva survivorship (paired t tests, for () () fecundity: t ϭ 1.13, df ϭ 4, p ϭ 0.322; for survivorship: Nt ϩ 1 ϭs1 y s2fyNt. t ϭ 0.534, df ϭ 4, p ϭ 0.621). In other words, burning is We assumed that population growth rates (ln[s1(y) good for Fender’s blue butterflies. Because fire kills lar- s2 f(y)]) vary from year to year, following a normal dis- vae, however, all available habitat cannot be burned in tribution. Thus, the ultimate model of population dy- any given year. From the experimental data, it is not namics, which includes the effects of fire and the effects immediately clear how much to burn or how often. To of year-to-year variability, is investigate acceptable burning strategies, we developed () () () a mathematical model of butterfly population dynamics Ntϩ1ϭs1ys2fyNtexp ⑀r , which incorporates the effects of different burning re- where ⑀r is normally distributed with mean 0 and vari- gimes. ance estimated from Hammond’s annual censuses at Baskett Butte (see below).

Parameter Estimation. We estimated each of these param- eters using standard maximum likelihood methods (Edwards 1972), and we used likelihood profiling (Hil- born & Mangel 1997) to calculate confidence intervals. Data used to estimate each parameter and error assump- tions were as follows. Based on the experimental data (Fig. 1), burning kills almost all larvae from the generation of a burn, but egg–postdiapause larva survivorship is not affected in subsequent years following a burn (survivorship in con- Figure 1. Results from burning experiment at Baskett Butte. trol versus burn plots, excluding post-burn year, likeli- 2 Data are from 1994–1996 assessments. Fender’s blue oviposi- hood ratio test, ␹ ϭ 0.215, df ϭ 1, p ϭ 0.643). Egg-larva tion response to burning (a); survivorship of larvae after a survivorship is therefore s1(y) ϭ a1 if this is a burn year burn (b). (y ϭ 0) and s1(y) ϭ b1 if this is not a burn year (y Ͼ 0),

246 Restoration Ecology SEPTEMBER 1998 Restoring Butterfly Habitat

Table 1. Parameters used in model of butterfly dynamics in response to burning.

Parameter Definition

s1(y) ϭ survivorship of eggs to larvae y years after burning (y ϭ 0 in burn years, %/year) a1 ϭ s1(y) if y ϭ 0; survivorship of eggs to larvae in the burn year b1 ϭ s1(y) if y Ͼ 0; survivorship of eggs to larvae in all nonburn years s2 ϭ survivorship of larvae to adult butterflies (%/year) f(y) ϭ fecundity y years after burning (eggs/female/ha) f1(y) ϭ fecundity in the step function c1 ϭ f1(y) if y Ͻ 2 d1 ϭ f1(y) if y у 2 f2(y) ϭ fecundity in the exponential function c2 ϭ intercept in the exponential function d2 ϭ decay rate in the exponential function (%/year) m ϭ time-scale measure* m1 ϭ number of “good” years after a fire in step function m2 ϭ number of years for habitat to return to pre-burn conditions in exponential function

*See uncertainty analysis for use of these parameters. where y indexes the number of years since burning distributed survivorship and normally distributed en- (habitat is burned at y ϭ 0) and a1 and b1 are survivor- vironmental variance in fecundity (following methods ship estimates (Table 1). We assumed that survivorship similar to those of Kendall 1998). was binomially distributed, as is common for this type Per capita fecundity is clearly elevated after burning of data (Hilborn & Mangel 1997; Kendall 1998). Esti- (Fig. 1). But to predict the possible effects of different mates for a1 and b1 are shown in Table 2. burning protocols on butterfly population dynamics (see We do not have data from the burn experiment to below), we need to know how butterfly fecundity changes estimate larva-adult survivorship because butterflies with time after a burn. Given that poison oak will rein- move over areas much larger than the experimental vade after a burn, we assumed that habitat quality— area. Lacking data, it was assumed that s2 is indepen- and associated butterfly fecundity—declines in years dent of burning. s2 was set so that the average rates of after burning. In other words, expected per capita fe- population growth in control areas were similar to the cundity is a function of time since burning. Thus, in the average trends in long-term census data from Baskett experiment neither the burn plots nor the control plots Butte, given the estimates of s1 and f (Table 2). Our esti- maintain the same habitat quality from one year to the mated value for s2, 0.050, is similar to estimates of larva- next. Data from Wilson and Clark’s experiment do not adult survivorship from another Oregon population of give us any statistical or biological ability to distinguish Fender’s blue (0.025–0.060, C. B. Schultz, unpublished between many possible forms of this function. To data). Confidence limits were set assuming binomially bound the range of shapes for this function, we explore

Table 2. Parameter estimates (see Table 1 for definitions of parameters).

90% Confidence Limit Error Parameter Estimate Lower Upper Distribution Source of Data Egg-larva survivorship a1 0.005 0.001 0.016 binomial experimental plots b1 0.094 0.074 0.119 binomial experimental plots Larva-adult survivorship s2 0.043 0.025 0.117 binomial Hammond’s censuses: 1993–1996, s1, and fecundity from control plots Environmental variance ⑀r 0.473 0.905 0.262 normal Hammond’s censuses: 1993–1996, assuming Poisson-distributed demographic stochasticity Fecundity c1 300 170 620 log-normal experimental plots d1 73 50 140 log-normal experimental plots c2 305 160 660 log-normal experimental plots d2 0.200 0.060 0.340 log-normal experimental plots

SEPTEMBER 1998 Restoration Ecology 247 Restoring Butterfly Habitat

normally distributed environmental variance in popula- tion growth rates (following methods analogous to those described by Kendall 1998) for each Fender’s blue site at Baskett Butte (Table 2). These environmental variance estimates were used to simulate population dynamics after burning (see below).

Exploration of Burning Strategies. At Baskett Butte, habitat can be managed by varying two aspects of burning: the fraction of habitat burned each year and the number of years between burns. The timing of burns is fixed in the autumn, the only time of year when Willamette Valley prairies were historically burned. We consider burn in- tervals (years between burns) from one to five and burn fractions (fraction of habitat burned) of an eighth, a quarter, a third, and a half. Burn interval is the number Figure 2. Fecundity functions ( f (y)). Curves fit to parameters of years between burning any land at the site (Fig. 3). estimated from 1994–1996 data. Solid circles are data from We model simple rotations such that the land burned in burn plots. Solid triangles are data from control plots. Open squares are from 1997, added to show fit of model to new data. a given year is always the land that was burned least re-

two likely patterns of habitat change after burning (Fig. 2): (1) In the step function, average butterfly fecundity is elevated for 2 years following burning (the 2 years for which we have data) and is like fecundity in pretreat- ment and control plots two years after a burn: f1(y) ϭ c1 if this is less than two years after a burn (y Ͻ 2) and f1( y) ϭ d1 if this is two or more years after a burn (y у 2). (2) In the exponential function, average butterfly fecundity (c2) declines exponentially after burning (at rate d2): Ϫ () ()d2 f 2 y ϭc2yϪ1 . Based on an examination of residual variance around the data, we assumed that variance around both of these models was log-normally distributed. To bound the exponential function fitted to experi- mental data, we assumed that habitat in pretreatment plots was similar to habitat at least 6 years after burn- ing. The estimate of 6 years was based on the observa- tion that, because poison oak was a problem at Baskett Butte in 1991, poison oak had probably begun invading Baskett Butte by 1989 (Hammond & Wilson 1993). An upper bound on this time scale can also be set, based on the absence of poison oak when the preserve was estab- lished in 1969 (M. Naughton, personal communication). Lacking other information, the 6-year minimum value was used as a “maximum likelihood estimate” because it predicts lower butterfly population growth rates and more conservative management. See, however, the “un- certainty analysis” below. Finally, stochastic environmental variance (⑀r) in pop- ulation growth was estimated by fitting a maximum Figure 3. Example of a management strategy. In this case, we likelihood model to census data, assuming Poisson-dis- burn half the habitat every year (burn interval ϭ 1; burn frac- tributed demographic variance in population size and tion ϭ 1/2).

248 Restoration Ecology SEPTEMBER 1998 Restoring Butterfly Habitat cently. For example, if half of the habitat is burned ev- dence limits for fecundity, habitat recovery after burn- ery year, the number of years between burns in any ing, and survivorship. Uncertainty in the time scale of given half is two. This strategy is always better than poison oak re-invasion (see above) was included by set- burn intervals without rotation because it minimizes ting the control plots at 25 years post-burning in the ex- the average time since burning across all butterfly habi- ponential model and by increasing the number of years tat. These strategies are compared to butterfly dynam- of elevated habitat quality in the step model to 5 years ics with no burning. (Fig. 4). Using the model of population dynamics (equation 1) For each parameter, we ran a set of simulations with we simulated butterfly dynamics for 100 years, given one parameter set at the more pessimistic limit of its each of the two fecundity functions (step and exponen- 90% confidence interval. The other parameters were left tial) and a starting size of 500 adult butterflies. This is at their maximum likelihood estimates. For each set of the approximate butterfly density at some of the best simulations, we recorded the number of “acceptable” Fender’s blue butterfly sites. We assumed that the habi- strategies. Using Spearman’s rank correlations, we com- tat is one large patch of about 2 ha in size. Because pared the differences between the rank order of strate- Fender’s blue butterflies disperse about 1 km within lu- gies in maximum likelihood and the rank orders of pine areas (Schultz 1998), simulated butterflies traveled strategies in simulations with lower 90% confidence in- randomly throughout the habitat. Butterflies were as- sumed to spend equal amounts of time in all available habitat, with oviposition rates in any location deter- mined by years since burning at that location. Over this period, annual population growth rates (geometric mean of ln[Ntϩ1/Nt]) were calculated for each simula- tion. Based on 5000 replicate simulations, we calculated average annual growth rates and probabilities of popu- lation persistence for each model and each strategy. We evaluated strategies using two criteria. First, for each fecundity function, the best strategy—that yield- ing the highest expected long-term growth rate—was identified. Second, we determined those strategies yield- ing an average population growth rate (exp[ln[Ntϩ1/ Nt]]) greater than 1.1. In all strategies with this growth rate or higher, 95% of the simulated butterfly popula- tions persisted, assuming density-independent popula- tion growth (and the numerous caveats that accompany this assumption!). We refer to these as “acceptable” strategies.

Uncertainty Analysis. Given that confidence limits around parameter estimates were quite wide (Table 2), it is im- portant to know how sensitive our results are to error in parameter estimation. We used an “uncertainty analy- sis” in which parameters were set to values at the edge of the respective 90% confidence limits. This analysis differs from a traditional sensitivity/elasticity analysis (e.g., Caswell 1989) in that parameters were varied based on our confidence in the parameter estimate, not by a constant fraction. For example, elasticity analysis is designed to detect how a change in a demographic pa- rameter changes the population dynamics (via a change in the population growth rate). In this analysis, we Figure 4. Fecundity functions ( f(y)) used in the uncertainty asked how improving our knowledge of demographic analysis. Solid line is maximum likelihood estimate (MLE); parameters would improve our ability to predict the dashed line is function used in uncertainty analysis. Step relative success of different management strategies. model: step of 5 good years rather than 2 in MLE (a); exponen- Specifically, we simulated dynamics using the more tial model: control plots set at 25–27 years since burning rather pessimistic of the parameter values from the 90% confi- than 6–8 in MLE (b).

SEPTEMBER 1998 Restoration Ecology 249 Restoring Butterfly Habitat tervals. This analysis did not include the “no burning” habitat parameters were set to the most pessimistic val- strategy, which always ranked lowest regardless of the ues in maximum likelihood simulations and were more parameter estimates. optimistic in the uncertainty analysis. On the other hand, the rank order of possible burning Results strategies was strikingly similar across uncertainty in most parameters (r2 Ͼ 0.95 for egg-larva survivorship Best Strategies (s1), larva-adult survivorship (s2), maximum fecundity in exponential model (c2), control values in step model Burning is necessary for Fender’s blue to persist, and (d1), and decay in the exponential model (d2); Fig. 7). burns must be relatively frequent; within these con- Rank order shifted substantially with uncertainty in straints, however, there is a lot of flexibility in how to maximum fecundity after burning (c1) in the step model; burn (Figs. 4 & 5). Several strategies (burn an eighth to a all treatments in which half of the habitat was burned half of the habitat every year; burn a quarter to a half of became substantially worse (Fig. 6). Presumably, im- the habitat every 2 years; burn half the habitat every 3 proved fecundity after burning was no longer adequate years) led to likely persistence for all models of fecun- to offset mortality. But the most substantial changes in dity dynamics after burning. The step fecundity func- ranks occurred due to uncertainty in time-scale param- tion led to fewer acceptable strategies than the exponen- eters: step length in the step model (m1) and years to tial fecundity function, but it predicted slightly more- reach unburned conditions in the exponential model optimistic growth rates in the absence of burning. (m2).

Uncertainty Analysis Discussion All pessimistic simulations indicated that far fewer strat- Based on our results, we recommend burning, on aver- egies might be acceptable than predicted by maximum age, a third of a Fender’s blue area every year (if funds likelihood models (Fig. 6). This was consistent across permit) or every 2 years (if funds don’t permit). This all parameters, but was particularly striking for larva- strategy yields the highest long-term population growth adult survival, for which we had the most substantial rate for Fender’s blues in both the step function model uncertainty in our parameter estimates. Changing the and the exponential decay function model. The differ- time scale of habitat decay, on the other hand, increased ence between these options and several others (Fig. 4) is the number of acceptable strategies. This is because small, however, and many strategies (burn an eighth, a

Figure 5. Population growth rate and percent of simulated populations that persist 100 years of each of 21 management strategies (burn interval ϭ 1, 2, 3, 4, or 5 years combined with burn fraction ϭ 1/2, 1/3, 1/4, or 1/8 and a never-burn strategy). Results based on maximum likelihood parameter estimates. Ordinate axis indicates burn strategy and rank for each model (e.g. (2, 1/3) ϭ 1 indi- cates that a strategy of burning a third of the habitat every 2 years is the best strategy). Percentage of simulated populations that persist 100 years in the step model (a), and percentage of simulated populations that persist 100 years in the exponential model (b).

250 Restoration Ecology SEPTEMBER 1998 Restoring Butterfly Habitat

Figure 7. Spearman rank correlations comparing the ranks of strategies in the maximum likelihood model versus the ranks of strategies in which one of the parameters was set to its lower 90% confidence limit.

The results of our uncertainty analysis show that it is important to ground recommendations for management in our confidence in the parameters. Standard 95% prob- Figure 6. “Acceptable” strategies in models with maximum ability of persistence is 95% probable only if we are cer- likelihood estimates (MLE) of all parameters and in models in tain of our parameter estimates (Ludwig 1996). At the which one parameter was set to its lower 90% confidence limit. same time, as we saw in our analysis, management rec- Circle diameters are proportional to average annual popula- ommendations can be meaningful even with parameter tion growth rates. Solid circles had at least 95% of simulated uncertainties. Our rank ordering of the best to worst populations survive for 100 years. strategies remained robust to error in many of the pa- rameter estimates. Given this uncertainty, prioritizing future research quarter, a third, or a half of the habitat every year, burn a needs based on these models will depend on the intent quarter, a third, or a half of the habitat every 2 years; or of the managing groups. Better estimation of butterfly burn half of the habitat every 3 years) led to likely but- survivorship and fecundity in burned and unburned terfly persistence. Based on the uncertainty analysis for habitats will improve our understanding of predicted post-burn fecundity, we reject burning half the habitat absolute values for population growth and persistence. (c1, Fig. 6, drop strategies of burning half the habitat ev- Given that these numbers are based on biologically sim- ery 1, 2, or 3 years), leaving five acceptable strategies. ple models, however, it is not clear that precise num- Thus, although the “best” strategies varied with our as- bers will give us a clear prediction of the butterfly’s ac- sumption about habitat recovery, several strategies tual future population dynamics. On the other hand, were acceptable regardless of assumption of habitat dy- improved understanding of habitat dynamics for sev- namics. eral years after burning will improve our estimates of Incorporating our uncertainty about the data into the the relative merits of different management strategies analysis emphasizes how little we know about actual (Fig. 7), which are under our control and therefore more “probability of persistence” for the Fender’s blue under important to understand. Interestingly, this kind of different management strategies (Fig. 6). Long inter- long-term recovery data is noticeably absent from the burn intervals became unacceptable as parameters were literature on burning for management. set to more pessimistic values. In addition, if parame- Finally, we suggest that designing experiments to ex- ters such as larva-adult survivorship (s2) or maximum plore management strategies is different from manag- fecundity (c1 or c2) were close to our lower 90% confi- ing. Experiments should help sort out different man- dence intervals rather than the means, the outlook for agement options. In the case of the Fender’s blue at the Fender’s blue is grim. With these parameter esti- Baskett Butte, the relative merits of our 21 strategies de- mates, few strategies led to 95% of simulated butterfly pend most heavily on time-scale parameters such as populations surviving for 100 years. the length of time a burn affects the habitat and how

SEPTEMBER 1998 Restoration Ecology 251 Restoring Butterfly Habitat quickly weeds reinvade. Other issues have either been Collins, S. L., and D. J. Gibson. 1990. Effects of fire on community addressed through other studies (e.g., the initial effects structure in tall-grass and mixed-grass prairie. Pages 81–98 in of fire on the butterflies and characterizing butterfly S. L. Collins and L. L. Wallace, editors. Fire in North American tallgrass prairies. University of Oklahoma Press, Norman. dispersal) or, for the Fender’s blue, will not help us Edwards, A. W. F. 1972. Likelihood: an account of the statistical identify the relative benefits of different strategies (e.g., concept of likelihood and its application to scientific inference. autumn is the only potential burn season). Experiments Cambridge University Press, Cambridge, United Kingdom. that garner long-term data (3–6 post-treatment) will be Hammond, P. C. 1996. 1995 study of the Fender’s blue butterfly most helpful in differentiating alternative management (Icaricia icariodes fenderi) in Benton, Polk and Yamhill Coun- ties. Report to the U.S. Fish and Wildlife Service and the Ore- strategies. gon Natural Heritage Program, Portland, Oregon. Hammond, P. C. 1997. 1996 study of the Fender’s blue butterfly (Icaricia icariodes fenderi) in Benton, Polk and Yamhill Coun- Acknowledgments ties. Report to the U.S. Fish and Wildlife Service and the Ore- gon Natural Heritage Program, Portland, Oregon. We thank M. V. Wilson and D. L. Clark for providing Hammond, P. C., and M. V. Wilson. 1993. Status of the Fender’s experimental data for the study and P. Hammond for blue butterfly (Icaricia icariodes fenderi). Report to the U.S. Fish and Wildlife Service, Portland, Oregon. providing census data for the Fender’s blue. To obtain Hasting, M. S., and J. M. DiTomaso. 1996. Fire controls yellow star details on Wilson and Clark’s experiment, contact M. V. thistle in California grasslands: test plots at Sugarloaf Ridge Wilson at the Department of Botany and Plant Pathol- State Park. Restoration and Management Notes 14:124–128. ogy, Oregon State University, Corvallis, Oregon 97331, Hilborn, R., and M. Mangel. 1997. The ecological detective: con- U.S.A. The following people helped collect field data on fronting models with data. Princeton University Press, Prince- ton, New Jersey. the Fender’s blue at Baskett Butte: M. Bartels, S. Cross, Ingersoll, C. A., and M. V. Wilson. 1991. Restoration plans of a K. Dlugosh, C. Hartway, H. Lux, and S. Philpott. This western Oregon remnant prairie. Restoration and Manage- paper greatly benefited from the comments of E. Holmes, ment Notes 9:110–111. P. Kareiva, J. Kingsolver, L. Reed, G. Orians, D. Peter- Kendall, B. 1998. Estimating the magnitude of environmental son, M. V. Wilson, and a anonymous reviewer. Funding stochasticity in survivorship data. Ecological Applications 8: 184–193. for the experiment at Baskett Butte was provided by the Kuykendall, K., and T. Kaye. 1993. Lupinus sulphureus spp. kincai- U.S. Fish and Wildlife Service. C. Schultz was supported dii and reproductive studies. Report to the Bureau of Land by a National Science Foundation Training Grant in Management and the Oregon Department of Agriculture, Mathematical Biology (BIR 9256532), and E. Crone was Salem, Oregon. supported by a National Science Foundation postdoc- Ludwig, D. 1996. Uncertainty and the assessment of extinction probabilities. Ecological Applications 6:1067–1076. toral fellowship in Biosciences related to the Environ- Miller, W. E. 1979. Fire as an management tool. Entomolog- ment (BIR 9509451). ical Society Bulletin 25:147–150. Noss, R. F., E. T. LaRoe, III, and J. M. Scott. 1995. Endangered eco- systems of the United States: a preliminary assessment of LITERATURE CITED loss and degradation. Biological report 28, U.S. Department of the Interior, Washington, D.C. Agee, J. K. 1996. Achieving conservation biology objectives with Randall, J. M. 1996. Weed control for the preservation of biologi- fire in the Pacific Northwest. Weed Technology 10:417–421. cal diversity. Weed Technology 10:370–383. Anderson, R. C. 1990. The historic role of fire in the North Ameri- Schultz, C. B. 1996. Status of the Fender’s blue butterfly (Icaricia can grassland. Pages 8–18 in S. L. Collins and L. L. Wallace, icariodes feneri) in Lane County, Oregon: population ups and editors. Fire in North American tallgrass prairies. University downs. Report to U.S. Fish and Wildlife Service and the Ore- of Oklahoma Press, Norman. gon Natural Heritage Program, Portland, Oregon. Anonymous. 1996. Endangered and threatened wildlife and plants: Schultz, C. B. 1998. Dispersal and its implications for reserve de- review of plant and taxa that are candidates for listing sign in a rare Oregon butterfly. Conservation Biology 12: as threatened or endangered. Federal Register 61:7596–7613. 284–292. Caswell, H. 1989. Matrix population models: construction, analy- Warren, S. D., C. J. Scifres, and P. D. Teel. 1987. Response of grass- sis and interpretation. Sinauer Associates, Sunderland, Mas- land to burning: a review. Agriculture, Ecosys- sachusetts. tems and Environment 19:105–130.

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