Abstract

Florida scrub-jays Aphelocoma coerulescens are listed as threatened under the Endangered Species Act due to loss and degradation of scrub habitat. This study concerned the development of an optimal strategy for the restoration and management of scrub habitat at Merritt Island National Wildlife Refuge, which contains one of the few remaining large populations of scrub-jays in Florida. There are documented differences in the reproductive and survival rates of scrub-jays among discrete classes of scrub height (<120 cm or “short”; 120–170 cm or “optimal”; >170 cm or “tall”; and a combination of tall and optimal or “mixed”), and our objective was to calculate a state-dependent management strategy that would maximize the long-term growth rate of the resident scrub-jay population. We used aerial imagery with multistate Markov models to estimate annual transition probabilities among the four scrub-height classes under three possible management actions: scrub restoration (mechanical cutting followed by burning), a prescribed burn, or no intervention. A strategy prescribing the optimal management action for management units exhibiting different proportions of scrub-height classes was derived using dynamic programming. Scrub restoration was the optimal management action only in units dominated by mixed and tall scrub, and burning tended to be the optimal action for intermediate levels of short scrub. The optimal action was to do nothing when the amount of short scrub was greater than 30%, because short scrub mostly transitions to optimal height scrub (i.e., that state with the highest demographic success of scrub-jays) in the absence of intervention. Monte Carlo simulation of the optimal policy suggested that some form of management would be required every year. We note, however, that estimates of scrub-height transition probabilities were subject to several sources of uncertainty, and so we explored the management implications of alternative sets of transition probabilities. Generally, our analysis demonstrated the difficulty of managing for a species that requires midsuccessional habitat, and suggests that innovative management tools may be needed to help ensure the persistence of scrub-jays at Merritt Island National Wildlife Refuge. The development of a tailored monitoring program as a component of adaptive management could help reduce uncertainty about controlled and uncontrolled variation in transition probabilities of scrub-height and thus lead to improved decision making.

Introduction

The Florida scrub-jay Aphelocoma coerulescens (Figure 1) is an endemic species that is designated as threatened under the U.S. Endangered Species Act as amended (ESA 1973; Stith et al. 1996; Root 1998). Scrub-jays are restricted to Florida scrub (hereafter, just scrub), which is a rare habitat characterized by evergreen, xeromorphic shrubs including oaks, repent palms (Serenoa repens, Sabal etonia), and ericaceous shrubs (Lyonia spp., Vaccinium spp.; Foster and Schmalzer 2003). Scrub is maintained by frequent fire, and landscape fragmentation and fire suppression have resulted in many scrub communities that are no longer capable of supporting scrub-jay populations (Breininger and Carter 2003). Prescribed burning has thus become the primary management tool in reserves where the viability of scrub-jays and other scrub species is an important objective.

Scrub-jays at Merritt Island National Wildlife Refuge (hereafter Refuge) and adjacent government properties constitute one of the few remaining large populations within the species' shrinking range (Stith et al. 1996). The Refuge contains over 8,500 ha of oak scrub, but in 2005 only about 23% of this was considered in optimal condition for scrub-jays (Supplemental Material, Data S1; http://dx.doi.org/10.3996/012011-JFWM-003.S1). Little fire management occurred on the Refuge prior to 1981, when extensive wildfires prompted managers to accelerate a program of prescribed burning to reduce hazardous fuel loads (Adrian 2003). Since 1993 more emphasis has been placed on restoration and maintenance of wildlife habitat, but Refuge managers face constraints on the timing and location of burns due to the associated fire and smoke hazards to Kennedy Space Center, which is co-located with the Refuge. Neighboring cities, suburbs, and the Cape Canaveral Air Force Station provide additional constraints. Within these constraints, managers must decide what frequency of fire in a collection of management units will best ensure the long-term persistence of the Refuge's scrub-jay population. In addition, scrub sites with a long history of fire suppression first require restoration, which involves cutting of the scrub so it can be burned effectively (Schmalzer and Boyle 1998; Schmalzer et al. 2003). Decisions concerning restoration and prescribed burning are difficult because of an incomplete understanding of fire dynamics, plant community succession, and the demographic responses of scrub-jays to controlled and uncontrolled environmental factors.

The purpose of this study was to develop a formal decision analysis for the restoration and burning of scrub-jay habitat on the Refuge. The product of this decision analysis is a management policy that prescribes an optimal management action for potential habitat states and that effectively accounts for uncontrolled and unanticipated changes in habitat condition. We also explore how uncertainty in the mean response of scrub habitat to management actions can affect the state-dependent management strategy. Finally, we propose methods and programmatic elements necessary to reduce these uncertainties so that management performance can be improved over time.

A decision-theoretic approach

Formal methods of decision making in natural resource management combine dynamic models of an ecological system with an objective function, which values the outcomes of alternative management actions. A common decision-making problem involves a temporal sequence of decisions, where the optimal action at each decision point may depend on time, system state, or both (Possingham 1997). The goal of the manager is to develop a decision rule (or management policy) that prescribes management actions for each time or system state that are optimal with respect to the objective function. Examples of this kind of decision problem include direct manipulation of plant or animal populations through harvesting, stocking, or transplanting, as well as indirect population management through manipulation of habitat. Often, these problems also have a spatial aspect, wherein management decisions are required simultaneously at different locations.

A formal analysis of such decision problems requires specification of 1) an objective function for evaluating alternative management policies; 2) predictive models of system dynamics, formulated in quantities relevant to the stated management objectives; 3) a finite set of alternative management actions, including any constraints on their use; and 4) a monitoring program to follow the system's evolution and responses to management. The objective function specifies the value of alternative management actions and usually accounts for benefits and costs, as well as conditional constraints. The predictive models must be realistic enough to mimic the relevant behaviors of ecological systems, which often are complex (i.e., include many interacting components), nonlinear, and characterized by spatial, temporal, and organizational heterogeneity. Thus, specification of an objective function and of useful system models can be a demanding and difficult task in applications of decision theory to resource-management problems.

Another challenge is the need to explicitly account for uncertainty in the predictions of management outcomes. This uncertainty may stem from incomplete control of management actions, errors in measurement and sampling of ecological systems, environmental variability, and incomplete knowledge of system behavior (Williams et al. 1996). A failure to recognize and account for these sources of uncertainty can significantly depress management performance and, in some cases, lead to severe environmental and economic losses (Ludwig et al. 1993).

Accordingly, there has been a growing interest in the theory of stochastic decision processes and in practical methods for deriving optimal management policies (Hilborn 1987; Williams 1989; Puterman 1994; Williams 2001). There also has been an increasing emphasis on methods that can account for uncertainty about the dynamics of ecological systems and their responses to both controlled and uncontrolled factors (Walters 1986; Williams 2011). This uncertainty can be characterized by continuous or discrete probability distributions of model parameters, or by discrete distributions of alternative model forms, which are hypothesized or estimated from historic data (e.g., Walters and Hilborn 1978; Johnson et al. 1997). An important conceptual advance has been the recognition that these probability distributions are not static but evolve over time as new observations of system behaviors are accumulated from the management process (Walters 1986; Williams 2011). The popular notion of adaptive resource management involves efforts to account for the dynamics of uncertainty in making management decisions (Walters 1986; Williams et al. 1996; Walters and Holling 1990; Williams 2001; Allen et al. 2011).

Problem formulation

We characterized the problem of scrub-jay habitat management at the Refuge as a sequential-decision problem consisting of the following generic elements (Puterman 1994):

  • a set of decision epochs (i.e., a time horizon with regularly spaced decision intervals);

  • a set of system states;

  • a set of available management actions;

  • state and action dependent habitat transitions; and

  • state and action dependent returns.

If system dynamics can be described as Markovian (i.e., habitat transitions depend only on current system state and action and not on states or actions in the past), an optimal, state-dependent management policy can be calculated using dynamic programming (Bellman 1957; Walters and Hilborn 1978; Williams 1989). Dynamic programming provides a solution to a Markov decision process that is consistent with the Principle of Optimality (Bellman 1957), which states that

An optimal policy has the property that, whatever the initial state and decision are, the remaining decisions must constitute an optimal policy with regard to the state resulting from the first decision.

Thus, a key advantage of dynamic programming is its ability to produce a feedback policy, which is one that specifies an optimal decision for each possible future system state rather than state-specific decisions for expected future states (Walters and Hilborn 1978). Although dynamic programming is not practicable for problems of high dimension (nor for systems in which the dynamics are non-Markovian), it has been used successfully to address an array of conservation issues (e.g., Richards et al. 1999; McCarthy et al. 2001; Tenhumberg et al. 2004; Moore and Conroy 2006). Generalized software for dynamic programming, based on the C++ programming language, was developed by Lubow (1995). We used this public-domain software, called SDP, to derive optimal solutions for scrub-jay habitat management at the Refuge.

Decision Epochs, System States, and Management Actions

We assumed Refuge managers are faced with making annual decisions, although the analytical framework is general and could easily accommodate decisions made with a different frequency. For the purpose of calculating optimal policies we arbitrarily specified a 200-y time horizon, although we found much shorter time horizons were sufficient for deriving stationary policies. Stationary policies are those in which decisions depend only on the state of the system and not on the decision epoch (Puterman 1994).

Of the many scrub attributes affecting scrub-jay demography (Breininger et al. 1998), perhaps the most important is scrub height (Breininger et al. 1995; Breininger and Carter 2003). Following the classification scheme of Breininger and Carter (2003), we classified scrub height less than 120 cm as short (S), 120–170 cm as optimal (O), greater than 170 cm as tall (T), and a mix of tall and optimal as mixed (M). Optimal-height scrub acts as a reliable source habitat for jays, while short, tall, and mixed scrub always act as sinks (Breininger and Oddy 2004). System state was defined as the proportion of each scrub-height class in a single management unit. These proportions can be enumerated using the method of Breininger et al. (2010), in which a regular grid of square 10-ha plots is overlaid on low-level, color, high-resolution aerial photography of the management units. The dominant scrub height in each of the 10-ha plots is then classified. Plots 10 ha in size were used because they approximate the size of a scrub-jay breeding territory (Breininger et al. 1995). System state Xt for a management unit also included an indicator variable (0, 1) expressing whether the unit had ever been subject to scrub restoration.

Possible management actions were A ∈ {0  =  do nothing, 1  =  burn, 2  =  restore} in a given management unit characterized by system state Xt. We assumed prescribed burns would be conducted in a manner similar to those conducted on the Refuge during 2003–2005, and that restoration would involve mechanical cutting of all aboveground vegetation, followed by a prescribed burn within 6 mo (Schmalzer et al. 2003). We also assumed that a management unit can be burned in any year but can be restored only once in deference to the extraordinary cost associated with this management action. Otherwise, our analysis did not account for the differential costs of management actions, although they ultimately could be accommodated in a variety of ways (e.g., by recognizing a fixed budget for treating multiple management units in a single year).

State- and Action-Dependent Transitions

We restricted this study to 64 of the 137 extant management units at the Refuge (Figure 2). We selected these 64 management units by using the regular grid of 10-ha plots and by identifying those units that contained the centers of any plots classified by Breininger and Oddy (2004) as “primary” (principally oak) or “secondary” (principally oak and palmetto) scrub (Supplemental Material, Data S2; http://dx.doi.org/10.3996/012011-JFWM-003.S2). Transitions of scrub-height classes were estimated based on low-level, high-resolution aerial imagery acquired by Brevard County in December 2003 and February 2005 and from records of prescribed burns conducted from January 2004 to January 2005 inclusive. Of the 64 management units, 10 were burned by Refuge managers during the interval between December 2003 and February 2005, providing 367 10-ha plots for estimating scrub transition probabilities (ψ) associated with a unit burn (Table 1). Within the remaining 54 management units that were not burned, 1,322 10-ha plots of scrub were available for analysis.

Figure 1.

Florida scrub-jay Aphelocoma coerulescens on Merritt Island National Wildlife Refuge. Photo by David R. Breininger.

Figure 1.

Florida scrub-jay Aphelocoma coerulescens on Merritt Island National Wildlife Refuge. Photo by David R. Breininger.

We estimated habitat-state transition probabilities using a multistate, capture–recapture model (Williams et al. 2002) implemented in the public domain software MARK (White and Burnham 1999). For both burned and unburned units, the total number of 10-ha plots exhibiting various “capture” histories was tallied (in this case, pair-wise combinations of successive scrub heights). Detection probabilities and “survival rates” were fixed at 1.0 (i.e., transitions were completely observable and the number of plots was constant over time) to obtain estimates of transition probabilities. We assumed that transitions in 10-ha plots were independent of transitions in other plots. Our approach to modeling habitat dynamics is easily implemented in program MARK and provides maximum-likelihood estimates of transition probabilities and associated sampling variances (see Breininger et al. 2010).

A transition probability ψ is the probability that scrub in a particular height class in year t will transition to one of the four height classes in year t + 1. We estimated scrub transitions for the do-nothing alternative at  =  0 as

 
formula

The corresponding matrix of standard errors was

 
formula

So, for example, in the absence of management intervention 38% of short scrub is expected to remain short 1 y later, while proportions of 52% and 10% are expected to transition to optimal and mixed height, respectively. Standard errors of the transition probabilities were relatively small, reflecting the relatively large number of sample plots that were part of management units not receiving a prescribed burn. Based on the set of transition probabilities, complete suppression of fire would eventually result in a system characterized by 91.9% mixed and 8.1% tall scrub, which is the composition derived in the same manner as the asymptotic stable-stage distribution predicted from a population projection matrix (Caswell 2001). The matrix of transition probabilities has a damping ratio (Caswell 2001) of 1.03, suggesting relatively slow convergence to the stable stage distribution. The rate of successional change can be described by the turnover time of a particular scrub-height class and is defined as the reciprocal of the probability of transitioning out of that height class (Hill et al. 2004): τi  =  (1 − ψii)−1. The estimated turnover time of optimal-height scrub is only 3.7 y, confirming that, absent disturbance, good habitat for scrub-jays is remarkably ephemeral.

A transition probability under the burn alternative (at  =  1) is a confounded product of the probability that a plot actually burned conditional on a management-unit burn and the probability of a height-class transition given that the plot burned. Therefore, estimated transition probabilities account for incomplete control over fire. We estimated the transition probabilities for a prescribed burn as

 
formula

The corresponding matrix of standard errors was

 
formula

Notice that a prescribed burn in a management unit appears to be relatively ineffective at returning mixed and tall scrub to shorter scrub classes, and that it is only partially effective in maintaining short and optimal-height scrub. Note also that the standard errors of the transition probabilities with a prescribed burn are generally much higher than those for the do-nothing action, reflecting the smaller sample size than that available for the do-nothing action. Based on the estimated transition probabilities associated with a prescribed burn, the system would eventually be comprised of 12.6% short, 14.7% optimal, 67.9% mixed, and 4.8% tall if it was burned every year.

The transition probabilities associated with the restoration alternative (at  =  2) were

 
formula

Restoration transition probabilities were not estimated but assumed given that mechanical cutting is under complete control of the manager. Also, recall that a management unit can be restored only once, after which time only the do-nothing and burn actions are available to the manager.

State- and Action-Dependent Returns

To specify management returns, we relied on published estimates of average survival (s) and recruitment (r) rates of scrub-jays in varying scrub-height classes (Breininger and Carter 2003) and then used these values to calculate potential, scrub-height-specific population growth rates as λ  =  s + r. We used breeder survival rates of 0.70, 0.86, 0.76, and 0.76 in short, optimal, mixed, and tall scrub, respectively. Corresponding rates of recruitment were 0.035, 0.270, 0.115, 0.09, which were derived from the published estimates based on an assumption of an even sex ratio of yearlings (Woolfenden and Fitzpatrick 1984). Thus, the resulting population growth rates for scrub-jays in each scrub-height class were λS  =  0.735, λO  =  1.130, λM  =  0.875, and λT  =  0.850.

To account for the presence of multiple scrub-heights within a management unit, we predicted the composite population growth rate of scrub-jays as

 
formula

where S, O, M, and T are the proportions of short, optimal, mixed, and tall 10-ha plots, respectively. This formulation of the composite population growth rate specifies the potential response by scrub-jays to habitat conditions 1 y following a management action. Using the scrub-height–specific population growth rates, the minimum proportion (p) of optimal-height scrub required in a management unit to prevent a decline in scrub-jay abundance can be calculated using

 
formula

which in our case yields p  =  0.49.

We specified a management objective to maximize the population growth rate of scrub-jays (λ) in a management unit over the entire time horizon (τ):

 
formula

where V* is the value of the optimal state and time dependent policy (At|Xt). Although state-specific population growth rates of scrub-jays are subject to temporal variation (Breininger and Carter 2003), this variation could be ignored in the calculation of an optimal policy because population growth rates did not influence habitat dynamics.

This framing of the Markov decision problem incorporates a number of simplifying assumptions:

  • the number of scrub-jay territories in each scrub-height class is proportional to the number of 10-ha plots in each scrub class (i.e., the habitat in a management unit is fully occupied by scrub-jays and territories are uniform in size);

  • scrub-jay responses to habitat changes can be adequately characterized by fixed growth rates associated with varying scrub-height classes; and

  • there is no density-dependent response in population growth.

We also assumed that management actions can only be implemented at the level of a management unit and that habitat dynamics are homogeneous among management units. Future work will focus on relaxing these assumptions.

Optimal management strategy

The optimal management policy was nearly stationary (i.e., no time dependence) after 25 time steps, and appeared to be completely stationary by the 200th time step. Assuming that the optimal management policy was followed, we would expect the average annual growth rate of the scrub-jay population to be λ  =  0.8914. This compares with an expected λ  =  0.8730 with no management and λ  =  0.8905 under a management regime in which burning is conducted every year. The average annual growth rate expected under the current management regime of burning about every 4 y is 0.8802. Thus, a long-term decline in scrub-jay abundance is predicted under any of these management regimes. Taken at face value, these results suggest that management actions other than restoration or prescribed burning of whole management units may be needed to ensure the persistence of scrub-jays.

Based on the optimal policy, the best management action is to do nothing whenever units contain 30% or more short scrub, regardless of whether the unit has been previously restored or not. On the other hand, when the unit contains no short scrub, restoration or prescribed burning is always optimal regardless of the proportions of the other scrub classes (Figure 3). In these cases, however, the choice of action depends on whether the unit has been previously restored. In restored units with no short scrub, the optimal action is to burn regardless of the amount of the other scrub classes. On unrestored sites with no short scrub, the optimal action is to burn whenever the proportion of optimal scrub is 20% or greater. When the amount of optimal-height scrub is less than 20%, the prescription to restore or burn the unit depends on the amounts of mixed and tall scrub; more tall scrub increases the chances that restoration is the optimal action. When intermediate proportions of short scrub (i.e., 10 and 20%) are present, there is greater variation in the state-dependent actions. When the amount of short scrub is 10%, the optimal action in previously restored units is to burn regardless of other scrub states. On unrestored sites, burning is optimal only if the amount of optimal scrub is 20% or more. If the amount of optimal-height scrub is less than 20%, the best action depends on the amounts of optimal, mixed, and tall scrub. In management units with 20% short scrub, the optimal action is to burn both restored and unrestored sites whenever the amount of optimal-height scrub is 50–60%. Otherwise, the optimal management action tends to be do-nothing for all states except where the amount of tall scrub is very high in unrestored sites (in which case, restoration is the optimal action).

Figure 2.

Management units (all polygons) at Merritt Island National Wildlife Refuge in Florida that were used (polygons with white outlines) to investigate the dynamics of Florida scrub-jays Aphelocoma coerulescens, which are listed as threatened under the Endangered Species Act, in response to prescribed burning.

Figure 2.

Management units (all polygons) at Merritt Island National Wildlife Refuge in Florida that were used (polygons with white outlines) to investigate the dynamics of Florida scrub-jays Aphelocoma coerulescens, which are listed as threatened under the Endangered Species Act, in response to prescribed burning.

To summarize, restoration is the optimal action only under a small range of scrub states due to the short-term sacrifice in scrub-jay growth rates associated with a management unit that contains 100% short scrub. Burning tends to be the optimal action at low levels of short scrub on both restored and unrestored sites. Presumably this helps maintain a temporal stream of optimal-height scrub, while avoiding the mixed and tall states that are difficult to return to short through burning. Finally, the optimal action is usually to do nothing whenever the amount of short scrub is 20% or more, regardless of the composition of the other scrub classes and whether the unit was previously restored or not. The likely reason for this pattern is that short scrub mostly transitions to optimal-height scrub in the absence of any intervention.

We simulated the optimal policy for a 200-y time horizon using an unrestored management unit consisting of 100% tall scrub as the initial state. The optimal decision was to restore the unit the first year and then to burn the unit every year after year 10. This is the reason that the optimal policy and a policy of burning every year predicted similar population growth rates of scrub-jays. The amount of optimal-height scrub in the simulation stabilized at 14.7%, far less than the 49% required to prevent a decline in scrub-jay abundance. We attribute this result to the ineffectiveness of prescribed burning as indicated by the estimated transition probabilities and by the one-time constraint on restoration.

Uncertainty concerning scrub transitions

The apparent ineffectiveness of prescribed burning for maintaining optimal scrub height is cause for concern, and so we were interested in whether more optimistic scenarios were plausible, given the sampling variation associated with our transition probability estimates. To that end, we investigated the implications of more effective burning by substituting the 90th percentiles for the probabilities of scrub height transitioning to short in the matrix of transition probabilities for the burn action. The 90th percentiles were derived from beta distributions, in which the shape and scale parameters were calculated by the method of moments using the estimated means and variances of short, optimal, mixed, and tall transitions at time t to short at time t + 1. Because the columns of the transition matrix must sum to one, we reduced the probabilities of transition to classes other than short using the proportional compensation method described by Caswell (2001). The nominal and alternative burn matrices, respectively, are provided below for comparison:

 
formula
 
formula

As can be seen from comparing the first row of the two matrices, the alternative burn matrix posits that a burn is more effective at setting back succession, which is periodically essential for providing optimal-height scrub (because mixed and tall scrub do not transition to the shorter scrub classes without a burn).

The optimal policy associated with the alternative burn matrix is similar to that using the nominal burn matrix, except that the do-nothing action is the optimal action whenever the amount of short scrub is greater than 10% compared with greater than 20% using the nominal matrix (Figure 4). This result is born out in simulations, which suggest the frequency of years requiring a prescribed burn would be reduced from 98 to 63%. However, simulations also suggested that the average amount of optimal-height scrub would be 12.9%, which is slightly less than the 14.7% expected using the nominal burn matrix. Accordingly, the expected population growth rate of scrub-jays associated with the policy using the alternative burn matrix is λ  =  0.8878 compared with λ  =  0.8914 using the nominal burn matrix. That the difference is so small is likely a result of the extreme persistence of mixed and tall scrub reflected even in the alternative burn matrix.

Figure 3.

Optimal management actions (0  =  do nothing, 1  =  burn, 2  =  restore) to maximize population growth of Florida scrub-jays Aphelocoma coerulescens for varying proportions of scrub-height classes on unrestored and previously restored sites, based on empirical estimates of scrub-height transition probabilities. The abscissa in each graph represents the proportion of optimal-height scrub, and the ordinate represent the proportion of mixed-height scrub. The proportion of short scrub is fixed at the proportion labeled in each graph. The proportion of tall scrub is not shown explicitly but can be derived by subtraction.

Figure 3.

Optimal management actions (0  =  do nothing, 1  =  burn, 2  =  restore) to maximize population growth of Florida scrub-jays Aphelocoma coerulescens for varying proportions of scrub-height classes on unrestored and previously restored sites, based on empirical estimates of scrub-height transition probabilities. The abscissa in each graph represents the proportion of optimal-height scrub, and the ordinate represent the proportion of mixed-height scrub. The proportion of short scrub is fixed at the proportion labeled in each graph. The proportion of tall scrub is not shown explicitly but can be derived by subtraction.

A second source of uncertainty concerns the effects of scrub restoration. Schmalzer et al. (2003) reported that restoration involving mechanical clearing and then burning of long unburned scrub resulted in an increase in the rate at which scrub grew in height and also reduced the cover of saw palmetto Serenoa repens (thus, reducing the flammability of the landscape). These effects persisted at least 7 y post-restoration (the length of the study). Therefore, we posed these effects as an alternative model for scrub-class transitions following restoration. For the do-nothing action, we assumed that succession of short and optimal-height scrub proceeded at a rate 75% greater than that under the null model. This rate is consistent with the most extreme findings of Schmalzer et al. (2003). We assumed no difference in the transitions for mixed and tall scrub because the empirical estimates under the null model indicated rapidly absorbing states. Thus, the alternative post-restoration transitions for the do-nothing action are

 
formula

For the burn action, we assumed that post-restoration fires are less effective at returning all scrub classes to lower succession states. Although we had no empirical data upon which to base these transitions, our hypothesized rates appear to be reasonable in light of the transitions for the do-nothing and burn actions under the null model, and the assumed reduction in flammability following a restoration event is

 
formula

Under the alternative model, restoration is no longer optimal for any scrub-class configuration of an unrestored site (Figure 5). Burning is always optimal on both restored and unrestored sites whenever there is no short scrub, regardless of the composition of other the scrub classes. When the amount of short scrub is 30% or more, the optimal action is to do nothing on unrestored sites (same as the null model), but on restored sites burning can be the best action even when the amount of short scrub is very high. Presumably, this is due to the more rapid succession of scrub on restored sites. For intermediate levels of short scrub, the optimal, state-dependent actions tend to be similar to those under the null model, except that burning is the optimal action for more scrub states than under the null model.

Figure 4.

Optimal management actions (0  =  do nothing, 1  =  burn, 2  =  restore) to maximize population growth of Florida scrub-jays Aphelocoma coerulescens for varying proportions of scrub-height classes on unrestored and previously restored sites, using a model that posits greater effectiveness of prescribed burns than that implied by the empirical estimates of scrub-height transition probabilities. The abscissa in each graph represents the proportion of optimal-height scrub, and the ordinate represent the proportion of mixed-height scrub. The proportion of short scrub is fixed at the proportion labeled in each graph. The proportion of tall scrub is not shown explicitly, but can be derived by subtraction.

Figure 4.

Optimal management actions (0  =  do nothing, 1  =  burn, 2  =  restore) to maximize population growth of Florida scrub-jays Aphelocoma coerulescens for varying proportions of scrub-height classes on unrestored and previously restored sites, using a model that posits greater effectiveness of prescribed burns than that implied by the empirical estimates of scrub-height transition probabilities. The abscissa in each graph represents the proportion of optimal-height scrub, and the ordinate represent the proportion of mixed-height scrub. The proportion of short scrub is fixed at the proportion labeled in each graph. The proportion of tall scrub is not shown explicitly, but can be derived by subtraction.

Figure 5.

Optimal management actions (0 = do nothing, 1 = burn, 2 = restore) to maximize population growth of Florida scrubjays Aphelocoma coerulescens or varying proportions of scrub-height classes on unrestored and previously restored sites, using an alternative model that posits faster scrub growth and reduced landscape flammability following scrub restoration than that implied by the empirical estimates of scrub-height transition probabilities. The abscissa in each graph represents the proportion of optimalheight scrub, and the ordinate represents the proportion of mixed-height scrub. The proportion of short scrub is fixed at the proportion labeled in each graph. The proportion of tall scrub is not shown explicitly but can be derived by subtraction.

Figure 5.

Optimal management actions (0 = do nothing, 1 = burn, 2 = restore) to maximize population growth of Florida scrubjays Aphelocoma coerulescens or varying proportions of scrub-height classes on unrestored and previously restored sites, using an alternative model that posits faster scrub growth and reduced landscape flammability following scrub restoration than that implied by the empirical estimates of scrub-height transition probabilities. The abscissa in each graph represents the proportion of optimalheight scrub, and the ordinate represents the proportion of mixed-height scrub. The proportion of short scrub is fixed at the proportion labeled in each graph. The proportion of tall scrub is not shown explicitly but can be derived by subtraction.

Under the alternative model, the expected population growth rate of scrub-jays is λ  =  0.8914 for unrestored sites (the same as under the null model) and λ  =  0.8790 for restored sites. Restored and unrestored sites exhibit different population growth rates of scrub-jays because, unlike the null model, we assumed that once a site is restored it permanently assumes different transition probabilities for the do-nothing and burn actions.

Discussion

The structured approach to decision analysis described herein led to a number of interesting insights and provides a useful first step in the development of an improved habitat-management program for scrub-jays at the Refuge. Our analysis clarified the difficulties associated with ensuring the persistence of a species that requires midsuccessional habitat. Such habitat is transient by definition, and maintenance of adequate amounts of such habitat may be very difficult. This difficulty points to another important message of this analysis—that effectiveness of management may be much more limited than is appreciated or recognized. Without explicit models of habitat transition probabilities associated with different management actions, we could not ask whether even optimal management is capable of accomplishing management objectives. Such recognition of the limits of current management actions is important and is not an uncommon outcome of serious decision analysis (e.g., see Martin et al. 2011). This recognition should prompt managers to think hard about developing new approaches to habitat and/or scrub-jay management that at least have the potential to achieve management objectives.

It is nonetheless important to recognize that estimated transition probabilities were subject to several sources of uncertainty, and thus far we have only explored the implications of a small subset of alternatives. In particular, we had no measures of temporal or spatial variability in management effects, and an explicit accounting of such variability may be important in predicting scrub-jay population growth rates and calculating optimal policies. That said, our analyses generally supported the conclusion that prescribed burning as practiced by the Refuge was relatively ineffective at setting back succession, particularly in the taller scrub classes. Moreover, Refuge managers typically scheduled a prescribed burn about every 4 y in the management units examined for this study. This is slightly longer than the estimated turnover time of optimal scrub of 3.7 y, suggesting that more frequent fires may indeed be beneficial, especially given the apparent limitations of prescribed burning.

More effective habitat management at the Refuge may also depend on a better understanding of the spatial dynamics of fire within a management unit. For this study we estimated scrub-class transitions at a scale of 10 ha, but for a collection of 10-ha plots in a unit that was subject to a prescribed burn or not. Shao and Duncan (2007) developed a remote-sensing protocol for mapping fire scars at the Refuge from LANDSAT satellite imagery, and the resulting fire-scar maps can be used to determine which 10-ha plots actually carried a fire and thus to better understand how fire spreads in a unit as a function of various environmental conditions. Based on application of this protocol, it is clear that management units did not burn uniformly and at least some of the 10-ha plots in burned units escaped fire altogether (Duncan et al. 2009). This is probably part of the reason there were not dramatic differences in the transition probabilities for scrub in burned and unburned units. Therefore, we suggest that incorporation of this remote-sensing protocol in a tailored monitoring program could help reduce uncertainty about the spatial dynamics of fire and thus provide an important component of an adaptive approach to decision making.

A limitation of this study was the reliance on fixed measures of scrub-jay fitness in different scrub-height classes. Although differences in scrub-jay fitness as a function of scrub height are well documented (e.g., Breininger and Carter 2003), there currently is no inexpensive way of evaluating whether these differences would be realized as a function of the management policies described herein. Merritt Island National Wildlife Refuge conducted a Refuge-wide scrub-jay survey based on point counts during 1999–2006, and we initially hoped that it could provide a basis for measuring scrub-jay responses to management. However, an evaluation of the survey (Johnson et al. 2006; Supplemental Material, Report S1; http://dx.doi.org/10.3996/012011-JFWM-003.S3) suggested that it could not be conducted intensively enough to monitor scrub-jay responses at the scale of a management unit. Ecologically significant, Refuge-wide changes in scrub-jay abundance might be detectable, but it's not clear how sensitive these changes might be to the cumulative effect of habitat changes occurring at a relatively small scale. A scrub-jay response variable that is sensitive to small-scale changes in habitat would be most efficient for the purposes of learning about the effects of management and, thus, for improving future management decisions. We are currently working on development of an approach to modeling and inference that includes scrub-jay occupancy as a state variable.

Finally, we wish to impress upon the reader that alternative formulations of the decision problem are possible and ultimately may be necessary to ensure the persistence of scrub-jays and other midsuccessional scrub species at the Refuge. For example, the current formulation may not embody a sufficient characterization of key habitat attributes. The demographic performance of scrub-jays depends on a host of other factors besides scrub height, including the presence of sandy openings for caching acorns and a lack of tall trees that are used as roosts by predatory hawks (Breininger et al. 1998). Also, spatial dependence among units in scrub-jay response is likely, but accounting for it will require a better understanding of scrub-jay distribution and dispersal in response to habitat change. Spatial dependence greatly increases the complexity of the optimization problem, such that it would not be feasible to compute management strategies using dynamic programming. Quasi-optimization methods, such as reinforcement learning (Fonnesbeck 2005), would be necessary to deal effectively with this increased level of complexity. Lastly, other management actions may be feasible (e.g., selective cutting within management units), but the costs of (and constraints on) all management actions will eventually need to be considered as well.

Since we conducted our analyses, the Refuge has taken a much more aggressive approach to the problem of managing scrub-jay habitat. New aerial imagery has been acquired that will allow a better understanding of scrub transition probabilities and associated sources of variation. The Refuge, in collaboration with one of the authors of this article, has intensified and expanded efforts to monitor the demography of scrub-jays in response to management activities. Finally, and perhaps most importantly, the Refuge has begun to explore innovative management techniques for setting back succession in tall scrub and for ensuring that scrub-jay habitat requirements beyond proper scrub height are achieved and sustained. Thus, our decision analysis effectively promoted double-loop learning (Lee 1993), in which the basic elements of adaptive management (objectives, actions, predictive models, monitoring) are periodically revisited and revised to more effectively address conservation goals.

Table 1.

The number of 10-ha plots on Merritt Island National Wildlife Refuge of the specified height of Florida scrub-jays Aphelocoma coerulescens, which are listed as threatened under the Endangered Species Act, that were observed to make various transitions in height, depending on whether the associated management unit was burned in the interval 2004–2005. Scrub height was short, less than 120 cm; optimal, 120–170 cm; tall, greater than 170 cm; or mixed, a mix of tall and optimal.

The number of 10-ha plots on Merritt Island National Wildlife Refuge of the specified height of Florida scrub-jays Aphelocoma coerulescens, which are listed as threatened under the Endangered Species Act, that were observed to make various transitions in height, depending on whether the associated management unit was burned in the interval 2004–2005. Scrub height was short, less than 120 cm; optimal, 120–170 cm; tall, greater than 170 cm; or mixed, a mix of tall and optimal.
The number of 10-ha plots on Merritt Island National Wildlife Refuge of the specified height of Florida scrub-jays Aphelocoma coerulescens, which are listed as threatened under the Endangered Species Act, that were observed to make various transitions in height, depending on whether the associated management unit was burned in the interval 2004–2005. Scrub height was short, less than 120 cm; optimal, 120–170 cm; tall, greater than 170 cm; or mixed, a mix of tall and optimal.

Supplemental Material

Please note: The Journal of Fish and Wildlife Management is not responsible for the content or functionality of any supplemental material. Queries should be directed to the corresponding author for the article.

Data S1. Breininger DR. (n.d.) Classification of scrub height at Merritt Island National Wildlife Refuge, Florida. Orsino, Florida: Innovative Health Applications. Unpublished data.

Found at DOI: http://dx.doi.org/10.3996/012011-JFWM-003.S1 (24 KB XLSX).

Data S2. ArcView shapefiles for management units and habitat classification for Florida scrub-jays at Merritt Island National Wildlife Refuge. The metadata.txt file provides the attributes of the data. Map datum is State Plane NAD83 Meters Florida Zone 0901.

Found at DOI: http://dx.doi.org/10.3996/012011-JFWM-003.S2 (252 KB ZIP).

Report S1. Johnson FA, Beech T, Dorazio RM, Epstein M, Lyon J. 2006. Abundance and detection probabilities of Florida scrubjays at Merritt Island National Wildlife Refuge, Florida, using spatially replicated counts. Gainesville, Florida: U.S. Fish and Wildlife Service. Unpublished report.

Found at DOI: http://dx.doi.org/10.3996/012011-JFWM-003.S3 (572 KB PDF).

Acknowledgments

We are grateful to U.S. Fish and Wildlife Service staff, especially M. Epstein, R. Hight, C. Hunter, and M. Legare, who encouraged us to explore the potential use of adaptive management to help ensure the persistence of Florida scrub-jays at Merritt Island National Wildlife Refuge. This study was funded by the U.S. Fish and Wildlife Service, the U.S. Geological Survey, and the National Aeronautics and Space Administration. Any use of trade, product, or firm names in this article is for descriptive purposes only and does not imply endorsement by the U.S. Government.

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Author notes

Fred A. Johnson,* David R. Breininger, Brean W. Duncan, James D. Nichols, Michael C. Runge, B. Ken Williams

Johnson FA, Breininger DR, Duncan BW, Nichols JD, Runge MC, Williams BK. 2011. A Markov decision process for managing habitat for Florida scrub-jays. Journal of Fish and Wildlife Management 2(2):234–246; e1944-687X. doi: 10.3996/012011-JFWM-003

The findings and conclusions in this article are those of the author(s) and do not necessarily represent the views of the U.S. Fish and Wildlife Service.