Should Habitat Trading Be Based on Mitigation Ratios Derived from Landscape Indices? A Model-Based Analysis of Compensatory Restoration Options for the Red-Cockaded Woodpecker

Abstract

Many species of conservation concern are spatially structured and require dispersal to be persistent. For such species, altering the distribution of suitable habitats on the landscape can affect population dynamics in ways that are difficult to predict from simple models. We argue that for such species, individual-based and spatially explicit population models (SEPMs) should be used to determine appropriate levels of off-site restoration to compensate for on-site loss of ecologic resources. Such approaches are necessary when interactions between biologic processes occur at different spatial scales (i.e., local [recruitment] and landscape [migration]). The sites of restoration and habitat loss may be linked to each other, but, more importantly, they may be linked to other resources in the landscape by regional biologic processes, primarily migration. The common management approach for determining appropriate levels of off-site restoration is to derive mitigation ratios based on best professional judgment or pre-existing data. Mitigation ratios assume that the ecologic benefits at the site of restoration are independent of the ecologic costs at the site of habitat loss. Using an SEPM for endangered red-cockaded woodpeckers, we show that the spatial configuration of habitat restoration can simultaneously influence both the rate of recruitment within breeding groups and the rate of migration among groups, implying that simple mitigation ratios may be inadequate.

Appendix: Modeling RCW Dispersal

We used the equations and parameters described in Letcher and others (1998) to model probability of nesting, the probability of nest success, and the number of fledglings produced. The model is both age and stage structured, uses a seasonal time step (3 months per step), and assumes that biologic processes proceed in the following order: reproduction (season 1 only), mortality, natal dispersal, territorial competition, and then dispersal.

We assumed that all old-growth habitat cells in our landscape start with a breeding pair. Letcher’s model assumes that fecundity is only a function of the ages of male and female breeders and the number of helpers in a territory. The age of each breeder was randomly chosen from a normal distribution with a mean of 4 (Reed and others 1988) and variance of 1. The average number of helpers observed in old-growth longleaf pine habitat, based on 2 years of observations, were 1 and 1.6 helpers per territory (Engstrom and Sanders 1997). We randomly selected half of the territories for the addition of two helpers.

The probability of an individual’s transition among life stages depends on the interaction between demography, behavior, and landscape spatial structure. The model assumed that all female fledglings surviving the first year became floaters or breeders but never helpers. Male RCWs stay as helpers approximately 81% of the time to gain access to breeding territories, either their territory or an adjacent territory (Letcher and others 1998). Walters and others (1988) observed that female RCWs remain as helpers on their natal territory only 1% of the time, usually dispersing to become floaters. When a helper takes over a territory after the male RCW’s death, >90% of the time the adult female RCW disperses to avoid inbreeding (Daniels and Walters 2000). If the male breeder dies, and no helpers are present, it has been observed that 83% of the time the female breeder remains in the territory and acquires a new mate (Daniels and Walters 2000).

The ability of birds to detect and acquire breeding vacancies will have a large impact on the persistence and population structure in a fragmented landscape. In absence of empiric estimates of a bird’s perceptual range, the model uses assumptions thought plausible by Letcher and others (1998), who assumed that all fledglings, helpers, floaters, and solitary male RCWs can compete for breeding vacancies within 3.5 km of their current location.

The alternative model describing the probability that male fledglings delay dispersal for the forest-based SEPM was based on the study by Pasinelli and Walters (2002). The simulation model already predicted the number of male fledglings within a brood and number of vacant territories within 3.5 km (5 cells, intercentroid distance). Relative nestling mass was excluded because no estimates for the variation in nestling mass within broods were available. Based on a Spearman rank correlation, relative nestling mass was not found to be correlated with any of the other independent variables (Pasinelli and Walters 2002); therefore, excluding this variable should not significantly bias model results. For territory quality, we assumed that all old-growth remnants were of equal quality, as estimated by average group size of 3.6 (Engstrom and Sanders 1997). We assumed that second-growth pine stands restored for RCWs are perceived by the birds has having an average group size of 2.6 (i.e., lower habitat quality), based on observations made in restored second-growth stands at the Apalachicola National Forest (James and others 2001). Therefore, the probability of male natal dispersal (P[D_m,nat]) can be estimated as (Eq. A1):

$$ P{\left[ {D_{{m,{\text{nat}}}} } \right]} = \frac{{e^{{d_{0} + d_{1} {\text{FL}}_{m} + d_{2} T_{{{\text{1km}}}} + d_{3} T_{{{\text{nat}}}} + d_{4} T_{{{\text{vac3km}}}} }} }} {{1 + e^{{d_{0} + d_{1} {\text{FL}}_{m} + d_{2} T_{{{\text{1km}}}} + d_{3} T_{{{\text{nat}}}} + d_{4} T_{{{\text{vac3km}}}} }} }}, $$

where FL_m is the number of male fledglings, T_1km is the number of territories in old-growth pine within 1 km of the natal territory, T_nat is the quality of the natal territory, and T_vac3km is the number of vacant territories within 3.5 km. Table A1 reports the parameter values fitted to the logit function by Pasinelli and Walters (2002). When this equation was incorporated into our model, unnaturally large number of helpers were retained within a territory (i.e., ≤10 helpers) when density of old-growth longleaf pine was high in the landscape. In the Sandhills Region, only 30% of groups contained at least 1 helper, and 5% of groups contained >1 helper, with 3 being the maximum number of helpers (Walters and others 1988). Although Pasinelli and Walters (2002) found that the number of adults within a group did not affect the probability of male RCW natal dispersal, they indicated that the maximum number of helpers observed in any RCW group is 4. The probability of male natal dispersal was calculated with the previous equation when <3 helpers are present but set to unity otherwise, which created a maximum of 4 helpers when habitat density was high. To more closely approximate Letcher’s SEPM, the random-straight model assumes the probability of male RCW natal dispersal is a constant equaling 0.19 (Letcher and others 1998).

After seasonal competition is completed, floating behaviors are modeled. Based on Pasinelli and Walters (2002), we assume that fledglings are aware of the forest structure within a 3.5-km radius of their natal territory, which will be referred to as their natal neighborhood. Therefore, we assume that birds choose their initial direction of travel based on the density of habitat at the edge of their natal or, for displaced female breeders, breeding neighborhood. If no habitat is found at the 3.5-km perimeter, the birds will orient to the greatest density of secondary growth. Therefore, the forest-based model assumed that both sexes choose their initial direction of travel during natal dispersal based on the direction providing the greatest density of RCW habitat. In contrast, the random-straight model assumed that birds choose their initial direction of travel at random, as included in Letcher and others (1998).

Dispersal speed for all female floaters averaged 4.8 km per season and for first year male floaters (natal dispersal) was estimated at 5.1 km per season (Letcher and others 1998). Our model assumes that all female RCWs and first year male floaters disperse 4.9 km per season (i.e., seven cells). Older male floaters on average moved 2.3 km per season (Letcher and others 1998). We assumed that male floaters move 2.12 km per season or (three cells). Each floater is allowed to compete for territorial vacancies in cells adjacent to its current location before taking the next step.

We assume that birds make directional choices based on either forest structure (Connor and Rudolph 1991), the tendency to disperse in a straight line (Letcher and others 1998), or a combination of both factors. Assuming that no vacancies exist, each of the eight adjacent cells is assigned a probability of occupancy based on plausible dispersal rules (Zollner and Lima 1999). We assigned four levels of preference to adjacent cells in which the first level was twice as attractive as the second, the second was 2.5 times as attractive as the third, and the third was 4 times as attractive as the fourth (Table A2). The level of preference assigned to each cell was based on two contrasting sets of rules for dispersal: straight versus forest based. If the birds show preference for straight movement, the model assigns four levels of preferences for the direction of travel in the next step based on the direction of travel in the previous time step (Table A2). If the birds choose their next step based on habitat quality in adjacent cells (forest based), the model recognizes four levels of habitat quality (Table A2). The values in Table A2 are assigned to the eight-cell neighborhood providing matrices V (straight) and HQ (forest-based). Both preferences assign a zero probability of a bird not moving, and the straight-dispersal approach prevents backward movement. The matrices are combined within the following equation to estimate the probability that the individual will move to each cell given its location in the previous time step (L_t) and surrounding forest structure (HQ) (Eq. A2):

$$ P[L_{{t + 1}} |L_{t} ,{\text{HQ}}] = d_{v} V + d_{{hq}} {\left( {{\text{HQ}}/{\sum {{\text{HQ}}} }} \right)}, $$

where d_v and d_hq are the (0 to 1) weighting factors assigned to each matrix (d_v + d_hq = 1). Matrix P[L_t+1|L_t,HQ] was transformed into cumulative probability distribution and compared with a u[0,1] random number to determine the bird’s location in the next time step. For the present analysis we constrained the model to simulate forest-based dispersal only, [d_v, d_hq] = [0, 1] or straight-dispersal, [d_v, d_hq] = [1, 0].

Table A1 Parameter values used to estimate probability of male natal dispersal (Eq. A1)^a

Table A2 Preferences assigned in alternative models of dispersal behaviors (Eq. A2)