Southeastern Naturalist E.A. Rigby and D.A. Haukos 2014 26 Vol. 13, Special Issue 5 A Matrix Population Model for Mottled Ducks (Anas fulvigula) of the Western Gulf Coast Elizabeth A. Rigby1,* and David A. Haukos2,3 Abstract - According to three surveys performed annually since the mid-late 1980s, the Anas fulvigula (Mottled Duck) population in Texas has declined substantially. Factors contributing to the observed trend are not well understood. Assessing the relative influence of vital rates on the population growth-rate is necessary to make management and conservation decisions regarding Mottled Ducks. We gathered estimates and associated variance estimates for vital rates of Mottled Ducks on the western Gulf Coast. We constructed a matrix population-model based on female vital rates and assumed birth-pulse reproduction, and parameterized it with a pre-breeding census. We calculated mean and standard error estimates for composite vital rates such as population growth rate (λ), fertility, and recruitment using 1000 iterations of the model. We also performed 20 meta-iterations of the population model to obtain mean coefficient of determination (r2) values for the linear regression of each vital rate and composite rates on λ. Overall λ was low, 0.541 (SE = 0.070). Fertility was also low, F = 0.071 (SE = 0.058). The elasticity analysis suggested that proportional changes in both fertility (r2 = 0.675) and survival (r2 = 0.322) played major roles in explaining the variation in λ. For the vital rates comprising F, breeding incidence (r2 = 0.270) and nest success (r2 = 0.200) explained the most variation in λ. Results indicated that the Mottled Duck population is in a steep decline, with low fertility and annual survival both influencing annual growth. We suggest targeting management efforts towards increasing adult survival, breeding incidence, and nest success for Mottled Ducks on the western Gulf Coast. Introduction Anas fulvigula Ridgway (Mottled Duck), a non-migratory dabbling duck species, is found along the western Gulf of Mexico coast from Veracruz, Mexico, to Alabama, as well as peninsular Florida (Bielefeld et al. 2010). Genetic evidence suggests that the species is made up of 2 genetically distinct populations: one on the western Gulf Coast (WGC; which includes Mexico, Texas, Louisiana, Alabama, and Mississippi) and one in Florida (McCracken et al. 2001, Williams et al. 2005). In addition to genetic separation, the Florida and the WGC populations of Mottled Ducks occupy disparate habitats and are separated by the boundaries of state and federal agencies (Bielefeld et al. 2010). The core of the WGC population resides in coastal marshes and associated habitats of the Chenier Plain of Texas and Louisiana, including agricultural lands used for rice cultivation (Haukos 2010). Johnson (2009) analyzed band-recovery data and hunter-returned age-ratio data from 1994–2006 to estimate finite annual growth rates (λ) based on annual fertility 1University of Minnesota, 135 Skok Hall, 2003 Uppper Buford Circle, St. Paul, MN 55108. 2USFWS, Department of Natural Resources Management, Texas Tech University, Box 42125, Lubbock, TX 79409-2125. 3Current address - Kansas State University, 205 Leasure Hall, Manahattan, KS 66506. *Corresponding author - elizabethrigby@gmail.com. Manuscript Editor: Clifford Shackelford Proceedings of the 5th Big Thicket Science Conference: Changing Landscapes and Changing Climate 2014 Southeastern Naturalist 13(Special Issue 5):26–40 Southeastern Naturalist 27 E.A. Rigby and D.A. Haukos 2014 Vol. 13, Special Issue 5 and survival estimates for Mottled Ducks. He found λ was considerably less than 1 for all age-sex cohorts for all environmental conditions during that time period (male geometric mean λ = 0.85 (range: 0.65–1.15), female geometric mean λ = 0.79 (range: 0.49–1.16)) (Johnson 2009). He concluded that the species was undergoing a dramatic population decline on the western Gulf Coast (Johnson 2009). However, Johnson (2009) used age-ratio in the harvest as an index to annual fertility and was therefore unable to evaluate the relative influence on λ of vital rates comprising fertility. He concluded that the survey that best reflects population trends of WGC Mottled Ducks in Texas is the breeding pair survey on national wildlife refuges (NWRs) conducted annually since 1985. The debate regarding WGC Mottled Duck population status is contentious: although several surveys are conducted annually, most data have been collected regionally. A range-wide annual breeding survey was established in 2010 and currently lacks sufficient data to estimate trends or document population change. The annual breeding-pair survey on Texas NWRs has been conducted since 1985 and consists of aerial counts adjusted with a visibility index derived from ground surveys (Haukos 2010). These data indicate a population peak for Mottled Ducks in the mid-1990s and a substantial decline since. The 2012 breeding pair survey estimated 1.04 Mottled Duck pairs/km2, which represents a decline of 65% from the 26-year long-term average of 3.38 pairs/km2 (USFWS 2013). This population decline in Texas is corroborated by other annual surveys. Texas NWRs also conduct aerial monthly winter surveys. The cumulative count for monthly surveys in winter 2006–2007 (the last reported survey season) was 6879—33% below the 22-year long-term average of 10,295 (USFWS 2013). Midwinter inventory (MWI) surveys count Mottled Ducks in both Texas and Louisiana and include areas outside of NWRs. The Texas MWI estimated 18,096 Mottled Ducks in surveyed coastal areas in 2012 (USFWS 2013). This represents a 62% decline from 1994 and a 30% decline from the 28-year long-term average, paralleling the NWR breeding pair survey (USFWS 2013). MWI trends in Louisiana have been flat or increasing, with a 0.8% annual increase as compared to a 2.7% annual decrease in Texas over the long term (USFWS 2013). Annual surveys only provide an index to Mottled Duck populations, and estimates of the entire WGC population vary widely, from 169,300 (Stutzenbaker 1988) to 630,000 (North American Waterfowl Management Plan 2004). Two intensive surveys have attempted to estimate the entire population. Ballard et al. (2001) estimated 220,000 (SE ≈ 52,500) Mottled Ducks in Texas during 1994–1995 using aerial circling surveys of a stratified sample of wetlands along the Texas Gulf Coast. This estimate likely represents a peak population, as it was conducted during the years when the Mottled Duck population peaked according to annual index surveys (Haukos 2010). An experimental range-wide survey was conducted in 2009–2012 using airplane surveys adjusted with a visibility correction factor derived from helicopter surveys on a subset of transects (USFWS 2013). In 2012, this survey estimated 164,745 (SE = 32,227) Mottled Ducks in Texas and Louisiana and 65,830 (SE = 24,382) in Texas alone. Southeastern Naturalist E.A. Rigby and D.A. Haukos 2014 28 Vol. 13, Special Issue 5 Because Mottled Ducks are non-migratory, birds in the WGC population are limited to coastal wetlands and associated habitats for their entire life cycle. Gulf Coast wetlands are increasingly threatened by both anthropogenic and natural processes. Wetland area in Texas and Louisiana has declined more than 51% over the last 2 centuries (Dahl 1990). Threats to Gulf Coast wetlands include subsidence (White and Tremblay 1995), sea-level rise and related saltwater intrusion (Salinas et al. 1986), natural and human-caused shoreline erosion and river-sediment diversion (Esslinger and Wilson 2001), urbanization and real estate development (Morton and Paine 1990), and a decrease in rice agriculture (Esslinger and Wilson 2001). Other environmental and anthropogenic factors impacting the WGC Mottled Duck population include (1) loss or degradation of reproductive habitats (e.g., pair ponds, suitable nesting cover, and brood-rearing habitats); (2) loss and degradation of nonbreeding habitats (i.e., winter, molt); (3) reduction of ecological disturbance (e.g., cattle- and goose-grazing or prescribed burning), (4) redistribution of populations (i.e., from Texas to Louisiana; Haukos 2010); and (5) continued exposure to lead from spent shot shells (Merendino et al. 2005). Because of concern for the status and future of Mottled Ducks, the US Fish and Wildlife Service (USFWS) declared the species a primary species in the Migratory Bird Program Focal Species Strategy (USFWS 2013). As threats to coastal wetlands increase, managers must set priorities and make land management decisions that will affect coastal species like Mottled Ducks without a complete understanding of the species’ population dynamics (e.g., GCJV 2007). Decisions regarding conservation of Mottled Ducks on the western Gulf Coast would be greatly aided by a population demography model. Such a model would allow an analysis of the effects of various vital rates on the population growth rate and indicate where management resources should be allocated. Information from this model could also inform hypotheses about Mottled Duck ecology, population dynamics, and management. Our objective was to construct a population demography model for Mottled Ducks on the western Gulf Coast and analyze the relative effect of the individual vital rates on population growth. Study Area On the western Gulf Coast, Mottled Ducks inhabit a narrow strip of coastal marsh habitat from northeast Mexico to Alabama, with densities highest in Texas and Louisiana (Bielefeld et al. 2010). Coastal marsh habitats are categorized based on salinity level as saline marsh, brackish marsh, intermediate marsh, and fresh marsh (Stutzenbaker 1999). Mottled Ducks tend to avoid saline marsh (salinity ≥10 ppt) but use all other marsh types (Haukos et al. 2010, USFWS 2006). Remaining coastal prairie and some agricultural lands adjacent to coastal marshes, particularly intermittently flooded rice fields and cattle pastures, are also valuable habitats (Stutzenbaker 1988). Functional Gulf Coast marshes can be considered as highdisturbance environments historically affected by hurricanes, fire, flood, drought, grazing, and vegetation eat-outs by Ondatra zibethicus (L.) (Muskrat) and large (>100,000) flocks of wintering geese (Bhattacharjee et al. 2007, USFWS 2005). Southeastern Naturalist 29 E.A. Rigby and D.A. Haukos 2014 Vol. 13, Special Issue 5 The climate within Mottled Ducks’ WGC range is humid-subtropical, with annual precipitation of 107–165 cm (Ning and Abdollahi 2003). Methods Model parameterization We gathered vital-rate estimates and corresponding variance estimates for Mottled Ducks on the western Gulf Coast from published articles, academic theses, and reports from state and federal agencies (Table 1). Although we prioritized peerreviewed articles, a great deal of Mottled Duck research has never been published in scientific journals. We included information from gray literature to fully populate the model with vital rates that otherwise would have been unavailable. We prioritized post-1990 vital-rate estimates over older rates because they were more likely to reflect current conditions. Recent annual age- and sex-specific survival has been estimated from recovery data from Mottled Duck banding efforts in Louisiana (1994–2010) and Texas (1997–2010) (Haukos 2010, Johnson 2009). Survival estimates based on banding from 1962–1977 are also available (Stutzenbaker 1988), but these estimates likely do not represent current conditions and thus were not included in the model. Although seasonal adult survival rates are known to differ for Mottled Ducks in Florida (Bielefeld and Cox 2006), differential seasonal survival rates are currently unavailable for Mottled Ducks on the western Gulf Coast. Breeding season-specific Table 1. Vital rates of Mottled Ducks on the western Gulf Coast, extracted from existing literature. Rates include: BI = breeding incidence, CS = clutch size, H = hatchability, NS = nest success, DS1 = duckling survival (days 1–2), DS2 = duckling survival (days 3–30), JS = juvenile survival (days 31–365), RP = renesting effort, and S = annual female survival. Process variance (σprocess; White 2000) was calculated for vital rates for which >2 estimates were available (BI, CS, NS). Variation for all other vital rates (H, DS1, DS2, JS, RP, S) is reported as a standard error (SE). We estimated SE for H and RP vital rates using the binomial distribution (Snedecor and Cochran 1968:207); reported SE for H is a weighted average of estimates. Vital rate Mean σprocess or SE Sources BI 0.420 0.214 Finger et al. 2003, Rigby and Haukos 2012 CS 9.214 0.583 Johnson et al. 2002, Finger et al. 2003, Durham and Afton 2006 H 0.947 0.0106 Finger et al. 2003, Stutzenbaker 1988 NS 0.158 0.0758 Durham and Afton 2003, Finger et al. 2003A, Holbrook et al. 2000, Walters et al. 2001 DS1 B 0.612 0.0731 Baker 1983 DS2 B 0.687 0.183 Rigby 2008 JSB 0.402 0.0299 Haukos 2010, Johnson 2009 RPC 0.567 0.0077 Arnold et al. 2010 S 0.47 0.04 Haukos 2010, Johnson 2009 AApparent nest success in Finger et al. (2003) transformed to approximate Mayfield nest success (Green 1989, Johnson 1991). BSurvival and SE estimates transformed using the delta method (Powell 2007, 2012) to reflect temporal scale necessary for the model. CRenesting effort estimate unavailable for Mottled Ducks; estimate for Mallards used instead. Southeastern Naturalist E.A. Rigby and D.A. Haukos 2014 30 Vol. 13, Special Issue 5 survival has been estimated for females in 2 studies (Finger et al. 2003, Rigby and Haukos 2012) but without information from other seasons, we were not able to partition survival seasonally. We modeled Mottled Duck reproduction using estimates of nest success (NS; Durham and Afton 2003, Finger et al. 2003, Holbrook et al. 2000, Walters et al. 2001), breeding incidence (BI; Finger et al. 2003, Rigby and Haukos 2012), clutch size (CS; Durham and Afton 2006, Finger et al. 2003, Johnson et al. 2002) and hatchability (H; Finger et al. 2003, Stutzenbaker 1988) (Table 1). NS estimates were calculated using Mayfield’s (1961) methods or transformed to approximate Mayfield estimates (Green 1989, Johnson 1991). Earlier nest-success estimates are also available (Baker 1983, Engeling 1950, Singleton 1953, Stutzenbaker 1988), but these estimates likely do not represent current conditions and thus were not included in the model. Renesting effort (RP) has not been quantified for Mottled Ducks on the western Gulf Coast, but Mottled Ducks are considered “determined renesters”, and renesting is “commonplace” (Stutzenbaker 1988: 84–85). To approximate RP for Mottled Ducks, we used an RP estimate for Anas platyrhynchos L. (Mallards), which are described as “persistent renesters” (Table 1; Arnold et al. 2010:212). BI is difficult to estimate, because many radio telemetry studies catch females on the nest and thus only follow nesting females. Rigby and Haukos (2012) and Finger et al. (2003) estimated BI for females caught in swim-in traps, decoy traps, and rocket nets, but both studies were hampered by the possibility that they had not found all nests. Still, their estimates are the most accurate available for Mott led Duck BI. Annual (S) and juvenile (JS) survival were estimated using band-recovery data and Brownie models in Program MARK (Table 1; Haukos 2010, Johnson 2009). JS in our model represented survival of juvenile females for 335 days only; we transformed the reported annual survival and variance estimates into 335-day estimates using the delta method (Powell 2007, 2012). Duckling survival (DS) was estimated from hatch to 30 days, a standard estimation after which juvenile survival is considered appropriate (Rotella and Ratti 1992). Due to the properties of the available data (Table 1), we split DS into 2 components: DS1 (days 1–2) and DS2 (days 3–30). DS2 was parameterized with data from Rigby (2008) and transformed to a 28-day survival estimate using the delta method (Powell 2007, 2012). We were unable to include duckling survival estimates from a similar study (Finger et al. 2003) because the authors did not report sample size for ducklings (necessary to calculate process variance), and they did not report daily duckling survival rates for 2 of 3 years (though survival in those years was known to be low). Because Rigby (2008) did not catch ducklings at the nest, and travel from the nest to brood habitat is considered a time of especially high risk to ducklings (Arnold et al. 2010), we added DS1 to the model to more fully capture mortality risk from hatch to 30 days. We estimated DS1 using data from Baker (1983), who followed broods from the nest. We used those brood observations to estimate daily duckling survival during the 2–day period in program MARK using the known-fate procedure (White and Burnham 1999) and transformed it to a 2-day survival estimate (DS1) using the delta method (Powell 2007, 2012). Southeastern Naturalist 31 E.A. Rigby and D.A. Haukos 2014 Vol. 13, Special Issue 5 We calculated process variance (White 2000) for vital rates for which >2 estimates were available. When possible, years within a study were considered as discrete parameter estimates for process variance calculation. We estimated variance for H and RP vital rates using the binomial distribution (Snedecor and Cochran 1968:207). Because 2 estimates were available for H, we calculated SE as the square root of the weighted average of variance estimates for H. Model structure We constructed a matrix population model based on female vital rates, as male influence on Mottled Duck fertility is unknown. We parameterized the model with a pre-breeding census and assumed birth-pulse reproduction (Caswell 2001). Overall model structure and estimation of fertility were similar to Koons et al. (2006). We considered the start of the breeding season to be 1 March (Baker 1983, Durham and Afton 2006, Johnson et al. 2002). We used 2 age classes: second-year females (SY, age = 1 year) and after-second-year females (ASY, age ≥ 2 years). We defined fertility as the average number of female offspring produced per female, per year (Caswell 2001), and assumed it to be similar between age classes. Mottled Duck females are reproductively active at 1 year of age (Stutzenbaker 1988), and no information is available regarding differential reproduction in females based on age. The matrix model (A) was A = FSY FASY SSY SASY where Fi = fertility of age class i, and Si = survival of age class i (Fig. 1). In practice, there are no data differentiating Mottled Duck fertility or survival between age classes, so we assumed FSY = FASY and SSY = SASY. Fertility (F) was modeled as: F = 0.5 × BI × [CS × H × NS + (1 - NS) × RP × CS × H × NS] × DS1 × DS2 × JS, where F = fertility, BI = breeding incidence, CS = clutch size, H = hatchability, NS = nest success, RP = renesting effort, DS1 = duckling survival (days 1–2), DS2 = duckling survival (days 3–30), and JS = juvenile survival (days 31–365). The 0.5 value comes from an assumption that half of offspring are female (i.e., a 1:1 sex ratio among eggs [Koons et al. 2006]). We chose a starting Mottled Duck population of 200,000 at t = 0, which is greater than a recent estimate (USFWS 2013) but less than an earlier estimate (Ballard et al. 2001). Because there is debate about Mottled Duck population size, we also tested starting population values of 100,000 and 630,000 with 10 meta-iterations of the model (using the same vital rate and process variance estimates). Differing starting values did not affect estimates of λ, and population values (such as N1, the female population in year 1) changed in proportion to the change in starting value. Hereafter we report results only for a population of 200,000 at t = 0. We also assumed a 1:1 sex ratio, resulting in an estimate of N0 = 100,000 female Mottled Ducks. We estimated the age structure of the female Mottled Duck population at Southeastern Naturalist E.A. Rigby and D.A. Haukos 2014 32 Vol. 13, Special Issue 5 time t = 0 (N0, SY = 48,690, N0, ASY = 51,310) using an existing estimate of the age ratio of juvenile to adult females (0.9491: Johnson 2009). We described the female Mottled Duck population in year 1 as N1 = N0*A, and the population growth rate (λ) as λ = N1/N0. We ran 1000 iterations of the population matrix model in Excel (Microsoft, Redmond, WA). All vital rates were parameterized to include variation. To estimate CS1, we calculated the inverse of the normal cumulative distribution parameterized by the mean (C̅S̅) and the process variance (σprocess CS) with probability between 0 and 1 determined by a random number generator (= NORMINV[RAND(),C̅S̅, σprocess CS]). For all vital rates that are logically bounded by 0 and 1 (H, NS, RP, DS1, DS2, JS, SSY, SASY), we estimated the rate in year 1 (x1) by calculating the inverse of the cumulative beta distribution parameterized by α and β with probability between 0 and 1 determined by a random number generator, where α = x̅[x̅([1 - x̅]/σprocess 2) - 1] and β = (1 - x̅)([x̅(1 - x̅)/σprocess 2] - 1) (= BETAINV[RAND(),α, β]). Beta distribution estimates were thus constrained by 0 and 1, preventing nonsensical results (for example, negative survival). We also estimated Mottled Duck recruitment for comparison to other studies. We defined recruitment (R) as the number of female offspring produced per adult female that survive to 30 days after hatch (R = F/JS). For all estimates for which process variance was unavailable (Table 1), we used the standard error of the estimate as σ. We calculated the mean and standard error for all composite rates (λ, N1, N1 SY, N1 ASY, F, R) across the 1000 iterations. We Figure 1. Model used to describe population dynamics of Mottled Ducks on the western Gulf Coast, where F = fertility and S = survival. Mottled Ducks were classified by age class: SY = second year, ASY = after second year. The model was parameterized with a prebreeding census on 1 March and assumed birth-pulse reproduction (Caswell 2001). Southeastern Naturalist 33 E.A. Rigby and D.A. Haukos 2014 Vol. 13, Special Issue 5 performed 20 meta-iterations of the population model to obtain mean coefficient of determination (r2) values for the linear regression of each vital rate and each composite rate on λ. Elasticity, defined as the proportional change in λ with proportional changes in life-stage parameters (Caswell 1989), is closely related to r2. By assuming a linear relationship between vital rates and λ, r2 is approximated by r2 = s i 2 *[variance of the vital rate / variance of λ], where si = the sensitivity of λ to changes in the vital rate (Wisdom and Mills 1997). Thus, r2 approximates the behavior of elasticity, and the vital rate with the greatest effect on λ will have the greatest r2 value and the greatest mean elasticity (Wisdom and Mills 1997). Results Our estimated average population growth rate for Mottled Ducks was low, λ = 0.541 (SE = 0.070; Table 2), where λ = 1 indicates a stable population and λ < 1 indicates population decline. The average estimated female Mottled Duck population in year 1 was N 1 = 54,093 (SE = 7019), reduced from N0 by almost half. Fertility and recruitment were low and variable, F = 0.071 (SE = 0.058) and R = 0.176 (SE = 0.143). One-year old females (N1 SY) only made up 13% of the female portion of the population in year 1. The elasticity analysis suggested that variation in F (r2 = 0.675) primarily explained the variation in λ (Table 3, Fig. 2), though S (r2 = 0.322) also explained a substantial amount of variation. For the vital rates that comprised F, BI (r2 = 0.270) and NS (r2 = 0.200) explained the most variation in λ (Table 3, Fig. 3). DS1 (r2 = 0.0187), and DS2 (r2 = 0.0754) explained more variation in λ than JS (r2 = 0.00616) Table 2. Composite vital rates were estimated for female Mottled Ducks on the western Gulf Coast. Rates were calculated via 1000 iterations of the matrix population model. Summary statistics (mean, standard error (SE), minimum, and maximum) represent average rates calculated across 20 meta-iterations of the model. F = fertility; N1 SY = female population age =1, year 1; N1 ASY = female population age ≥ 2 , year 1; N1 = total female population, year 1; λ = population growth rate; R= recruitment. F N1 SY N1 ASY N1 λ R Mean 0.0707 7066 47,027 54,093 0.541 0.176 SE 0.0578 5780 4000 7019 0.0702 0.143 Minimum 0.000959 96 34,393 37,144 0.371 0.00231 Maximum 0.419 41,852 59,764 91,118 0.911 1.010 Table 3. Coefficient of determination (r2) values between vital rates and the population growth rate (λ) for Mottled Ducks on the western Gulf Coast. Mean r2 and standard error estimates were produced from 20 meta-iterations of the population model. Vital rates are: F = fertility, S = annual adult female survival, BI = breeding incidence, NS = nest success, JS = juvenile survival (days 31–365), CS = clutch size, DS1 = duckling survival (days 1–2), DS2 = duckling survival (days 3–30), H = hatchability, and RP = renesting effort. F S BI NS JS CS DS1 DS2 H RP r2 0.675 0.322 0.270 0.200 0.00616 0.00342 0.0187 0.0754 0.00099 0.00098 SE 0.0219 0.0243 0.0265 0.0343 0.00368 0.00283 0.00713 0.0112 0.00118 0.00126 Southeastern Naturalist E.A. Rigby and D.A. Haukos 2014 34 Vol. 13, Special Issue 5 (Table 3, Fig. 3). None of the remaining vital rates (H, CS, RP) used to estimate F explained much of the variation in λ (Table 3, Fig. 3). Discussion Our estimated population growth rate (mean λ = 0.541) for WGC Mottled Ducks was well below the rate necessary to maintain a stable population (λ = 1). This finding supports annual surveys that indicate WGC Mottled Duck populations have declined since the mid-1990s (Haukos 2010, USFWS 2013). For comparison, Johnson (2009) found the geometric mean of λ for female Mottled Ducks was 0.79 (range = 0.49–1.16). The difference in λ estimates between studies is due to the difference in fertility estimation—Johnson (2009) used age ratios derived from hunter-killed wings as an index to fertility, whereas we used vital rate estimates. For Mallards in eastern Canada, Hoekman et al. (2006) reported λ for 5 sites: one site had λ = 0.50, all others had 0.87 ≤ λ ≤ 1.05. Hoekman et al. (2002) found λ = 0.824 for mean parameter values of mid-continent Mallards. Recruitment was very low (R = 0.176) compared to other species (e.g., R > 0.79 for Mallards at 4 of 5 sites in eastern Canada; Hoekman et al. 2006). Rigby (2008) estimated that a recruitment rate of R = 0.91 was necessary to maintain population stability for WGC Mottled Ducks; less than 0.2% of simulated recruitment estimates were ≥0.91. Variation in fertility contributed 67.5% of the variation in λ. The relative importance of variation in survival and fertility in affecting variation in λ differed slightly from Johnson (2009), who found survival contributed 59.4% of the variation in λ for female Mottled Ducks and fertility contributed 40.6%. Our extremely low Figure 2. Linear regression of survival (S) and fertility (F) on population growth rate (λ) of Mottled Ducks on the western Gulf Coast for 1 meta-iteration of the model. Due to the nature of the matrix model, exact values of S, F, and λ change for every meta-iteration. F explained 67% of the variation in λ and S explained 32% (mean values for 20 meta-iterations of the model (Table 3). Southeastern Naturalist 35 E.A. Rigby and D.A. Haukos 2014 Vol. 13, Special Issue 5 fertility estimate (F = 0.0707) suggests that the decline in the Mottled Duck population is in large part due to a low average annual rate of reproduction. The variation in vital rates occasionally resulted in simulated excellent years with high F; the Figure 3. Linear regression of components of fertility (F) on population growth rate (λ) of Mottled Ducks on the western Gulf Coast for 1 meta-iteration of the model, arranged in descending value of r 2: breeding incidence (BI), nest success (NS), duckling survival for days 3–30 (DS2), duckling survival for days 1–2 (DS1), juvenile survival (JS), clutch size (CS), hatchability (H), and renesting effort (RP). All vital rates were parameterized to include variation, causing exact values for each parameter to change for every meta-iteration of the model. R 2 values listed here are mean values for multiple iterations (Table 3). BI explained 27% of the variation in λ; NS explained 20%. JS, CS, H, and RP each explained <1% of variation in λ. Southeastern Naturalist E.A. Rigby and D.A. Haukos 2014 36 Vol. 13, Special Issue 5 highest value across 20,000 iterations was F = 0.587. These years were rare, however, and less than 1% of simulated years had F > 0.3. Within the current estimated range for Mottled Duck vital rates, years with fertility at a rate that would maintain a stable population (given current estimates of adult survival) occur too rarely to maintain current population size. Within fertility, nest success and breeding incidence had the greatest effects on variation in λ (Table 3), indicating that increases in these vital rates would likely have the greatest positive effect on population growth. Variation in λ due to duckling survival may be artificially low due to our inability to include data from Finger et al. (2003). Further research into the true range of duckling survival on the western Gulf Coast would improve the accuracy of this model. Average nest success for Mottled Ducks may appear low (NS = 0.158), but low nest success is frequently found for many waterfowl species. For example, Greenwood et al. (1995) found nest success varied from 7–17% for 5 species across 4 years. Breeding incidence, however, is often assumed to equal or approach 1 in waterfowl population dynamics (Mauser and Jarvis 1994), but BI was only 0.420 for WGC Mottled Ducks. BI does appear to approach 1 for Mallards (BI = 0.968 [SE = 0.040] across n = 11 studies [Hoekman et al. 2002]; BI = 0.951 [SE = 0.034] to BI = 0.980 [SE = 0.020] [Hoekman et al. 2006], BI = 0.84 [SD = 0.08] [Coluccy et al. 2008]), but is more widely varied in other species, particularly diving ducks: e.g., Aythya affinis (Eyton) (Lesser Scaup) BI=0.11 (95% CI = 0.05–0.24) – 0.68 (SE = 0.08) for different estimation methods (Martin et al. 2009), Aythya valisineria (Wilson) (Canvasback) BI = 0.54–0.94 for juveniles, and BI = 0.74–0.95 for adults (Anderson et al. 2001), and 68.9% of Oxyura jamaicens (Gmelin) (Ruddy Duck) spring-harvested females showed signs of breeding (Alisauskas and Ankney 1994). However, breeding incidence was also well below 1 for Mottled Ducks in Florida: 25%–56% among years (Varner et al. 2013). Nest success in that study was high (28%), which appeared to offset low breeding incidence: Varner et al. (2013) did not explicitly calculate λ, but density estimates in Florida show a weakly increasing trend (Bielefeld et al. 2010). This balance between breeding incidence and nest success does not appear to occur on the WGC, where both vital rates are low and population declines are evident in Texas (Haukos 2010, USFWS 2013). Variation in survival was responsible for 32.2% of the variation in λ, indicating that maximizing survival of adults via management could have a positive effect on population growth. For band-recovery analyses, the highest ranked model for survival included the interaction of age, sex, and year, indicating that Mottled Duck survival varies temporally (Haukos 2010). For the 1997–2008 banding years, Haukos (2010) estimated annual survival rates were 0.27–0.69 for adult females and 0.17–0.68 for juvenile females, with averages of 0.47 for adults and 0.37 for juveniles. Stutzenbaker (1988) reported results of survival estimation for banding efforts during the late 1960s, but due to sample size did not differentiate sex, only age. His estimate of annual survival was 0.701 for adults and 0.443 for juveniles, which indicates a more drastic decline in adult survival than juvenile survival. If Mottled Duck survival again reached levels seen in the 1960s, population growth could increase beyond the range estimated by our model. Southeastern Naturalist 37 E.A. Rigby and D.A. Haukos 2014 Vol. 13, Special Issue 5 Management Implications We recommend that management efforts target increasing 3 vital rates for WGC Mottled Ducks: adult survival, nest success, and breeding incidence. There was enough variation in these rates that substantial increases in λ could result from improving these statistics within their current range. Additionally, historical rates for adult survival (Stutzenbaker 1988) indicate that increases in this rate are possible beyond the range used in this model, which would increase λ beyond the range estimated here. Daily bag limit for Mottled Ducks in Louisiana was reduced from 3 to 1 in 2009 (Louisiana Department of Fisheries and Wildlife 2012, USFWS 2013), but it is not yet known if this change has affected adult survival rates. Daily bag limit for Mottled Ducks in Texas has not exceeded 1 since 1985 (USFWS 2013). We suggest that improvement of nesting habitat quality is the best course of action to increase Mottled Duck fertility, though over-riding environmental factors that dictate breeding incidence are not fully understood and deserve further research. Improving nesting habitat quality includes managing for optimal Mottled Duck nesting habitat (coastal prairies that include heavy grass cover, particularly native Spartina spp. [cordgrasses] Stutzenbaker 1988) in areas adjacent to marshes suitable for brood-rearing. Predator removal in nesting areas also deserves consideration and study. WGC marshes are increasingly affected by human disturbance (Morton and Paine 1990), and nest predator reactions to altered landscapes are complex (Chalfoun et al. 2002). Little is known about predator densities in WGC marshes, and the costs of predator removal on a landscape scale are unknown but likely would be expensive. Still, Holbrook et al. (2000) found that Mottled Duck nest success reached 67.1% on individual dredge-spoil islands with few or no predators, suggesting that predator removal could have a positive effect on nest success. 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