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Received: 4 July 2018 | Revised: 14 December 2018 | Accepted: 21 December 2018 DOI: 10.1002/zoo.21477 RESEARCH ARTICLE Reproductive Viability Analysis (RVA) as a new tool for ex situ population management Karen Bauman1 | John Sahrmann2 | Ashley Franklin2 | Cheryl Asa2 | Mary Agnew2 | Kathy Traylor-Holzer3 | David Powell1 1 Saint Louis Zoo, Saint Louis, Missouri 2 AZA Reproductive Management Center, Many animal populations managed by the Association of Zoos and Aquariums’ (AZA) Saint Louis Zoo, Saint Louis, Missouri Species Survival Plans® (SSPs) have low rates of reproductive success. It is critical that 3 IUCN SSC Conservation Planning Specialist individuals recommended to breed are successful to achieve genetic and demographic Group, Apple Valley, Minnesota goals set by the SSP. Identifying factors that impact reproductive success can inform Correspondence managers on best practices and improve demographic predictions. A Reproductive Karen Bauman, Saint Louis Zoo, 1 Government Drive, Saint Louis, MO 63110. Viability Analysis (RVA) utilizes data gathered from Breeding and Transfer Plans, Email: firstname.lastname@example.org studbooks, and SSP documents, and through modeling identifies factors associated with reproductive success in a given species. Here, we describe the RVA process, including different statistical models with the highest accuracy for predicting reproductive success in fennec foxes (Vulpes zerda) and Mexican wolves (Canis lupus baileyi). Results from the RVA provide knowledge that can be used to make evidence- based decisions about pairing and breeding strategies as well as improving reproductive success and population sustainability. KEYWORDS ex situ, reproductive success, sustainability 1 | INTRODUCTION Mexican grey wolves Canis lupus baileyi, a species extinct in the wild, into Arizona and New Mexico in 1998 (USFWS, 2017). There are now Cooperative breeding and management programs in professionally more than 500 SSPs and similar programs in other regional zoo and managed zoos and aquariums in the United States, administered by the aquarium associations. Association of Zoos and Aquariums (AZA), have been organized since However, studies by several authors have demonstrated that not the 1980's (Ballou et al., 2010, and see Powell, Dorsey, & Faust, this all managed programs are meeting their target genetic and demo- issue). Each of these programs, called Species Survival Plans® [SSP], graphic goals and are not sustainable (Lees & Wilcken, 2009; Leus et al., focuses on a single species, with a studbook as its foundation; the 2011; Long, Dorsey, & Boyle, 2011; and see Che-Castro et al., this studbook is a computerized genealogy for every individual in the SSP issue). The historic separation between the ex situ and in situ population. All SSPs were originally designed to be insurance or ‘ark’ communities is now gradually being replaced by a mutual respect for populations, which were demographically and genetically sustainable the roles each plays in species recovery and conservation, allowing to maintain 90% of the gene diversity from the founding population for efforts in both realms to be integrated (Conde, Flesness, Colchero, 200 years [later revised to 100 years] (Ballou et al., 2010; Soule, Gilpin, Jones, & Scheuerlein, 2011; Conde et al., 2015; Maunder & Byers, Conway, & Foose, 1986; and references therein). Cooperative 2005; McGowan, Traylor-Holzer, & Leus, 2016; Pritchard, Fa, Oldfield, breeding programs have directly aided in the recovery of some & Harrop, 2011). The “One Plan Approach” promotes this collaborative species (Conde et al., 2013; Hoffmann et al., 2010), and have served as process to develop a single integrated species conservation plan a source of animals for release, for example, the reintroduction of (Byers, Lees, Wilcken, & Schwitzer, 2013; Traylor-Holzer, Leus, & Zoo Biology. 2019;38:55–66. wileyonlinelibrary.com/journal/zoo © 2019 Wiley Periodicals, Inc. | 55
56 | BAUMAN ET AL. Byers, 2018). Moreover, intensive species prioritization tools have tool that analyzes the inherent biological and reproductive character- been created, for example, the IUCN SSC Conservation Planning istics of individual animals (e.g., age, parity, rearing type) and of Specialist Group's new Integrated Collection Assessment and Planning breeding pairs (e.g., experience as a pair, age difference) that correlate (CPSG ICAP) process that can be used to guide ex situ global or regional with successful reproduction, that is, the “reproductive viability” of a collection planning (Traylor-Holzer et al., this issue). Yet, if the ex situ given species. The RVA is similar to a PVA in that it utilizes a variety of community is to be increasingly relied upon for conservation roles, we data inputs, is data intensive, and through modeling determines what must assure that cooperative breeding programs are efficient and we factors impact outcomes (in this case reproductive success), and thus are managing robust, viable populations. are key to population persistence. Unlike a PVA, though, the RVA SSP sustainability has been addressed in several ways. AZA has process generally ignores environmental and management factors and partnered with the Lincoln Park Zoo and the AZA Population does not make projections about the future status of populations. Management Center (PMC) to conduct population viability analyses Here we describe the RVA process and present results from the (PVAs) on many SSPs (Che-Castaldo et al., this issue). A web-based first two RVAs, conducted for Mexican wolves (Canis lupus baileyi) and program called PMCTrack, was developed as a tool to improve fennec foxes (Vulpes zerda). These species were selected because they population sustainability (Faust et al., 2011). PMCTrack maintains had good quality source data readily available, the reproductive studbook data, as well as the SSP Breeding and Transfer Plans (BTP) physiology of both species has been well studied (Asa & Valdespino, recommendations, and through a user interface tracks breeding and 1998; Valdespino, Asa, & Bauman, 2002), and canids were identified as transfer recommendation fulfillment (or lack thereof) to identify a taxon of concern (Agnew & Asa, 2014; Asa et al., 2014). The AZA obstacles so they can be addressed. A recent analysis of SSP breeding Fennec Fox SSP program, like many small canid programs, has recommendations found that on average only 20% of breeding struggled to maintain a sustainable population due to inconsistent recommendations were being fulfilled (Faust et al., this issue). reproductive success (Bauman, Mekarska, Grisham, & Lynch, 2010). In Unfulfilled recommendations were the result of many factors, some contrast, the AZA Mexican Wolf SSP has had relatively reliable being logistical or related to institutional compliance (e.g., institutional reproduction in general but higher inbreeding than most populations failure to transfer, weather preventing transfer, failure to put animals since there were only seven founders. together), while others were likely due to biological factors such as Several different modeling approaches are used in the RVA incompatibility (see Martin-Wintle et al., this issue) or fertility (animals process (see section 2) to determine which has the best power at were put together, but did not produce offspring). AZA addressed the predicting reproductive success. For these species, we predicted that issues relating to logistics by re-structuring programs, providing an experience-based model, where the variables to be tested against participation incentives, and changing management practices. How- reproductive success are identified in advance by species coordinators ever, poor or inconsistent reproduction was not being systematically with extensive knowledge of the species and for which there is a robust addressed across SSP programs. Therefore, the AZA expanded the scientific literature, would perform best. purview of the AZA Wildlife Contraception Center (WCC, now called the AZA Reproductive Management Center or RMC) to identify taxa 2 | METHO DS with high rates of reproductive failure, and suggest approaches to mitigate problems. The initial focus was largely on carnivores and 2.1 | Data sources ungulates, as studies with elephants, rhinos, wildebeest, felids, and canids had shown that a common cause of reproductive failure was Consideration of all pairs, successful or not, is vital to the RVA process for uterine pathology associated with delayed first reproduction or proper analysis of factors that promote or hamper reproductive prolonged periods without production of young, which are manage- success of a species. We used two primary data sources: the BTPs, ment strategies often used when SSPs are at capacity—a phenomenon and the studbooks with the histories of each individual, as well as characterized as “use it or lose it” (Asa et al., 2014; Penfold, Powell, supplementary information from the documents maintained by the SSP Traylor-Holzer, & Asa, 2014; and references therein). However, Coordinators and in other AZA databases. BTPs are individual-based uterine pathology does not explain reproductive failure in all species. recommendations (breeding/non-breeding, transfer/do not transfer) Many SSPs have low reproductive efficiency—the number of generated each time (every 1–3 years) a SSP meets with the PMC (or recommended breeding pairs far exceeds the number of offspring other population advisor) to review the demographic and genetic status born. Analyses conducted of the lion [Panthera leo] (Daigle et al., 2015) of the population as it relates to the long-term goals for the SSP. These and tiger (Panthera tigris) (Saunders, Harris, Traylor-Holzer, & Good- recommendations are based upon an analysis of studbook data, along rowe-Beck, 2014) SSPs provided a valuable starting point for our goal with animal (e.g., health, behavior, history, and age) and institutional to establish a method that could be used efficiently in a wide diversity information are then considered for all animals in the population. of species to identify the factors that drive reproductive success All of the source data were directly entered by hand into Excel, (Agnew & Asa, 2014). We developed the Reproductive Viability however, subsequent to the completion of these initial two RVAs, a Analysis (RVA) process to analyze past breeding recommendations and method for populating the RVA data fields directly from PMCTrack produce timely results from which evidenced-based management into an Access database was developed by the RMC which should decisions could be made to improve SSP sustainability. The RVA is a make future RVAs more efficient.
BAUMAN ET AL. | 57 A list of the RVA variables with a description along with their had ever served or were currently serving as an animal ambassador. source(s) is provided in Table 1. The RVA process relies on a core set of This is important for this RVA, as approximately one third of the variables, but is designed to be flexible, so variables may be added animals in this SSP are used for education programs. depending on the species and its biology. For example, fennec foxes can have multiple litters per year so fields were added to include data relating 2.3 | Definition of reproductive success to any second or third litters. Additionally, species-specific data fields can also be included to address variables that might be important for breeding For the RVA, we assigned success (or failure) for each pair based on success in a given species as suggested by the scientific literature (e.g., whether offspring were born (including stillborn offspring) within the lineage effects in Mexican wolves, see Asa et al., 2007) or management active period of the BTP. We defined this active period as starting on experience (e.g., ambassador animal history in fennec foxes). For some the date the BTP was finalized until the date the next Plan was species, parameters such as social groupings might be relevant. finalized, for example, if a BTP was finalized in July of 2001 with next plan in 2002, the active period would be July 2001 until July 2002. We focused on the production of, rather than survival of, offspring because 2.2 | Data collection birth is the primary indicator that reproduction has been successful. Data from all available BTPs for each species were used to identify all recommended breeding pairs. Each pair was assigned a pair type: a 2.4 | Statistical analyses “new” pair was two individuals recommended to breed together for the first time; a “carryover” was a pair that had been previously together Data for any pair that was not given the opportunity to breed were but had never had offspring together; or an “experienced” pair was one removed from the primary dataset and analyzed separately using that had offspring together previously. When one individual had a descriptive statistics as these data provide important information on recommendation to breed with more than one partner, each possible causes of logistical failures. They also can be informative in predicting pairing was entered as a separate recommendation. overall likelihood of breeding recommendation success (e.g., probabil- Studbook data were used to provide individual-specific data for ity of success if transfer is required, see Faust, this issue) and are each animal in the pair at the time of the breeding recommendation, as valuable for calculating the number of pairs needed to meet population well as providing information on any offspring the recommended pair demographic goals. produced. Both studbook software programs (PopLink (Faust, Descriptive statistics were run on all variables in Table 1 for all Bergstrom, Thompson, & Bier, 2012) and SPARKS [www. pairs given the opportunity to breed (primary dataset). Variables that Species360.org]) have reproductive reports that provide information had insufficient sample sizes (e.g., prior use of contraception) or had on parity, details on offspring (birth date, number of offspring born, low variability (e.g., only one Mexican wolf was hand-reared) were not other parent of offspring, etc.) and number of years since the last litter. included in additional analyses. All additional analyses were conducted Studbook data were also used to identify any offspring produced by within R version 3.2.1 (R Core Team, 2015) on the subset of variables. any pairs who had not been recommended to breed. Because staff For fennec foxes these included female age, male age, age difference, experience and management protocols have been associated with rearing type, pair parity, pair type, litter last 5 years, litter last 10 years, reproductive success in some species (Saunders et al., 2014), for each both at breeding location, and year; whereas for Mexican wolves these pair we recorded whether the institution receiving the breeding were female age, male age, age difference, female inbreeding, male recommendation had successful reproduction in the previous 5-year inbreeding, pair parity, pair type, litter last 5 years, litter last 10 years, period and 10-year period for that species. The studbook was also used both at breeding location, and year. Success of a pair was treated as a to provide information on “specialty” fields such as rearing type for binary response variable. A unique identifier was assigned to each pair fennec foxes, and lineage for Mexican wolves. that served as a random effect in each model to account for Although not available for every SSP, whenever possible, dependencies in the data resulting from some pairs receiving more information provided by the SSP Coordinator on any additional pairs than one recommendation. The year in which the recommendation that might have been recommended to breed between published plans was made was included to test for any change in the rate of success (interim recommendations) as well as relevant notes including whether over time independent of the other variables under consideration, for attempts were made to fulfill recommendations (or not), whether the example, if husbandry improved. recommended pair had an opportunity to breed (i.e., were housed Four different modeling approaches were utilized in the analysis. together for a sufficient period of time), and mating behaviors or The first approach, hereafter referred to as the experience-based copulation observed are included in the RVA dataset. The majority of approach, began with the design of eight models consisting of different these data existed for Mexican wolves, including mate access date numbers and combinations of the explanatory variables. Variables information gathered as part of an annual SSP report for US Fish and were chosen based on results from descriptive statistics of the RVA Wildlife Service. For fennec foxes, interim recommendations and notes dataset, consensus from SSP Coordinators regarding what variables about attempts to fulfill recommendations were available, and the they believed were relevant to success in the species, and a review of Coordinator gathered data on opportunity to breed and used the literature (Burnham, Anderson, & Huyvaert, 2011; Dochtermann & institutional records to determine whether the individuals in the pair Jenkins, 2011; Saunders et al., 2014). Individual models were
58 | BAUMAN ET AL. TABLE 1 Description of variables used in the RVA with definition and data source information Variable name Definition Data source Attributes of pairs RecAttempta “Yes” or “No” depending on if there was an attempt to follow the SSP coordinator and/or Institutional breeding recommendation (animals transferred/animals put together/ Representative etc.). Successa “Yes” if the pair successfully produced offspring (live or stillborn) during Studbook the B&T Plan period. “No” if the pair was unsuccessful. BTYeara Master Plan/Breeding & Transfer Plan the pair is listed in (year only); or Breeding & Transfer Plan; SSP coordinator for year of interim recommendation Interim Recommendations Locationa Institution where the pair was recommended to breed in Master Plan/ Breeding & Transfer Plan; SSP coordinator for Breeding & Transfer Plan Interim Recommendations AtLocationa “Yes” if both the male and female in the pair are at the same institution Breeding & Transfer Plan; Studbook already prior to the date the B&T plan was published. “No” if one or both individuals has to be transferred to a new institution to fulfill the breeding recommendation IntSuccess5 Has the institution successfully bred this species in the five years prior Studbook to the published date of the B&T plan? “Yes” or “No” IntSuccess10 Has the institution successfully bred this species in the ten years prior to Studbook the published date of the B&T plan? “Yes” or “No” PairType “New” if pair has the opportunity to breed together for the first time; Breeding & Transfer Plans; Studbook (for non- “experienced” if the pair had a previous opportunity together and recommended breeding); SSP coordinator for they successfully produced offspring; or “carryover” if the pair had a interim pairs previous opportunity together but has never produced offspring. PairParity “Parous” if both individuals are parous; “Nulliparous” if both individuals Calculated field; requires male and female parity are nulliparous; “Mixed” if parous individual paired with nulliparous variables individual PairRearing “Parent” if both individuals were parent reared; “Hand” if both Calculated field; requires male and female rearing individuals were hand reared; “Mixed” if a parent reared individual is type variables paired with a hand reared individual AgeDiff Difference in age (in years) between the male and female. Calculated field; requires male and female age variables Attributes of individuals MSBa Male's Studbook Number Breeding & Transfer Plans; Studbook (for non- recommended breeding); SSP coordinator for interim pairs FSBa Female's Studbook Number Breeding & Transfer Plans; Studbook (for non- recommended breeding); SSP coordinator for interim pairs Agea Individual's age at the time the breeding recommendation was made Breeding & Transfer Plan Parity Individual's parity at the time the breeding recommendation was made Studbook RearingType “Parent” if individual was parent reared; “Hand” if individual was hand Studbook reared Inbreeding Inbreeding coefficient of the individual Calculated in PMx or other software from studbook data Contraception “Yes” if the individual has ever previously been contracepted; else “No” RMC's contraception database Lineage Can be used to identify genetic lineages (e.g., Mexican wolf) Studbook Role This variable can be used to identify animals with different roles, such as Studbook education or ambassador animals. Origin “Captive” born or “Wild” born Studbook NumYrLastLitter Number of years since the female last gave birth Calculated from studbook a Indicates data that in the future will be directly imported from PMCTrack for RVAs.
BAUMAN ET AL. | 59 compared using Akaike's information criterion with a correction for BTPs representing a 10-year population management history (2004 to small sample sizes (AICc—the best model has the smallest value), and 2014) that included 162 breeding recommendations. Nine records model averaging was used to obtain a single, final model (Burnham were excluded from the fennec fox dataset due to missing data and 22 et al., 2011; Symonds & Moussalli, 2011). (14.2% of all recommended pairs) records were excluded because The second approach considered models containing all subsets of foxes were not given the opportunity to breed. Records were excluded the ten or eleven explanatory variables used for fennec fox and Mexican from the Mexican wolf dataset due to missing data (N = 5) and an wolf, respectively. Because of the limited sample size, no interaction additional 223 records (31.7% of all recommended pairs) were terms were included, resulting in 1,024 unique models for fennec fox excluded because the recommended pair was not given the and 2,048 unique models for Mexican wolves. Models were assessed opportunity to breed due to logistical reasons. Logistical reasons with AICc, and model averaging was used to generate a single model. resulting in the recommendations not being attempted were similar The third approach made use of the least absolute shrinkage and between the two species; these included shipment problems (import selection operator (LASSO) regression technique to fit a single model canceled, facility could not get animal transferred due to weather, etc.), including all explanatory variables. LASSO regression optimizes the fit or a facility refused to or could not comply with recommendations. to the data while constraining its complexity; therefore the regression Of the remaining 131 and 482 breeding recommendations for coefficients for some of the explanatory variables are forced to fennec fox and Mexican wolves respectively, only 24.4% (32 of 131) of become zero, resulting in simpler models compared to traditional the fennec fox pairs and 45.9% (221 of 482) Mexican wolf pairs regression techniques, decreasing the likelihood of overfitting and produced at least one litter within the active period. Descriptive improving the accuracy of predictions made on new data (James, statistics for the pair-related variables related to reproductive success Witten, Hastie, & Tibshirani, 2014). are presented in Table 2 (fennec fox) and Table 3 (Mexican wolf), The fourth approach used was the creation of a conditional random forest (CRF) model (Strobl, Boulesteix, Kneib, Augustin, & TABLE 2 Descriptive statistics for pair-related variables’ impact on Zeileis, 2008; Strobl, Malley, & Tutz, 2009) to generate the predictions reproductive success in fennec fox pairs given the opportunity to for the probability of reproductive success. The CRF model constructs breed a “forest” of conditional inference trees, which are grown based on Fennec Fennec fox % bootstrapping samples with only a subset of variables available for Pair condition fox, N successful (N) splitting each node. For generating predictions, weighted means of all Pairs with opportunity to breed 131 24.4% (32) the observed responses (or decisions) from all the inference trees Pair type created are used. While conditional inference trees utilize significance Sexually experienced pairs 27 59.2% (16) tests for determining the splitting variables and split points for the Carryover pairs 32 12.0% (4) creation of nodes within the decision trees, there are no classical New pairs 72 16.6% (12) significances for the explanatory variables. Rather, variable importance Pair previous success measures are assigned (Strobl et al., 2008; Strobl et al., 2009). The four approaches were compared by using the resulting models Both in pair were previously 31 58.0% (18) successful (parous) to predict the probability of success for selected recent BTP for each Both in pair were previously 62 24.0% (12) species with known outcomes, which had not been used to fit the unsuccessful (nulliparous) models (Fennec foxes 2014 and 2015 BTPs for 37 pairs; Mexican One in pair was previously 38 7.8% (3) wolves 2016 BTP for 26 pairs). Performance was measured using the successful and other was not area under the receiver operating characteristic (ROC) curve (AUC). Pair rearing type AUC has been used in a variety of settings to assess the accuracy of Both in pair were hand-reared 22 45.5% (10) models over a range of thresholds for classifying a binary outcome (Jiménez-Valverde, 2012). Values range from 0 to 1, with an AUC of Both in pair were parent-reared 18 33.0% (6) 0.5 expected as being the same as random and values close to 1 Mixed rearing type pair 91 17.6% (16) representing high accuracy in predicting realized outcomes. Pairs carried over beyond the original recommendation Pairs carried over for 1 year 21 19.0% (4) Pairs carried over for 2 year 4 0.0% (0) 3 | RE SULTS Pair carried over for 3 year 1 0.0% (0) Number of litters born within the time period for successful pairsa The AZA Mexican Wolf SSP has created annual BTPs since 1983, with Successful pairs that had only 1 32 69.0% (22) 710 breeding recommendations made between 1983 and 2015 thus litter the Mexican wolf RVA dataset represents 32 years of data. In contrast, Successful pairs that had 2 litters 32 28.0% (9) the AZA Fennec Fox SSP BTPs were issued biennially from 2004 until Successful pairs that had 3 litters 32 3.0% (1) 2010 and yearly thereafter when population instability necessitated a more frequent planning. Therefore, for the fennec fox, we used eight Period of the Breeding and Transfer Plan: 1–2 years.
60 | BAUMAN ET AL. TABLE 3 Descriptive statistics for pair-related variables’ impact on TABLE 4 Descriptive statistics for individual-related variables’ reproductive success in Mexican wolf pairs given the opportunity to impact on reproductive success in fennec fox pairs given the breed opportunity to breed Mexican Mexican wolf % % successful Pair condition wolf, N successful (N) Individual foxes N (N) Pairs with opportunity to breed 482 45.9% (221) Individual previous success Pair type Previously unsuccessful males (any ages) 86 16.3% (14) Sexually experienced pairs 140 66.4% (93) Previously successful males (any age) 46 39.1% (18) Carryover pairs 97 27.8% (27) Previously unsuccessful females (any 85 15.2% (13) age) New pairs 245 41.2% (101) Previously successful females (any age) 47 40.4% (19) Pair previous success Age of females given the opportunity to breed Both in pair were previously 158 66.5% (105) successful (parous) 0 (less than 1 year) 8 50.0% (4) Both in pair were previously 239 29.3% (70) 1 13 38.4% (5) unsuccessful (nulliparous) 2 26 26.9% (7) One in pair was previously 85 54.1% (46) 3 15 46.6% (7) successful and other was not 4 18 27.7% (5) Pairs carried over beyond the original recommendation 5 14 21.4% (3) Pairs carried over for 1year 71 33.8% (24) 6 5 20.0 % (1) Pairs carried over for 2 year 21 16.6% (3) 7–14 32 0.0% (0) Pair carried over for 3 year 4 0.0% (0) whereas individual-related variables are in Tables 4 and 5 for fennec rearing type, and the age difference of the pair, in various fox and Mexican wolves respectively. Briefly, results for fennec foxes combinations. The fennec fox model developed using the LASSO show that no female over age six has been successful despite a median regression technique was more restrictive, and only identified pair life expectancy for this species of 11 years (www.aza.org/species- type, female age, and male age as being significant predictors of survival-statistics). Pairs where an experienced (parous) individual was reproductive success and decreases as female age and male age paired with an inexperienced (nulliparous) individual were rarely increase. successful; similarly pairs with individuals of different rearing types The logistic equation produced from the LASSO regression is were not successful. Pairs that were carried over for 1 year did have presented in Figure 1a. When predictions for the reproductive success some success; however, pairs carried over for 2 or 3 years did not. For of pairs were generated by the conditional random forest, the top five Mexican wolves, carry over pairs were successful in the first and most important factors for the fennec fox population were pair type, second years, although the success rate in year 2 was much lower; like male age, female age, parity of the pair, and the age difference between the fennec fox, no Mexican wolf carry over pairs were successful in the male and female (Figure 2a). Consensus among the modeling year 3. Success decreased markedly in males with inbreeding methods evaluated illustrates that female age and experience as a pair coefficients greater than 0.3. are the factors most significantly associated with reproductive success in the AZA Fennec Fox SSP population: the probability of a breeding pair to be successful decreases as female age increases, and increases if 3.1 | Statistical prediction models the pair is “experienced.” Other factors identified among multiple methods included pair parity, male age, and the age difference 3.1.1 | Fennec fox between the male and female. The models constructed using the experience-based approach for fennec fox in order of AICc values are presented in Table 6. The 3.1.2 | Mexican wolf model containing female age, parity of the pair, pair type, and the difference between female and male ages had the lowest AICc. A For Mexican wolves, the models constructed using the experience- model containing those same variables, plus whether the female and based approach in order of AICc values are presented in Table 7. The male were at the same location at the time the breeding model containing female age, male age, parity of the pair, pair type, recommendation was made, performed almost as well. The null male inbreeding coefficient, and female inbreeding coefficient had the model containing no explanatory variables and the full model lowest AICc and was thus the best model. The null model containing no containing all explanatory variables performed worst. When looking explanatory variables performed worst in this analysis. When looking at all-subsets of the variables, there were three top performing at all-subsets of the variables, the top performing model included male models which included female age, parity of the pair, pair type, age, parity of the pair, male and female inbreeding coefficients, the age
BAUMAN ET AL. | 61 TABLE 5 Descriptive statistics for individual-related variables’ Figure 1b contains the logistic equation produced from the LASSO impact on reproductive success in Mexican wolf pairs given the regression. When predictions for the reproductive success of pairs opportunity to breed were generated by the conditional random forest for the Mexican wolf Individual wolves N % successful (N) population, parity of the pair, male age, male and female inbreeding Individual previous success coefficients, and pair type were the most important factors for Previously unsuccessful males (any age) 268 33.3% (89) predicting reproductive success (Figure 2b). Consensus factors among Previously successful males (any age) 214 61.7% (132) the modeling methods for the Mexican wolf population suggest that Previously unsuccessful females (any age) 295 32.9% (97) male age, pair parity, and male and female inbreeding coefficients are Previously successful females (any age) 187 66.3% (124) the factors most significantly associated with reproductive success: Age of females given the opportunity to breed probability of success increases if either the male or female are parous 0 (less than 1 year) 2 0.0% (0) (but highest if both are parous), and probability of success decreases as 1 37 32.4% (12) male age increases, and as male and female inbreeding coefficients 2 62 48.4% (30) increase. Additionally, pair type and prior institutional success within 3 58 48.3% (28) 10 years were identified among multiple modeling methods as 4 56 53.6% (30) influencing the probability of success for Mexican wolves. 5 55 43.6% (24) 6 48 54.2% (26) 3.2 | Comparison of modeling strategies 7 38 55.6% (21) Of the four modeling strategies, LASSO regression performed best 8 37 37.8% (14) according to AUC (Figure 3a) for fennec foxes, but for Mexican 9 39 43.6% (17) wolves the conditional random forest approach was better than all 10 27 48.1% (13) other models (Figure 3b). For both species, all models were superior 11 19 26.3% (5) to random as the AUC was above 0.5 in all cases. Figure 4 shows the 12 4 25.0% (1) predicted probability of success for each of the 37 and 26 test pairs, Male inbreeding coefficients respectively, for fennec foxes and Mexican wolves generated by 0 88 59.0% (52) each modeling strategy, overlaid upon the actual outcomes 0.05–0.099 51 49.0% (25) (success = 1, failure = 0) of those pairings. Predicted probabilities 0.1–0.124 22 59.0% (13) from the LASSO model fell within a narrower range between 0.1 and 0.125–0.149 108 47.0% (51) 0.5 for fennec fox and between 0.21 and 0.82 for Mexican wolf. By 0.15–0.199 118 45.7% (54) contrast, the experience-based, all subsets models, and the 0.2–0.299 70 37.1% (26) conditional random forest generated probabilities as low as near 0 0.3–0.499 33 18.2% (6) and as high as 0.92 for fennec and Mexican wolf. 0.5 and above 19 10.5% (2) 4 | DISCUSSION difference of the pair, and prior success at the institution within the last 10 years. Significant predictors of reproductive success in the Mexican RVA statistically identifies key pair- and individual-related factors that wolf LASSO model were parity of the pair, male age, male and female have affected reproductive success in a given population. This inbreeding coefficients, and prior success at the institution. information can be used as a tool by program leaders to improve TABLE 6 Comparison of ΔAICc and weights among models tested for fennec fox as part of the experience-based approach Variables in model ΔAICc Model weight Female age, pair parity, pair type, age difference 0 0.41 Female age, pair parity, pair type, age difference, both at breeding location 0.22 0.37 Female age, pair parity, pair type, age difference, rearing type, male age 3.27 0.08 Female age, pair parity, pair type, age difference, litter last 5 years, litter last 10 years 3.77 0.06 Female age, pair parity, pair type, age difference, litter last 5 years, litter last 10 years, rearing type, 4.84 0.04 both at breeding location Female age, pair parity, pair type, age difference, litter last 5 years, litter last 10 years, year 6.31 0.02 Null (no explanatory variables) 9.78 3E-3 Female age, pair parity, pair type, age difference, litter last 5 years, litter last 10 years, rearing 10.20 3E-3 type, both at breeding location, year, male age
62 | BAUMAN ET AL. (a) (b) FIGURE 1 The logistic equations produced from the LASSO regression, for fennec fox (a) and Mexican wolf (b), where: p(S) is the probability of success, E = 1 if the pair is experienced, otherwise E = 0, MA is the age of the male, FA is the age of the female, YY = 1 if both the male and female are parous, otherwise YY = 0, M = 1 if only one individual (the male OR the female) is parous, otherwise M = 0, PS = 1 if the pair is at an institution that has successfully bred Mexican wolves in the past 10 years, otherwise PS = 0, MF is the inbreeding coefficient of the male and FF is the inbreeding coefficient of the female the sustainability of their populations by making better-informed RVA dataset in the future, more subtle factors may be identified. The breeding recommendations. LASSO statistical model clearly performed the best for fennec foxes, The AZA Fennec Fox RVA process revealed that female age and and we believe it is likely to do so for other species with limited parity are key drivers of reproductive success in this species, with historical data. Because it limits complexity, LASSO prevents male age, pair experience, and age difference also being effective overfitting the data, which is probably why its predictions were predictors. Unfortunately, the sample size was too small to estimate better on the new pairs, as well as more moderated (i.e., LASSO gave all but the strongest effects (female age and parity, in this case); most new pairs a probability of success in the range 20–50%, however, if data from the EAZA Fennec Fox ESB were added to the whereas the other approaches tended to be all or nothing, 0% or 100%). In contrast, the data set for the AZA Mexican Wolf SSP was much larger, providing more statistical power to estimate smaller effects, as male age, pair parity, male and female inbreeding coefficients, and pair type were all effective predictors of reproductive success. Additionally, the larger sample size and associated increase in power provides more opportunity to investigate possible interactive effects between factors. The conditional random forest technique was the only predictive model used that considers possible interactions between factors, which may explain why this technique worked best for the Mexican wolf population, as it was able to better fine-tune the predictions. We believe this approach is likely to work well for other species with richer historical data sets. Beyond the statistical modeling in R as part of the RVA process, the data exploration we conducted to populate the R models also revealed some useful information. For example, in 2010, as part of a new breeding strategy, proven-breeder fennec foxes were paired with inexperienced individuals in the hope that the experienced individual would “teach” the inexperienced one. Likewise, some pairs were also purposely selected to be comprised of individuals with different rearing types (hand- and parent-reared), with the hope that the more relaxed hand-reared individual would provide some stability for its mate. However, RVA results suggest that these ideas may have been counter-productive, so these practices were discontinued in 2017. It is difficult to decide how long to leave an unsuccessful pair together, so FIGURE 2 Variable importance scores for each factor used in the the information that no “carryover” pair has been successful after 2 or creation of nodes within the conditional inference trees for the 3 years, in fennec fox and Mexican wolves, respectively, provides fennec fox (a) and Mexican wolf (b) random forest models. Factors with higher importance scores are the variables that are driving the valuable information. While the finding of female age effects in both predictions of reproductive success (or failure) species was potentially predictable, given the importance of this factor
BAUMAN ET AL. | 63 TABLE 7 Comparison of ΔAICc and weights among models tested for Mexican wolf as part of the experience-based approach Variables in model ΔAICc Model weight Female age, male age, pair parity, pair type, male inbreeding, female inbreeding 0 0.77 Female age, male age, pair parity, pair type, age difference, litter last 5 years, litter last 10 years, 2.42 0.23 both at breeding location, year, male inbreeding, female inbreeding Female age, male age, pair parity, pair type, litter last 5 years, litter last 10 years 16.22 2E-4 Female age, male age, pair parity, pair type, age difference, litter last 5 years, litter last 10 years, 17.4 1E-4 both at breeding location, year Female age, male age, pair parity, pair type, litter last 5 years, litter last 10 years, both at breeding location 17.47 1E-4 Female age, pair parity, pair type, both at breeding location 30.8 2E-7 Pair parity, pair type, both at breeding location 40.62 1E-9 Null (no explanatory variables) 65.64 4E-15 in the literature for mammals generally (Cohen, 2004; Lockyear, years) was a surprise. This pattern, described by Daigle et al. (2015) in Waddell, Goodrowe, & MacDonald, 2009; Ricklefs, Scheuerlein, & captive lions, was speculated to be related to husbandry, since wild Cohen, 2003) and for tigers through a similar process (Saunders et al., lionesses commonly reproduce until 12 or 13 years of age. Further 2014) confirmation through such a rigorous process for these two investigation into both husbandry correlates and possible differences species provides support that these factors should be weighted highly in ovulatory patterns by age for fennec foxes is merited. Another in population planning. The finding that female fennec foxes surprising finding was the impact of male age in Mexican wolves, which reproduced for less than half their lifespan (no reproduction after 6 also needs further investigation. Lastly, it is interesting that, despite institutional knowledge being important for reproductive success in tigers and lions (Daigle et al., 2015; Saunders et al., 2014), it was not at all so for Mexican wolves. This may be because the Mexican Wolf SSP has emphasized consistent husbandry practices due to the reintroduc- tion potential and binational nature of that SSP, so institutional knowledge has not been lost. We see a role for RVA in any cooperative breeding program where breeding efficiency, that is, a high proportion of breeding recommendations result in births, is lacking. Turnover of SSP coordinators can be high, making it difficult for many program leaders to have long-term insight into reproductive performance of the population. With time, program leaders accumulate more experience dealing with reproductive challenges and may learn from research in the population they manage. Still, it is challenging for even an experienced program leader to put together all of the pieces that impact reproductive success in their population. They may borrow insights from other species that may apply to their own program or make common-sense assumptions in the absence of data, as was done previously in fennecs, about factors that should promote better breeding success. However, these guesses could be wrong; results from the RVA provide information for making evidence-based decisions about pairing and breeding strategies. Reproductive success should be monitored following changes implemented after an RVA, especially since this is a new process. The ability to now connect the RVA data collection process to PMCTrack, means that over time, RVAs can easily be run periodically to determine whether the lessons learned previously still apply. In addition, FIGURE 3 Area under the receiver operating characteristic (ROC) reproduction management strategies change as SSPs evolve from a curve (AUC) for four modeling strategies tested on (a) 37 breeding “growth phase” to a “maintenance phase” at space capacity, which can pairs from the 2014 and 2015 Fennec Fox Breeding and Transfer Plans and (b) 26 breeding pairs from the 2016 Mexican Wolf alter reproductive success and lead to the need for additional Breeding and Transfer Plan information and management considerations.
64 | BAUMAN ET AL. FIGURE 4 Predicted probabilities of success for (a) 37 breeding pairs from the 2014 and 2015 Fennec Fox Breeding and Transfer Plans and (b) 26 breeding pairs from the 2016 Mexican Wolf Breeding and Transfer Plan generated by four different modeling strategies. Filled circles represent the actual results of the breeding recommendations (1 = success, 0 = failure) The RVA examines factors objectively, at least for biological and as part of the new species recovery plan (USFWS, 2017). pair-related variables, in a relatively straightforward and consistent Additionally, because we know that periods of contraception and way that may identify key variables not previously thought to be periods of non-breeding can affect fertility and reproductive health important. No single RVA model will perfectly predict the outcomes of (Asa et al., 2014; Penfold et al., 2014 and references therein), the breeding pairs, and over time, as more data are added to the dataset, AZA RMC is developing another modeling approach called Lifetime these models will change. The RVA is not meant to make perfect Reproductive Planning (LRP) to model the demographic and genetic predictions, but rather to find primary drivers of reproductive success impacts of various reproductive management scenarios (e.g., breed or failure to advise population management in order to meet genetic early and often, intersperse contraception with gender separation and demographic goals. during non-breeding cycles, or breed and cull). These stochastic LRP While RVA results can be used solely to improve breeding models, like PVAs, can utilize the RVA results to parameterize the efficiency, they also can be utilized as parameters for other analyses models. LRP should also assist program leaders by modeling best related to population sustainability. PVAs (see Lacy, this issue and strategies to space pregnancies that would facilitate females being Che-Castaldo et al., this issue) are important tools in predicting how bred at younger ages (prime fertility) while maintaining demographic animal populations will perform over time with regard to genetics, and genetic goals as well as target population sizes. demographics, and persistence. An understanding of the variables Effective management of zoo populations has never been more that affect the reproductive performance of individuals and breeding important, with increasingly human-dominated landscapes and more pairs/groups is critical to making PVAs more reliable. For example, species becoming “conservation reliant” (Redford, Amato, & Baillie, RVA results were used in the recent Mexican Wolf PVA conducted 2011; Scott, Goble, Haines, Wiens, & Neel, 2010). An increasing number
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