Marginal diversity analysis of conservation of Chinese domestic duck breeds

The present study aimed to systematically evaluate the genetic diversity of Chinese domestic duck breeds and ensure the most effective allocation and usage of conservation funds. We first performed an analysis of DNA genetic distance in 21 duck breeds by measuring short tandem repeats. Then, we calculated the extinction probability, contribution rate, and marginal diversity for each breed. The results showed that the extinction rate of the Zhongshan duck, Guangxi duck, and Ji’an duck were the highest at 0.67, 0.59, and 0.59, respectively, and that of the Linwu duck, Jinding duck, and Gaoyou duck were the lowest at 0.15, 0.18, and 0.19, respectively. The current diversity of populations was 7.72 and the expected diversity in five hundred years is 5.14 ± 1.15. The marginal diversity of the Chinese Muscovy duck was the largest (−2.20), accounting for 42.61% of the expected diversity, followed by the Guangxi duck (−0.49, 9.44%), whereas the Jinding duck was the smallest (−0.12; 2.32%). The protection potency of the Chinese Muscovy duck was the largest (0.61), followed by Guangxi duck (0.29), whereas the Jinding duck was the smallest (0.02). This study provides a reference for determining the conservation priority of Chinese domestic duck breeds or genetic resources.

Breed and genetic distance measurements. The objects of the study were Chinese domestic duck breeds or their genetic resources. Their name, sample size, and origin are shown in Table 1. Blood was collected according to pedigree, to ensure that samples were from unrelated individuals. The samples (0.5 mL) obtained from the vein of the ducks wings were carefully mixed with lysis solution and kept at 4 °C for subsequent DNA extraction. DNA extraction was performed according to the method described by Huang et al. 17 .
PCA and population structure analysis for all breeds. In this study, SPSS13.0 software was used for principal component analysis (PCA) of all the detected alleles 20 , and Structure 2.0 (http://rosenberglab.bioinformatics.med.umich.edu/distruct.htm) software was used for genetic Structure analysis of 21 populations. Extinction probability. Extinction probability is an important index for genetic resource diversity. Future changes in the diversity of local breeds or genetic resources can be measured as the extinction probability over time (500 years) 21 . In Weitzman's approach, the extinction probability (Zi) of each set is a variable that needs special attention. There are various methods for calculating Zi; however, we adopted the method proposed by Reust-Marti 11 . This method uses seven variables: the total population size (POS), its change over the past 10 years (CHA), distribution of the breed (DIS), risk of indiscriminate crossing (CRO), organization and conservation measures of breeding (ORG), special traits (SPE), and threat of production transition (PRO) ( Table 2). Different weights (w i ) were given to different variables to estimate Zi in the future 500 years. The estimate formula and correction formula are as follows:  .
For the set (S) containing a certain number (N) of breeds and genetic resources, and a breed i, the distance of j ∈ S can be expressed as d ij . According to Weitzman's recursive algorithm, the diversity variable D (S) can be calculated by an N × N distance matrix. The probability of a breed's existence in 500 years is 1-Zi, if Z is an N-dimensional vector containing Zi of N sets. K is an N-dimensional vector containing the indicator variable Ki (i = 1, 2, … N). Ki = 1 if the set i exists, whereas Ki = 0 if the set i is extinct. Therefore, K represents an overview of the status in which a subset of breeds exists and its complementary subset is extinct. The formula of the existence probability of a subset of breeds is as follows: i k i i D K is the diversity of the subsets safe from extinction. The expected diversity at the end of the time horizon (500 years) is calculated as: The variance of the expected diversity is: The marginal diversity of a breed or genetic resource reflects the variation of the expected diversity when the extinction probability is increased by one unit. The marginal diversity is calculated as follows: i i Based on the extinction probability and expected diversity of a breed or genetic resource, Weitzman suggested conservation potency as the optimal parameter to assess the genetic diversity over a given time horizon. The conservation potency (CP) is calculated as follows: i i i CP i represents a possible increase in the expected diversity of a breed or genetic resource when the threat is completely removed. According to previous work by Simianer et al. 10 , CP i is the optimal parameter for determining conservation schemes, with the highest CP i requiring a minimum amount of capital required for the protection scheme 22 . The breed or genetic resource with the highest CP i should be allocated the least funds in breeding conservation efforts 10,23 .

Influencing factor Abbreviation Grading standard
Total population size POS 0.3 < ten thousand; 0.2 = ten thousand to one hundred thousand; 0.1 = one hundred thousand to one million; 0 = one million Change of total population size over the past 10 years CHA 0.1 = decreasing (>20%); 0 = increasing or maintaining stability Distribution of the breed DIS 0.2 = county; 0.1 = city; 0 = trans-regional and trans-provincial areas  Table 2. Influencing factors and criteria of extinction probability.

Results
Genetic distance. Twelve simple sequence repeats were detected in the 21 duck breeds. Nei's standard genetic distance was estimated using Microsatellite-Toolkit and Dispan 24 . According to the genetic distance matrix (Table 3) and cluster analysis by the unweighted pair-group method with arithmetic means (Fig. 1) 25 , FY belonging to the Cairina breed forms a single set, whereas the other 20 duck breeds (Anas) form three large sets. The distance between GY and JA was the shortest, and the distance between FY and GX was the longest First bullet.  www.nature.com/scientificreports www.nature.com/scientificreports/ 12 breeds were clustered into one group. When K = 3 and K = 4, no single group was isolated. FY, LC, PT were clustered into one group. FY ducks were isolated as a single group until K = 5. When K = 7, BJ, JC, JS and ZS still formed a group.CH, DY and JX still gathered into one group: GX, GY, JA, JD CLUSTERED into the last one group.
Extinction probability. The average extinction probability for the 21 Chinese domestic duck breeds and genetic resources was 0.38% (Table 4). ZS, GX, and JA had the largest extinction probabilities, whereas LW, JD, and GY had the smallest. Current and expected future diversity. The current diversity of the 21 breeds and genetic resources was determined to be 7.72, and the expected diversity of all sets in 500 years is 5.14 ± 1.15. Therefore, an overall decrease of 2.58 (33.43%) is anticipated.
Contributions and marginal diversities of each breed. The term "contributions" is defined as the percentage of contribution of each breed to overall diversity. The contributions and marginal diversities of each of the 21 breeds are shown in Table 5 and Fig. 3. The contribution of FY was the largest (Table 3) followed by GX, whereas JD had the smallest contribution. Similarly, in terms of marginal diversity, FY showed the largest (Table 5), followed by GX, whereas JD has the smallest (−0.12, 2.32). Finally, FY had the highest conservation potency, followed by GX, and JD had the lowest.

Discussion
There are numerous domestic duck breeds in China including 27 indigenous breeds, two introduced breeds, and a few developing breeds. However, with the introduction and promotion of cherry valley duck, the number of local duck species in China has dropped sharply, and many species are facing the danger of extinction 26 . Conservation of genetic diversity plays an important role in sustaining the livestock breeds 27 . At present, Weitzman marginal diversity method has attracted more and more attention in the research on rational allocation of livestock and poultry resources protection funds, and has become one of the most dynamic theories in the field of livestock genetic resources protection and utilization 28,29 . There were many researches on animal genetic diversity in the world [30][31][32] , but few of them analyze the application of marginal diversity method To our knowledge, Reist-Marti et al.(2003) have estimated extinction probability in livestock breeds 11 . Bennewitz (2005) estimated the extinction probabilities of 5 German dual-purpose cattle breeds by population viability analysis 33 . And then (2006) he analyzed 44 North Eurasian cattle breeds using simplified determined extinction probabilities. The results show that the expected loss of diversity within the next 50 years is between 1 and 3% of the actual diversity 34 . The marginal diversity analysis of goat 29 , sheep 35 , cattle 36 , pigs 37 has been completed in China, which provides a reliable data reference for the division of conservation funds. After years of investigation of domestic duck resources and collection of blood samples, this paper analyzed the marginal diversity and extinction probability of local duck breeds in China for the first time.
In this paper, the PCA was used to explain the molecular genetic relationships among the populations and a plane distance map was constructed, reflecting the real genetic information and genetic relationships of the 21 populations. Structure cluster analysis use allelic and genotype data from multiple loci, such as SSR loci, to construct a cluster model. Structure 2.0 program was based on Bayesian probability theory, adopt Markov-Monte Carlo simulation algorithm, and used mixed model when running the program to reveal the unknown population genetic relationship and potential population Structure from all population levels 38 . The expected number of classification (K value) of the detected group was set at runtime, which can be used to divide all individuals and reflect www.nature.com/scientificreports www.nature.com/scientificreports/ the genetic structure of the group. It is especially suitable for the study of the genetic structure, the differentiation and migration of individuals. In this paper, the population Structure diagram and the maximum-likelihood tree 39 obtained based on Structure 2.0 program were consistent with the results from PCA, verifying the accuracy of population Structure inference.   The calculation for extinction probability considers all factors that might cause change in a breed or genetic resource, making it an accurate and reliable estimation 40 . However, due to the political and economic situation in China, as well as the distribution of indigenous duck breeds and resources, some factors were not considered in this study, such as natural disasters, reliability of the information source, and development of reasonable storage approaches. For this measurement, seven variables (POS, CHA, DIS, CRO, ORG, SPE, and TRA) were assigned to different weights as major factors. These variables have been proved to be important factors reflecting population diversity. Here, we calculated the current and expected population diversities of a total of 21 Chinese duck breeds, respectively. Importantly, we found that the expected diversity (within 500 years) were 33.43% lower than current diversity.
Some variables for calculating the extinction probability, such as CHA and CRO, only consider the conservation of a single breed or genetic resource, and do not account for the effect of the conserved breed on the genetic diversity of the entire population 41 . If limited breeding conservation funding is allocated based on extinction probability parameters, it may not be the most beneficial solution for the entire population, especially if that population includes numerous breeds and strains. Instead, the breed with the largest contribution should be given the highest priority 42,43 . In this study, the largest contributor was FY, followed by GX.
However, breed contribution is not the only consideration for conservation planning efforts, and its calculation does not consider extinction probability. In contrast, marginal diversity considers both contribution and the extinction probability, and can therefore act as a comprehensive measurement of the importance of each breed. According to Weitzman, marginal diversity parameters should be considered the preferred reference during breeding conversation planning 44 . Conserving the breed with the largest conservation potency is the most effective way to maintain overall genetic diversity. Therefore, the first two breeds prioritized should be FY and GX, followed by CH, JC, JS, JX, JA, PT, TW, LC, DY, SS, ZS, JJ, SM, MW, BJ, YX, LW, GY, and JD.
Based on the marginal diversity parameters, we identified the conservation priority of 21 local duck breeds and genetic resources. FY and GX are the first two breeds that should be protected. The conservation priority in this study can provide a reference for breed conservation planning.

Data Availability
The data generated and analyzed as a part of this study are included within this article.  Table 1.