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Table 3 Number of increased, new-born, dead and supplementary Red-crowned Cranes (RCs, Grus japonensis) per year and the number of cumulative supplementary RCs in captive populations during the 1999–2013 period in China

From: A growing captive population erodes the wild Red-crowned Cranes (Grus japonensis) in China

Year

Size of estimated captive population (N i )a

Increase in the number of RCs per year (N i+1N i )b

Number of new-born RCs per year (N b)c

Number of dead RCs per year (N d)d

Number supplementary RCs per year (N s)e

Number of cumulative supplementary RCs (N cs)f

1999

555

41

51

20

10

10

2000

596

44

55

21

11

21

2001

641

48

59

23

12

33

2002

689

51

63

25

13

46

2003

740

55

68

27

14

60

2004

795

59

73

29

15

75

2005

855

64

78

31

16

92

2006

918

69

84

33

17

109

2007

987

74

90

36

19

128

2008

1061

79

97

38

20

148

2009

1140

85

105

41

22

169

2010

1225

91

112

44

23

192

2011

1316

98

121

47

25

217

2012

1414

105

130

51

27

244

2013

1520

Total

965

1186

466

244

  1. aEstimated captive population size (N i ): \( N_{i + 1} = (1 + r)N_{i} \), where i refers to year; for example: N 2000 = N 1999 × (7.46% + 1) = 555 × 1.0746 = 596, N 2001 = N 2000 × (7.46% + 1) = 596 × 1.0746 = 641
  2. bIncrease in number of RCs per year = N i+1 − N i ; for example: the increase in number of birds between 1999 and 2000 = N 2000 − N 1999 = 596 − 555 = 41
  3. cNumber of new-born RCs per year (N b) = μN i ; for example: N b in 1999 = N 1999 × 9.17% = 555 × 9.17% = 51, N b in 2000 = 596 × 9.17% = 55
  4. dNumber of deaths per year (N d) = ϑN i; for example: N d in 1999 = N 1999 × 3.6% = 555 × 3.6% = 20, N d in 2000 = 596 × 3.6% = 21
  5. eNumber of supplementary RCs per year (N s) \( = N_{i + 1} - N_{i} + N_{\text{d}} - N_{\text{b}} \); for example: N s in 1999 = (increase in number of RCs in 1999) + (N d in 1999) − (N b in 1999) = 41 + 20 − 51 = 10. When N s is equal to or less than zero in a particular year, there is no erosion effect on the RC population in the wild
  6. fNumber of cumulative supplementary RCs (N cs) \( = \sum {N_{\text{s}} } \); for example: N cs between 1999 and 2001 = sum of the N cs in 1999, 2000 and 2001 = 10 + 11 + 12 = 33