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Genus

Journal of Population Sciences

Table 2 A 5-interval projection in a hypothetical three-state (path) membership model with states unaffiliated (U), joined (J), and active (A)

From: Rates, intrinsic linkages, and multistate population dynamics

 

Fraction in state (f)

z2t

Rates of transfer (Eqs. (20)–(21))

Time

U

J

A

 

m UJ

m JU

m JA

m AJ

A. Interval by interval calculations (Eq. (1))

 0

.85

.10

.05

–

–

–

–

–

 1

.82925

.10985

.06090

.70

.01317

.06586

.08474

.12106

 2

.81243

.11769

.06988

.71

.01335

.06674

.08291

.11678

 3

.79876

.12391

.07733

.72

.01357

.06785

.08026

.11147

 4

.78759

.12885

.08356

.73

.01384

.06921

.07698

.10545

 5

.77844

.13275

.08881

.74

.01419

.07093

.07318

.09890

B. Stable population values (Ï„j5) implied by time 5 rates

 5

.74184

.14837

.10979

     

C. Time 5 values calculated directly from time 0 populations and z values (Eq. (2))

 

 5

.77844

.13275

.08881

     
  1. Notes: Fixed values are w = 0.8, n = 5, and z 1 = m UJ/m JU = 0.20. Rate ratio z 2t = m JAt/m AJt increases as shown above. Stable population proportions are τ2t = z 1/(1 + z 1 + z 1 z 2t), τ3t = z 1 z 2t/(1 + z 1 + z 1 z 2t)
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