数学付録 IIa ロジスティック式:これはいろいろバリエーションがありますが、アマゾンで中古本$30.65の Kareiva, P., C. Yuan-Farrell, and C. O’Connor. 2006. Whales are big and it matters. Pp 377-385 in J.A. Estes, et al (eds.) The Influence of Whales and Whaling on Ocean Ecosystems. University of California Press: Berkeley , CA だと、 Nt = K/(1 + be ^rt) という簡易計算式を使ってますね。 ここで、Nt = は t 年後の個体数推定, K = 環境収容力(carrying capacity), b = (K - No)/No, で No = 出発年次個体数, r = 年増加率。
これで数種類の鯨類個体群について、モラトリアムが持続することを前提に2050年の資源状況を計算してます。 [ TABLE 30.1 Whale Population Estimates for 2050] ________________________________________________________________________________________ _______________________Current___Annual Growth___Carrying_____2050_________________ Species _______________Estimate___Rate (r) % ______Capacity (K)__Estimate<a>__% of K_ Eastern North Pacific____26,000 ____2.5____________37,364________33,301______89.1__ gray whale <b> Sperm whale (global____452,000_____0.9__________1,110,000_____1,092,520_____98.4__ population)<c> Bering Sea bowhead whale _8,000<d>__3.1<e>_______10,000________9,588_______95.9__ (conservative K) Bering Sea bowhead whale__8,000<d>__3.1<e>_______23,000<f>____17,424_______75.8__ (liberal K) Humpback whale___________33,600<d>__3.9 <g>____115,000<h>____85,519_______74.4__ (conservative r) Humpback whale___________33,600<d>__12.6<g>___115,000<h>____114,491______99.6__ (liberal r) ________________________________________________________________________________________________________ <a> For simplicity, all populations were assumed to grow logistically according to the equation Nt = K/(1 + be^rt), where Nt = the estimated population in 2050, K = carrying capacity, b = (K - No)/No, No = current population size, r = annual growth rate, and t = (2050 - year of current estimate). <b> Rugh et al. 1999. <c> Whitehead 2002. <d> Gerber et al. 2000. <e> Cited in Best 1993. <f> Cited in Sheldon and Rugh 1995. <g> Clapham et al. 2001 <h> Evans1987. 数値は最新のIWCのデータとすこし違います。あくまでも計算のやり方の例示ということで。