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。
Encyclopedia of marine mammals�/�eds.: William F. Perrin, Bernd Wu¨rsig, J.G.M. Thewissen San Diego�:�Academic Press,�2002 P.974- 【Population Dynamics】 PAUL R. WADE National Marine Fisheries Service,Seattle, Washington Population dynamics is the study of changes in population through time. In other words, it is the study of why populations increase, decrease, or remain the same. One fundamental concept in population dynamics is that the maxi- mum rate at which a population can increase is determined by the intrinsic life history characteristics of the species. Thus, much of the research on marine mammal population dynamics is focused on the better definition of life history parameters. Additionally, many extrinsic factors can potentially influence the dynamics of a population. These include environmental variability, disease, competition, and predation. There is also much interest in the role of density dependence in controlling marine mammal population dynamics. In addition to being sci- entifically interesting, basic concepts of density dependence have become important to the management and conservation of marine mammals.
I. Rates of Population Increase A. Population Growth of Long-Lived Animals Most long-lived animals, such as marine mammals and large terrestrial mammals, have relatively slow intrinsic rates of in- crease compared to most other kinds of animals. The modest population growth rates are the consequence of their life his- tory characteristics. Characteristics such as the age at which fe- males start reproducing, the number of years between births, and how many years a female will live and reproduce, deter- mine how quickly a population can increase. Most marine mam- mal species take many years to reach sexual maturity and have long gestation periods that result in the production of, at most, only one young a year. In fact, most species give birth only once every several years. Even when annual rates of survival are very high, these characteristics cause populations to grow slowly. Low rates of population growth make most species of marine mammals vulnerable to overexploitation, as shown by the rapid depletion of many whale populations by commercial harvest.
Population growth can be measured in two ways. In gen- eral, the most reliable estimates of population growth come from abundance data collected over many years. Population abundance can be estimated from surveys or counts, and when repeated over several years, the trend (percentage change per year) in a population can be estimated. Specifically, the slope of a linear regression on the natural logarithm of abundance represents the rate of increase (r) of a population experiencing exponential growth. Because population growth is slow and population estimates are imprecise, 10 or more years may be required to directly measure population growth rates.
A less direct way of estimating population growth is from life history data. Estimates of age of sexual maturity, birth rate, sur- vival rate, and maximum age can be compiled in a Leslie matrix or similar model, which can then be used to estimate the rate of increase (usually estimated as λ = e^r). Although such calcu- lations have been useful for exploring potential population growth rates, relatively few estimates of actual population growth have been made in this way. The main hindrance is the lack of direct data on survival rates of marine mammals. Only a few species have been amenable to survival estimation, usually from mark-recapture studies using individuals recognizable from tags, unique scars, or other markings. Such studies have been un- dertaken in California sea lions (Zcdophus calijvmianus'), bot- tienose dolphins (Tursiops truncatus), and killer (Orcinus area), humpback (Megaptera novaeangliae), bowhead (Balaena mys- ticetus), and right whales (Eubalaena spp.)
C. Taxonomic Differences (略) II. Extrinsic Factors Affecting Population Size A. Environmental Variance (略) B. Disease and Natural Toxins (略) C. Competition Competition from other species may influence the population dynamics of marine mammals, although there is little evidence for this. Whether this is due to competition being unimportant or whether it is simply too difficult to demonstrate is an open ques- tion. An increase in crabeater seals (Lobodon carcirwpJwga) was directly attributed to a release from competition following the se- vere depletion of several species of baleen whales in the Antarc- tic, leading to an increased availability of KRILL. This explanation has been reevaluated in light of evidence of environmental influ- ences on the population dynamics of Antarctic pinnipeds. It should be noted that some general textbooks (such as books on oceanography) state that competition for krill from Antarctic minke whales (Balaenoptera bonaerensis) has prevented the re- covery of depleted blue whales (B. musculus) in the Antarctic. However, the recent information indicates that the lack of recov- ery of blue whales in the Antarctic can be fully explained by pre- viously unknown ILLEGAL HARVESTS by the former Soviet Union.
D. Predation
Many marine mammals, especially smaller ones, are preyed upon by other animals, but predation has rarely been suggested as a strong controlling factor in their population dynamics. One exception is a recent study that suggested sea otters may have declined in one part of Alaska because of killer whale predation. Pinniped pups are often vulnerable to predation from predators such as leopard seals (Hydrurga leptonyx), great white sharks, and killer whales. While such predation has been shown to af- fect the growth of local ROOKERIES, it is unclear if it exerts a strong influence on the dynamics of an entire population. Sim- ilarly, some pelagic dolphin species experience predation from sharks, and killer whales prey on many cetacean species. Again, even though predation of cetaceans occurs, it is difficult to know whether it influences the dynamics of these populations.
III. Density Dependence A. Compensation Another area of great interest is the role of density depen- dence in controlling the population dynamics of marine mam- mals. It is generally accepted that marine mammal populations experience density dependence. In other words, as populations become relatively large, they tend to have lower population growth, and eventually stop increasing. This form of density dependence is termed compensation. The level at which a pop- ulation stabilizes is called its carrying capacity. Evidence has been found for density dependence in life history parameters such as the age of sexual maturity. Females from a population at a level well below K become sexually mature and start re- producing at an earlier age than females from a population at a level close to K. Presumably this is because of access to greater resources such as prey. For example, the age of sexual maturity apparently became younger for fin (Balaenoptera physalus) and sei whales (B. borealis) in the Antarctic as their populations were depleted by commercial harvest.
It has been hypothesized that the mechanism of the regu- lation of populations of long-lived mammals would follow a se- quence as a population increased, with density dependence first affecting the rate of immature survival, then the age of sex- ual maturity and the birth rate, and finally the adult survival rate. This hypothesis partially follows from the recognition that a long-lived species that reaches sexual maturity slowly and has a low intrinsic rate of increase must maximize adult survival in order to persist. Adult females of long-lived species may be able to forgo reproduction to maximize individual survival when conditions are poor, but it is unclear if there is necessarily a specific sequence in how density dependence affects all life history traits that are common to all marine mammals.
西アフリカのIWCギニア代表代理、アマドウ・ディアロ氏の場合、2004年に「発展途上国 がIWCに議席を持ち、投票するのはわれわれすべてにとって漁業が重要であり、我々の 国民に喰わせ、魚を他国に輸出する必要もあるからです」とBBC, 2004, ‘Surinam joins International Whaling Commission’ BBC Monitoring Americas, 19 July 2004.で立派に発言してます。
29−30頁で紹介されてるBox 1 Worrying about Whales Instead of Managing Fisheries: A Personal Account of a Meeting in Senegal という今年5月の会合の場合、 もっとひどくグロテスクなことになってます。こういう討論会は日本の子供たち には見せたくないなあ。