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ISBN-10: 3880851336

ISBN-13: 9783880851337

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Then Eq. 4) becomes 03& 3 (1 — Qz/θζ) +#3101+032^2 = 0. 5) Now consider the diagrams of Figs. 6(a), 6(b), and 6(c). Clearly, in Fig. 6(a), species 1 would vanish because it is eaten by 2 with no source to supply it. 4) would apply. In Fig. 6c) k2ß2<0, kzß3>0. 8b) qi= — (*3Ä/ö2i) + (an/an) ft (1—α^φι/anhßz). 9) then ^3>0. The second term in gi is also positive while the first term is negative. 10) If it is, then species 1 survives. If it is not, then the equilibrium population of species 1 is negative so that, from any initial distribution, it will pass zero, the point of the vanishing of the species in its trajectory toward the equilibrium point.

67) we find (2/*)Φ £ = Ψ „ + ( α - α Υ ) * . 69c) if we define \ = E/a and ^τ/α 1 ' 2 . 27). The ideas presented for the investigation of that case are immediately applicable here. One finds that if initially the population is N0 so that V0= log No/Θ, then P(V9 Vo; t) = (ak/wa2[l- exp ( - 2 a ^ ) ] ) 1 / 2 X exp - {[V- Vo exp (-aki) Jka/σ2 X [ l - exp(2afe0]}. 70) A PRIMITIVE STATISTICAL MODEL OF POPULATION GROWTH If the initial distribution of population is P(Vo, 0> then again we have [Mp(ViVo;t)P(V0lO)dVo.

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Animal traction in Africa (GTZ-Publikationen)

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