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Resumenes 98 The dynamic of logistic stochastic system it is modeled by mean of a deterministic differential equation that describes the probability distribution of the stochastic variable Nt (population size) for each t ≥ 0 . Let ( N t ) a stochastic process of births and deaths [1] with t≥0 rates λn and β n respectively, the change of the probability distribution function (p.d.f) correspondent to population size n, when time t changes, it is modeled by the followings differential equations: dP dt ( n, t) ( n − 1, t) λ + P( n + 1, t) β − P( n, t)( λ + β ) = P n−1 n+ 1 dP dt ( 1, t) dP dt = P ( 0, t) = P ( 1, t) β1 ( 2, t) β − P( 1, t)( λ + β ) 2 where P(n, t) is the probability that in the instant t ≥ 0 the population size let n. This p. d. f., it is studied when the population is in equilibrium state, that is, in the instant when the births and deaths rates are equal. Therefore, it has that: with dP dt ( n, t) = 0 ( n 1, t) λ + P( n + 1, t) β = P( n, t)( λ + ) P β − n− 1 n+ 1 The method presented by Daniels [4] for the p.d.f., called Saddlepoint approximation is presented; after some transformations it is obtained the truncated saddlepoint approximation f m ( x) , [5. 6], resulting the normal distribution for m = 2 and the Saddlepoint approximation for determine the population distribution with m = 3. In [5] it is recommend its use and they employ a approximation by truncation for the Saddlepoint approximation of p.d.f. Concretes examples applied for snail gardens, badgers and foxes populations are given, using the approximation by truncation p.d.f., showing the goodness adjustment for different approximations effectuated according the parameter involves and using approximate and exact cumulants. Referencias [1] Bailey, N. T. 1964. “The Elements of Stochastic Processes”, Wiley, New York. [2] Daniels, H. E. 1954. Saddlepoint approximations in statistics, Ann. Math. Statist., 25: 631-650. 1 1 n n n n
Resumenes 99 [3] Daniels, H. E. 1960. Approximate solution of Green’s type for univariate stochastic processes, J. Roy. Statist. Soc., B22: 376-401. [4] Jensen, J.L. Renshaw,E 1995. Sadlepoint Approximations. Oxford University Press. [5] Matis, J., Kiffe, T.R., Hassan, J., Renshaw, E. 2003. A simple Saddlepoint approximation for the equilibrium distribution of the stochastic logistic model of population growth, Ecol. Mod., 161: 239-248. [6] Matis J. H, Kiffe,, 2004. On stochastic logistic population growth with immigration and multiples births. Theoretical Population Biology 65, 89-104 [7] Maulén Yañez, M.A, González Olivares, E. 2004. Birth and death processes in a static environment, In R. Mondaini (Ed.) Proceedings of the Third Brazilian Symposium on Mathematical and Computational Biology, E-Papers Serviços Editoriais Ltda, Rio de Janeiro , Vol. 1, 1-12.
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ORGANIZADO POR LA SOCIEDAD LATINOAM
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(en orden alfabético) COMITÉ CIEN
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CURSILLOS Cursillo Nº1: Dinámica
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CONFERENCIAS INVITADAS
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Conferencias 10 Estabilidad y persi
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Conferencias 12 (K, the ‘carrying
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Conferencias 14 Víctimas Inmigrant
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Conferencias 16 Influencia de la di
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Resumenes 19 Bifurcaciones de Hopf
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Resumenes 21 where y = y(t) represe
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Resumenes 23 Dinámica del modelo d
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Resumenes 25 In this work, we propo
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Resumenes 27 Simulação computacio
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Resumenes 29 of the minisymposium:
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Resumenes 31 Honeybee, Apis mellife
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Resumenes 33 The minimum ratio is t
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Resumenes 35 [1] On the role of end
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Resumenes 37 Modelo matemático de
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Resumenes 39 Figure 1: Plano de fas
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Resumenes 41 Dinámica de poblacion
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Resumenes 43 El método de las solu
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Resumenes 45 Dinámica de un tumor
Page 49 and 50: Resumenes 47 Several cancer models
Page 51 and 52: Resumenes 49 process is physically
Page 53 and 54: Resumenes 51 For the analysis of fr
Page 55 and 56: Resumenes 53 Sustainability in floo
Page 57 and 58: Resumenes 55 Sincronismo em redes d
Page 59 and 60: Resumenes 57 Um modelo de autômato
Page 61 and 62: Resumenes 59 Um modelo matemático
Page 63 and 64: Resumenes 61 Redes de mapas acoplad
Page 65 and 66: Resumenes 63 Sobre la dinámica de
Page 67 and 68: Resumenes 65 Un modelo de depredaci
Page 69 and 70: Resumenes 67 There exists wide evid
Page 71 and 72: Resumenes 69 Modelado del control n
Page 73 and 74: Resumenes 71 Modelo de red neuronal
Page 75 and 76: Resumenes 73 Efectos de la radiaci
Page 77 and 78: Resumenes 75 Un modelo matemático
Page 79 and 80: Resumenes 77 Estudio comparativo de
Page 81 and 82: Resumenes 79 Introduction The proje
Page 83 and 84: Resumenes 81 formulation to obtain
Page 85 and 86: Resumenes 83 tiene un único punto
Page 87 and 88: Resumenes 85 [4] Courchamp, F., Clu
Page 89 and 90: Resumenes 87 An important part of a
Page 91 and 92: Resumenes 89 A(H3N2). Starting in V
Page 93 and 94: Resumenes 91 i) Panmixia, donde se
Page 95 and 96: Resumenes 93 punto de equilibrio y
Page 97 and 98: Resumenes 95 Un modelo epidemiológ
Page 99: Resumenes 97 Aproximación saddlepo
Page 103 and 104: Resumenes 101 bloqueados. El nudo q
Page 105 and 106: Resumenes 103 Referencias • Stauf
Page 107 and 108: Resumenes 105 Un modelo dinámico d
Page 109 and 110: Resumenes 107 Un modelo en ecuacion
Page 111 and 112: Resumenes 109 The mite show a prefe
Page 113 and 114: Resumenes 111 Ondas viajantes en un
Page 115 and 116: Resumenes 113 [5] Pregnolatto S. de
Page 117 and 118: Resumenes 115 All this will enable
Page 119 and 120: Resumenes 117 Extensión de un mode
Page 121 and 122: Resumenes 119 ∂C ∂C C = 0. = 0.
Page 123 and 124: Resumenes 121 Comparación de Enfoq
Page 125 and 126: Resumenes 123 Refúgios Espaciais e
Page 127 and 128: Resumenes 125 La dinámica del sest
Page 129 and 130: Resumenes 127 Dinámica poblacional
Page 131 and 132: Resumenes 129 Aproximación y simul
Page 133 and 134: Resumenes 131 An age-structured fin
Page 135 and 136: Resumenes 133 Respuestas demográfi
Page 137 and 138: Resumenes 135 Modelando el efecto A
Page 139 and 140: Resumenes 137 the Allee effect are
Page 141 and 142: Resumenes 139 Tratamientos de endom
Page 143 and 144: Resumenes 141 Implicaciones del efe
Page 145 and 146: Resumenes 143 phenomenon has been e
Page 147 and 148: Resumenes 145 Dinámica individual
Page 149 and 150: Resumenes 147 • f mixing ⇔ f mi
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Resumenes 149 Introduction The inve
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Resumenes 151 DNA microarrays are t
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Resumenes 153 V. Cholerae: Primeros
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Resumenes 155 Análisis cuantitativ
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Resumenes 157 Dinámica de un model
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Resumenes 159 Obtención de paráme
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Resumenes 161 [4] Nagy K. A (1987)
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Resumenes 163 diferencial automáti
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Resumenes 165 The localized peaks S
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Resumenes 167 obteniéndose que sie
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Resumenes 169 [CLARK 90] Clark, C.
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Resumenes 171 Numerical algorithms
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Resumenes 173 The second method of
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Resumenes 175 los parámetros son t
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Resumenes 177 Bifurcación hacia at
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Resumenes 179 Malaria is the tropic
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