Prologue |
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1 | (6) |
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1 Hunting Strategies Of Predators As Revealed In Field Studies Of Great Tits |
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7 | (19) |
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7 | (1) |
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1.2 Search Image Theory by Lukas Tinbergen |
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8 | (3) |
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1.3 Alternative Theory: Hunting by Profitability |
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11 | (10) |
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21 | (2) |
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1.5 Allotment of Hunting Time among Different Sites |
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23 | (2) |
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1.6 Hunting by Profitability as Principle |
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25 | (1) |
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2 The Paradox Of Crypsis: Is It Effective Against Visual Predation? |
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26 | (5) |
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3 Logistic Law Of Population Growth: What Is It Really? |
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31 | (21) |
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31 | (1) |
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3.2 The Classical Logistic Equation |
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32 | (2) |
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3.3 Fundamental Nature of Population Processes |
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34 | (1) |
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3.4 Ecological Significance of the Differential Equation: dx/dt = xƒ(x) |
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34 | (5) |
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3.5 Discrete-Time Processes |
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39 | (7) |
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3.6 Classical Logistic Model as Particular Case of Model (3.10) |
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46 | (2) |
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3.7 Reinterpretations of Parameters ρ and K |
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48 | (2) |
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3.8 Structual Problem of the Common--Version Logistic Model |
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50 | (1) |
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3.9 Final Remarks of Chapter |
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51 | (1) |
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Appendix 3A How to Solve a Differential Equation in the Models (3.1) |
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52 | (3) |
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Appendix 3B The Derivative d(eu)/du = eu |
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55 | (1) |
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Appendix 3C The Derivative d(ln v)/dv = 1/v, v > 0 |
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56 | (1) |
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Appendix 3D The Anomaly in the Common Version Logistic Equation (3.3c) |
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56 | (1) |
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Appendix 3E Mathematical Attributes of the Verhulst Equation (3.3a) |
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56 | (2) |
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4 Reproduction Curves And Their Utilities |
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58 | (34) |
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58 | (3) |
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4.2 Drawing a Reproduction Curve |
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61 | (1) |
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4.3 Generating the Population Series |
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61 | (2) |
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4.4 Mathematical Roles that the Model Parameters Play |
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63 | (3) |
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4.5 Problems with Population Size as a Non-negative Quantity |
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66 | (2) |
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4.6 Logarithmic Transformation of a Reproduction Curve |
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68 | (3) |
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4.7 An Application to Actual Data |
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71 | (4) |
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4.8 Variation in Dynamical Pattern of the Model Process (4.4b) |
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75 | (3) |
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4.9 Examples of Variations in Dynamical Pattern |
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78 | (4) |
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4.10 Difference between Discrete-Time and Continuous-Time Processes |
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82 | (1) |
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4.11 Ecological Feasibility of Variations in Discrete-Time Processes |
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83 | (2) |
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4.12 Endogenous and Exogenous Processes |
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85 | (4) |
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4.13 Application of an Endogenous---Exogenous Process Model to Wildlife Management |
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89 | (1) |
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4.14 The Origins of the Myths of the Logistic Law |
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90 | (1) |
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4.15 Final Remarks of Chapter |
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91 | (1) |
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Appendix 4A The Derivative of a Function Is a Measure of the Slope of the Curve Generated by the Function |
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92 | (3) |
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Appendix 4B The Derivatives of a Few Standard Functions |
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95 | (1) |
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Appendix 4C L'Hopital's Rule |
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96 | (1) |
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Appendix 4D Prototype Curve and Its Translation |
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96 | (2) |
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5 Generalization Of The Logistic Model |
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98 | (17) |
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98 | (2) |
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5.2 Negative Binomial Distribution |
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100 | (5) |
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5.3 Ecological Application of the Negative Binomial Distribution |
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105 | (3) |
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5.4 A General Model of Intraspecific Competition |
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108 | (4) |
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5.5 Model (3.10) as a Particular Case of Model (5.12) |
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112 | (1) |
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5.6 Interpretation of the Hassell Model: rt = xt+ 1/xt --- rm/(1 + axt)b |
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113 | (1) |
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5.7 One More Model to Examine |
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113 | (2) |
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115 | (1) |
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Appendix 5B Why the Name `Negative Binomial'? |
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115 | (1) |
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Appendix 5C How to Calculate the Mean and Variance of the Random Number m in (5.4) |
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116 | (2) |
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Appendix 5D Why Do the Terms jkj--x Qr(j) in (5.6) Vanish in the Limit (j → ∞)? |
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118 | (1) |
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Appendix 5E Convergence of the Sum {Σ[ (h + j -- 1)!/h!(j -- 1)!](kq)j--1} to (1 -- kq)--(h+1) |
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119 | (1) |
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6 Scramble And Contest Competition: What Is The Difference? |
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120 | (20) |
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120 | (1) |
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6.2 Drawing Reproduction Curves Based on Model (5.12) |
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121 | (5) |
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6.3 Broader Interpretation of Parameter h |
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126 | (2) |
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6.4 In the Weirdland of a Negative Hit |
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128 | (2) |
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6.5 Nature of Competition |
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130 | (2) |
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6.6 What Determines Parameter h in Actual Processes? |
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132 | (4) |
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6.7 Scramble and Contest as Elements of Competition |
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136 | (4) |
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6.8 Concluding Remarks of Chapter |
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140 | (1) |
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Appendix 6A The Logarithm of a Negative Real Number is a Complex Number |
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140 | (3) |
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Appendix 6B How to Estimate Parameters (Rm, h, c/h) to Fit Model (6.1a) to the Observed Reproduction Curve in Figure 6.3a |
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143 | (2) |
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7 Regulation Of Populations: Its Myths And Real Nature |
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145 | (32) |
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145 | (1) |
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7.2 Biological Population Processes As Stochastic Processes |
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146 | (4) |
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7.3 Defining Population Persistence |
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150 | (1) |
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7.4 Investigations into Mechanisms for Persistent State |
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151 | (2) |
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7.5 Density--Dependent Processes under Exogenous Influences |
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153 | (1) |
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7.6 Density--Independent Processes |
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154 | (4) |
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7.7 Algebra of Stipulation (7.3) for Population Persistence |
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158 | (3) |
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7.8 Random Walk As Unregulated Processes |
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161 | (1) |
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7.9 Density--Dependent Regulation |
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162 | (5) |
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7.10 Precise Nature of Density--Dependent Regulation |
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167 | (2) |
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7.11 Density--Independent Regulation |
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169 | (1) |
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7.12 Logical Problem in Climatic--Control Theories |
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170 | (4) |
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7.13 Myth of Density--Dependent Regulation |
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174 | (3) |
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7.14 Concluding Remarks of Chapter |
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177 | (1) |
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Appendix 7A Rules of Operations on the Expectations Used in the Present Chapter |
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177 | (1) |
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Appendix 7B Derivation of Relationship (7.5) |
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178 | (2) |
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Appendix 7C Calculation of an Autocovariance Function (ACVF) |
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180 | (1) |
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8 Predator---Prey Interaction Processes |
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181 | (40) |
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181 | (1) |
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8.2 Formulation of Endogenous Models of the Interaction Processes |
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181 | (5) |
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8.3 Simulation of the Dynamics of Predator---Prey Interactions |
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186 | (4) |
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8.4 Variation in Dynamical Patterns |
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190 | (7) |
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8.5 Effects of Random Exogenous Influences |
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197 | (9) |
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8.6 Reproduction Surfaces of a Predator---Prey Process |
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206 | (6) |
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8.7 Revealing Conditional Reproduction Curve in Observed Series |
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212 | (5) |
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8.8 Problems Inherent to Earlier Models |
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217 | (2) |
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8.9 Interactions between Predator Complex and Prey Complex |
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219 | (2) |
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Appendix 8A Ecological Mechanism Underlying the Equation q(xt) = [ 1 --- exp(--- bxt)] in (8.2) |
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221 | (1) |
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Appendix 8B How to Find the Equilibrium Levels of the X and Y Series in the Simultaneous Equations (8.4) |
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222 | (1) |
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Appendix 8C How to Generate Correlated Series of Random Numbers |
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223 | (2) |
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9 Interspecific Competition Processes |
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225 | (25) |
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225 | (1) |
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9.2 Formulation of Competition Model |
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225 | (2) |
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227 | (1) |
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9.4 Criteria for Coexistence and Elimination |
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228 | (17) |
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9.5 Reconsideration of the `Competitive Exclusion Principle' |
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245 | (3) |
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9.6 Alternative Ways of Viewing Nature |
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248 | (1) |
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9.7 Struggle for Existence vs Optimization of Profitability |
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249 | (1) |
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Appendix 9A How to Calculate x** and y** |
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250 | (1) |
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Appendix 9B Infeasibility of Category (v) in Table 9.1, Section 9.4 |
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250 | (1) |
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Appendix 9C How to Incorporate the Effect of Random Exogenous Influences in the Model |
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251 | (1) |
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10 Observations, Analyses, And Interpretations: A Personal View Through The Spruce Budworm Studies |
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252 | (19) |
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10.1 An Outline of the Spruce Budworm Studies |
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253 | (1) |
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10.2 Earlier View of Outbreaks |
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254 | (13) |
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10.3 Thoughts on the Basic Processes of Ecological Studies |
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267 | (3) |
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10.4 Concluding Remarks in the Quest for Certitude |
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270 | (1) |
References |
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271 | (2) |
Index |
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273 | |