THE SYSTEMATIC FORMULATION OF TRACTABLE SINGLE-SPECIES POPULATION MODELS

SUMMARY (3) We illustrate the use of the formalism in the construction and analysis of two models of laboratory insect populations: a detailed model of Nicholson's blowflies and a 'strategic' model of larval competition intended to refine the design of experiments in progress on the dynamics of the Indian meal-moth Plodia interpunctella (Hiibner). (4) The model of Nicholson's blowflies is dynamically identical to a model previously derived heuristically. We have fitted the parameters using a more comprehensive range of data, and have illustrated explicitly the passage of large, quasi-cyclic fluctuations through the age structure. (5) We use the larval competition model to distinguish the effects of 'uniform competition' (all larvae competing) and 'cohort competition' (larvae of a given age competing). The former can produce quasi-cycles of a type characteristic of delayed regulation, while the latter causes quasi-cycles consisting of 'bursts' of population propagating through the age structure. (6) We also use the larval competition model to demonstrate that apparently minor changes in the description of adult survival can induce dramatic alterations in model behaviour. This supports our emphasis on rigour in the formulation of the model, so as to distinguish genuinely interesting dynamics from mathematical artifacts. SUMMARY (3) We illustrate the use of the formalism in the construction and analysis of two models of laboratory insect populations: a detailed model of Nicholson's blowflies and a 'strategic' model of larval competition intended to refine the design of experiments in progress on the dynamics of the Indian meal-moth Plodia interpunctella (Hiibner). (4) The model of Nicholson's blowflies is dynamically identical to a model previously derived heuristically. We have fitted the parameters using a more comprehensive range of data, and have illustrated explicitly the passage of large, quasi-cyclic fluctuations through the age structure. (5) We use the larval competition model to distinguish the effects of 'uniform competition' (all larvae competing) and 'cohort competition' (larvae of a given age competing). The former can produce quasi-cycles of a type characteristic of delayed regulation, while the latter causes quasi-cycles consisting of 'bursts' of population propagating through the age structure. (6) We also use the larval competition model to demonstrate that apparently minor changes in the description of adult survival can induce dramatic alterations in model behaviour. This supports our emphasis on rigour in the formulation of the model, so as to distinguish genuinely interesting dynamics from mathematical artifacts. SUMMARY (3) We illustrate the use of the formalism in the construction and analysis of two models of laboratory insect populations: a detailed model of Nicholson's blowflies and a 'strategic' model of larval competition intended to refine the design of experiments in progress on the dynamics of the Indian meal-moth Plodia interpunctella (Hiibner). (4) The model of Nicholson's blowflies is dynamically identical to a model previously derived heuristically. We have fitted the parameters using a more comprehensive range of data, and have illustrated explicitly the passage of large, quasi-cyclic fluctuations through the age structure. (5) We use the larval competition model to distinguish the effects of 'uniform competition' (all larvae competing) and 'cohort competition' (larvae of a given age competing). The former can produce quasi-cycles of a type characteristic of delayed regulation, while the latter causes quasi-cycles consisting of 'bursts' of population propagating through the age structure. (6) We also use the larval competition model to demonstrate that apparently minor changes in the description of adult survival can induce dramatic alterations in model behaviour. This supports our emphasis on rigour in the formulation of the model, so as to distinguish genuinely interesting dynamics from mathematical artifacts. SUMMARY (3) We illustrate the use of the formalism in the construction and analysis of two models of laboratory insect populations: a detailed model of Nicholson's blowflies and a 'strategic' model of larval competition intended to refine the design of experiments in progress on the dynamics of the Indian meal-moth Plodia interpunctella (Hiibner). (4) The model of Nicholson's blowflies is dynamically identical to a model previously derived heuristically. We have fitted the parameters using a more comprehensive range of data, and have illustrated explicitly the passage of large, quasi-cyclic fluctuations through the age structure. (5) We use the larval competition model to distinguish the effects of 'uniform competition' (all larvae competing) and 'cohort competition' (larvae of a given age competing). The former can produce quasi-cycles of a type characteristic of delayed regulation, while the latter causes quasi-cycles consisting of 'bursts' of population propagating through the age structure. (6) We also use the larval competition model to demonstrate that apparently minor changes in the description of adult survival can induce dramatic alterations in model behaviour. This supports our emphasis on rigour in the formulation of the model, so as to distinguish genuinely interesting dynamics from mathematical artifacts.