A general distributed delay time varying life table plant population model: Cotton (Gossypium hirsutum L.) growth and development as an example

doi:10.1016/0304-3800(84)90071-1

Ecological Modelling

Volume 26, Issues 3–4, 15 December 1984, Pages 231-249

https://doi.org/10.1016/0304-3800(84)90071-1 Get rights and content

Abstract

A new general stochastic, time varying population plant model is reported, and is used specifically to model cotton (Gossypium hirsutum L.) growth and development. The model is validated against field data from Londrina, Parana, PR, Brazil. The model reproduced all aspects of the field data accurately including the phenology of crop growth, the pattern and magnitude of fruit dynamics, and dry matter allocation to leaf, stem plus root and fruit for the entire season. In the model all aspects of cotton growth and development are controlled by the ratio of photosynthate supply-demand. Computer experiments were made to examine the effects of temperatures, solar radiation and plant density on crop growth, development and yield.

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Reformulation of the Distributed Delay Model to describe insect pest populations using count variables
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A wide range of works highlight the reliability of the classical DDM in describing ectotherms such as plants and insects. For example, cotton (Gossypium hirsutum L.) cultivations were modelled by Gutierrez and Pizzamiglio (1984). Then Gutierrez et al. (1984) successfully extended the study to bean, tomatoes and cassava cultivations.
Among the models used to describe insect pest populations, the Distributed Delay Model has been applied in several case studies in recent years. Its success is due mainly to its simplicity, and its versatility to be easily included in software to calculate numerical solutions. In its original formulation, the Distributed Delay Model provides, as a solution, the distribution of the insects’ maturation flow; then, this is compared with monitoring in field applications. A different form of the model can be obtained, with the same assumptions, to describe the distribution of the number of individuals which are in a specific life stage at time t. The first aim of this work was to show the mathematical details in order to obtain the second form of the Distributed Delay Model, and to calculate its analytical solutions. The second aim was to analyse the model's behaviour in describing insect pest's population in varying environmental conditions, specifically in terms of temperature. To pursue this second aim, two case studies of noteworthy relevance in agriculture were considered: the pepper weevil, Anthonomus eugenii and the European grapevine moth, Lobesia botrana. For each case study, field populations were simulated with both the Distributed Delay Model versions, and the results were compared to determine the most appropriate model for application in the case of insect pest populations. Both the case studies highlighted that the novel formulation presented in this work significantly improves simulation, providing a more reliable representation of field data.
Development and validation of SUCROS-cotton: A potential crop growth simulation model for cotton
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A model for the development, growth and potential production of cotton (SUCROS-Cotton) was developed. Particular attention was given to the phenological development of the plant and the plasticity of fruit growth in response to temperature, radiation, daylength, variety traits, and management. The model is characterized by a comparatively simple code and transparent algorithms. The model was parameterized for Chinese cotton varieties and validated with extensive independent datasets on cotton growth and production from the Yellow River region and Xinjiang Province. The model validation showed that the phenology, growth and yield were simulated satisfactorily. The root mean square error (RMSE) for date of emergence, date of flowering, date of open boll stage and duration from sowing to boll opening was less than four calendar days, both for cotton grown in monoculture and cotton grown in a relay intercropping system with wheat. The RMSE of predicted total dry matter compared with observations was at most 6.6%, of lint yield 6.6%, and for number of harvestable bolls 10.0%. SUCROS-Cotton provides a tool to (1) assess production opportunities of cotton in various ecological zones in response to temperature, incoming radiation and management, (2) identify optimal cotton ideotypes for different agro-ecological conditions and for guiding breeding efforts, and (3) explore resource-use-efficient cropping systems, including intercropping options, and crop management practices such as plastic film mulching and sowing date.
The economics of biotechnology under ecosystem disruption
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Economic analysis of chemical pesticide use has shown that the interactions between plants, pests, damage control technology and state of the ecosystem are important variables to be considered. Hence, a bio-economic model was developed for the assessment of Bt variety and pesticide-based control strategies of the cotton–bollworm in China. The model simulates plant growth, the dynamics of pest populations and of natural enemies. The model predictions are used as major inputs for a stochastic micro-level profit model of alternative control strategies.
Results show that: (1) productivity effects of Bt varieties and pesticide use depend on the action of natural control agents, and (2) the profitability of damage control measures increases with the severity of ecosystem disruption. The findings highlight the importance of the choice of the counterfactual scenario in the assessment of the impact of agricultural biotechnology. Also, some doubts are raised whether the high benefits of Bt cotton varieties claimed by previous studies based on cross section comparisons are realistic.
Climatic limits of pink bollworm in Arizona and California: effects of climate warming
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Citation Excerpt :
The plant integrates the bottom-up effects of weather and edaphic factors and the top–down effects of herbivory and intra-specific competition (Gutierrez, 1996). These attributes make the predictive capacity of the model independent of time and place, allowing simulation of field data in locations as diverse as Arizona, California, Brazil, Egypt and the Sudan (Gutierrez et al., 1975, 1977, 1981, 1984, 1986; Stone and Gutierrez, 1986a, 1986b; Von Arx et al., 1984; Stone et al., 1986; Russell, 1995; Gutierrez and Ponsard, 2006 for Bt cotton). The model predicts the within season population dynamics of cotton and PBW, the temperature-photoperiod mediated larval diapause induction in PBW (i.e. winter dormancy) during fall, and the emergence of adults in spring at all locations.
The distribution and abundance of pink bollworm (Pectinophora gossypiella Saunders (PBW)) in cotton in Arizona and California was examined using a validated weather-driven, physiologically based demographic model of cotton and PBW integrated into a geographic information system (GIS). Survival of diapause larvae during winter as affected by low temperatures is a key factor determining the range of PBW. Winter survival was estimated using data from Gutierrez et al. (Can. Entomol. 109 (1977) 1457) and Venette et al. (Environ. Entomol. 29 (5) (2000) 1018). The model was run continuously over the period 1 January 1995 to 31 December 2003 using observed weather data from 121 locations. Three output variables were mapped as measures of PBW persistence: over-winter survival of diapause PBW larvae, cumulative daily PBW larval densities over the season, and the number of diapause larvae produced during the season. The distribution of pink bollworm is predicted to be restricted to the relatively frost-free cotton growing areas of Arizona and Southern California where it currently reaches pest status. The model predicts that extension of PBW's range into the Central Valley of California is unlikely. The analysis questions the efficacy of an ongoing area-wide effort to prevent the establishment of PBW in the Central Valley of California. Four global warming scenarios were examined to estimate the effects on the potential geographic range of PBW. Average observed daily temperatures were increased 1.0, 1.5, 2.0 or 2.5 °C, respectively, in the four scenarios. Scenarios with average increases of 1.5–2.5 °C predicted that the range of PBW would expand into the Central Valley of California and the severity of the pest would greatly increase in areas of current infestation.
Parameter estimation for distributed delay based population models from laboratory data: Egg hatching of Oulema duftschmidi Redthenbacher (Coleoptera, Chrysomelidae) as an example
2003, Ecological Modelling
The cohort development of poikilotherms under favorable temperature conditions may be described by the time-invariant distributed delay models that require three parameters, i.e. the thermal threshold T₀, the thermal constant W and the variability parameter H representing distributed maturation times, also known as time distributed or stochastic development. Here, a parsimonious method is developed that uses stage-frequency matrices obtained under controlled conditions. The analysis of these matrices permits the estimation of the three parameters, while the incorporation of both developmental threshold and thermal constant into the time-invariant distributed delay model permits the representation of stochastic cohort development under constant temperatures. The evaluated parameters can also be used in time-varying distributed delay models that are particularly useful for a wide range of fluctuating temperature conditions.
We consider stage-frequency matrices obtained from cohorts of eggs and larvae of Oulema duftschmidi Redthenbacher at different constant temperatures. A visual inspection of the matrices clearly shows the temperature dependent as well as the time distributed passage from the egg to the larval stage. Under the current range of temperatures, a linear model for developmental rate satisfactorily describes egg development, and estimates the thermal threshold (T₀=11.2 °C), the thermal constant (W=81.3 day-degrees) and the delay order parameter (H=70). The resulting model can be used to represent the development of cohorts of O. duftschmidi eggs in a favorable temperature range.
An emergent computational approach to the study of ecosystem dynamics
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Despite success in theory formulation and prediction of quantities and patterns in nature, traditional modeling approaches have not proven particularly valuable as “surrogate experimental systems” in applied ecology. Theoretical models, while useful as embodiments of ecological theory, are too simplistic to be effective surrogate systems. Although simulation models can represent systems of realistic complexity, they are limited by factors which arise from the way in which they are built. We propose an alternative paradigm for modeling biotic systems which promises to enhance their usefulness as surrogate experimental systems. This paradigm is based on the premise that dynamic behavior in biotic systems emerges from the low-level interactions of independent agents. It forms the basis for the new field of artificial life (ALife), which involves the study of life-like behavior in artificial systems. In an ALife model, the target biological system is modeled as a population of independent computer programs called machines. The complete behavioral repertoire of each individual, including its interaction with others, is specified within the entity itself. A spatially-referenced “environment” is provided within which the machines interact with each other and their local environment. There is no overall controlling program or agent. Thus, the overall behavior of the system emerges from local interactions between independent agents. In this paper, we examine the premises upon which ALife is based (including the concept of emergence) and discuss several examples of ALife models at ecological scales, which we call “artifical ecosystems”. We next introduce LAGER, an environment for producing and running artificial ecosystems. Finally, we present PARE, a host/parasitoid dynamics model built in LAGER, and compare its behavior to two similar systems in the literature.

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^☆: The analysis of the data was supported by USDA Grant #200040 and NSF Grant #DEB 77-25260, while the field work and travel were supported by IAPAR and EMBRAPA, Brazil.

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A general distributed delay time varying life table plant population model: Cotton (Gossypium hirsutum L.) growth and development as an example☆

Abstract

J. Theor. Biol.

J. Theor. Biol.

Simulation of growth and yield in cotton

Crop Sci.

Some remark on changing populations

A perspective on systems analysis in crop production and insect pest management

Annu. Rev. Entomol.

Multitrophic level models of predator-prey interactions. II. A realistic model of plant-herbivore-parasitoid-predator interactions

Can. Entomol.

Applied population ecology: models for crop production and pest management

An analysis of cotton production in California: a model for Acala cotton and the effects of defoliators on its yield

Environ. Entomol.

The interaction of pink bollworm (Lepidoptera: Gelichiidae), cotton and weather: a detailed model

Can. Entomol.

A model of verticillium wilt in relation to cotton growth and development

Phytopathology

Simulation of growth and yield in cotton: respiration and carbon balance

Crop Sci.