Simulating the effects of saline and sodic subsoils on wheat crops growing on Vertosols

Soils with high levels of chloride and/or sodium in their subsurface layers are often referred to as having subsoil constraints (SSCs). There is growing evidence that SSCs affect wheat yields by increasing the lower limit of a crop's available soil water (CLL) and thus reducing the soil's plant-available water capacity (PAWC). This proposal was tested by simulation of 33 farmers' paddocks in south-western Queensland and north-western New South Wales. The simulated results accounted for 79% of observed variation in grain yield, with a root mean squared deviation (RMSD) of 0.50 t/ha. This result was as close as any achieved from sites without SSCs, thus providing strong support for the proposed mechanism that SSCs affect wheat yields by increasing the CLL and thus reducing the soil's PAWC. In order to reduce the need to measure CLL of every paddock or management zone, two additional approaches to simulating the effects of SSCs were tested. In the first approach the CLL of soils was predicted from the 0.3-0.5 m soil layer, which was taken as the reference CLL of a soil regardless of its level of SSCs, while the CLL values of soil layers below 0.5 m depth were calculated as a function of these soils' 0.3-0.5 m CLL values as well as of soil depth plus one of the SSC indices EC, Cl, ESP, or Na. The best estimates of subsoil CLL values were obtained when the effects of SSCs were described by an ESP-dependent function. In the second approach, depth-dependent CLL values were also derived from the CLL values of the 0.3-0.5 m soil layer. However, instead of using SSC indices to further modify CLL, the default values of the water-extraction coefficient (kl) of each depth layer were modified as a function of the SSC indices. The strength of this approach was evaluated on the basis of correlation of observed and simulated grain yields. In this approach the best estimates were obtained when the default kl values were multiplied by a Cl-determined function. The kl approach was also evaluated with respect to simulated soil moisture at anthesis and at grain maturity. Results using this approach were highly correlated with soil moisture results obtained from simulations based on the measured CLL values. This research provides strong evidence that the effects of SSCs on wheat yields are accounted for by the effects of these constraints on wheat CLL values. The study also produced two satisfactory methods for simulating the effects of SSCs on CLL and on grain yield. While Cl and ESP proved to be effective indices of SSCs, EC was not effective due to the confounding effect of the presence of gypsum in some of these soils. This study provides the tools necessary for investigating the effects of SSCs on wheat crop yields and natural resource management (NRM) issues such as runoff, recharge, and nutrient loss through simulation studies. It also facilitates investigation of suggested agronomic adaptations to SSCs.

Exact solutions of coupled multispecies linear reaction–diffusion equations on a uniformly growing domain

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction–diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction–diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction–diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially–confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially–confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.

Exact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimension

Unlike standard applications of transport theory, the transport of molecules and cells during embryonic development often takes place within growing multidimensional tissues. In this work, we consider a model of diffusion on uniformly growing lines, disks, and spheres. An exact solution of the partial differential equation governing the diffusion of a population of individuals on the growing domain is derived. Using this solution, we study the survival probability, S(t). For the standard nongrowing case with an absorbing boundary, we observe that S(t) decays to zero in the long time limit. In contrast, when the domain grows linearly or exponentially with time, we show that S(t) decays to a constant, positive value, indicating that a proportion of the diffusing substance remains on the growing domain indefinitely. Comparing S(t) for diffusion on lines, disks, and spheres indicates that there are minimal differences in S(t) in the limit of zero growth and minimal differences in S(t) in the limit of fast growth. In contrast, for intermediate growth rates, we observe modest differences in S(t) between different geometries. These differences can be quantified by evaluating the exact expressions derived and presented here.

Survival probability for a diffusive process on a growing domain

We consider the motion of a diffusive population on a growing domain, 0 < x < L(t ), which is motivated by various applications in developmental biology. Individuals in the diffusing population, which could represent molecules or cells in a developmental scenario, undergo two different kinds of motion: (i) undirected movement, characterized by a diffusion coefficient, D, and (ii) directed movement, associated with the underlying domain growth. For a general class of problems with a reflecting boundary at x = 0, and an absorbing boundary at x = L(t ), we provide an exact solution to the partial differential equation describing the evolution of the population density function, C(x,t ). Using this solution, we derive an exact expression for the survival probability, S(t ), and an accurate approximation for the long-time limit, S = limt→∞ S(t ). Unlike traditional analyses on a nongrowing domain, where S ≡ 0, we show that domain growth leads to a very different situation where S can be positive. The theoretical tools developed and validated in this study allow us to distinguish between situations where the diffusive population reaches the moving boundary at x = L(t ) from other situations where the diffusive population never reaches the moving boundary at x = L(t ). Making this distinction is relevant to certain applications in developmental biology, such as the development of the enteric nervous system (ENS). All theoretical predictions are verified by implementing a discrete stochastic model.

Avocado Information Kit. Agrilink, your growing guide to better farming guide

Each Agrilink kit has been designed to be both comprehensive and practical. As the kits are arranged to answer questions of increasing complexity, they are useful references for both new and experienced producers of specific crops. Agrilink integrates the technology of horticultural production with the management of horticultural enterprises. REPRINT INFORMATION - PLEASE READ! For updated information please call 13 25 23 or visit the website www.deedi.qld.gov.au (Select: Queensland Industries - Agriculture link) This publication has been reprinted as a digital book without any changes to the content published in 2001. We advise readers to take particular note of the areas most likely to be out-of-date and so requiring further research: see detailed reprint information on first page of the kit. Even with these limitations we believe this information kit provides important and valuable information for intending and existing growers. This publication was last revised in 2001. The information is not current and the accuracy of the information cannot be guaranteed by the State of Queensland. This information has been made available to assist users to identify issues involved in the production of avocadoes. This information is not to be used or relied upon by users for any purpose which may expose the user or any other person to loss or damage. Users should conduct their own inquiries and rely on their own independent professional advice. While every care has been taken in preparing this publication, the State of Queensland accepts no responsibility for decisions or actions taken as a result of any data, information, statement or advice, expressed or implied, contained in this publication.

Papaw Information Kit. Agrilink, your growing guide to better farming guide

Each Agrilink kit has been designed to be both comprehensive and practical. As the kits are arranged to answer questions of increasing complexity, they are useful references for both new and experienced producers of specific crops. Agrilink integrates the technology of horticultural production with the management of horticultural enterprises. REPRINT INFORMATION - PLEASE READ! For updated information please call 13 25 23 or visit the website http://www.deedi.qld.gov.au/ (Select: Queenslands Industries - Agriculture Link) This publication has been reprinted as a digital book without any changes to the content published in 2000. We advise readers to take particular note of the areas most likely to be out-of-date and so requiring further research: see detailed information on first page of the kit. Even with these limitations we believe this information kit provides important and valuable information for intending and existing growers. This publication was last revised in 2000. The information is not current and the accuracy of the information cannot be guaranteed by the State of Queensland. This information has been made available to assist users to identify issues involved in the production of papaw. This information is not to be used or relied upon by users for any purpose which may expose the user or any other person to loss or damage. Users should conduct their own inquiries and rely on their own independent professional advice. While every care has been taken in preparing this publication, the State of Queensland accepts no responsibility for decisions or actions taken as a result of any data, information, statement or advice, expressed or implied, contained in this publication.

Mango Information Kit. Agrilink, your growing guide to better farming guide

Each Agrilink kit has been designed to be both comprehensive and practical. As the kits are arranged to answer questions of increasing complexity, they are useful references for both new and experienced producers of specific crops. Agrilink integrates the technology of horticultural production with the management of horticultural enterprises. REPRINT INFORMATION - PLEASE READ! For updated information please call 13 25 23 or visit the website www.deedi.qld.gov.au (Select: Queensland Industries - Agriculture link) This publication has been reprinted as a digital book without any changes to the content published in 1999. We advise readers to take particular note of the areas most likely to be out-of-date and so requiring further research: see detailed information on first page of the kit. Even with these limitations we believe this information kit provides important and valuable information for intending and existing growers. This publication was last revised in 1999. The information is not current and the accuracy of the information cannot be guaranteed by the State of Queensland. This information has been made available to assist users to identify issues involved in the production of mangoes. This information is not to be used or relied upon by users for any purpose which may expose the user or any other person to loss or damage. Users should conduct their own inquiries and rely on their own independent professional advice. While every care has been taken in preparing this publication, the State of Queensland accepts no responsibility for decisions or actions taken as a result of any data, information, statement or advice, expressed or implied, contained in this publication.

Citrus Information Kit. Agrilink, your growing guide to better farming guide

Each Agrilink kit has been designed to be both comprehensive and practical. As the kits are arranged to answer questions of increasing complexity, they are useful references for both new and experienced producers of specific crops. Agrilink integrates the technology of horticultural production with the management of horticultural enterprises. REPRINT INFORMATION - PLEASE READ! For updated information please call 13 25 23 or visit the website www.daf.qld.gov.au This publication has been reprinted as a digital book without any changes to the content published in 1997. We advise readers to take particular note of the areas most likely to be out-of-date and so requiring further research: see detailed information on first page of the kit. Even with these limitations we believe this information kit provides important and valuable information for intending and existing growers. This publication was last revised in 1997. The information is not current and the accuracy of the information cannot be guaranteed by the State of Queensland. This information has been made available to assist users to identify issues involved in the production of citrus. This information is not to be used or relied upon by users for any purpose which may expose the user or any other person to loss or damage. Users should conduct their own inquiries and rely on their own independent professional advice. While every care has been taken in preparing this publication, the State of Queensland accepts no responsibility for decisions or actions taken as a result of any data, information, statement or advice, expressed or implied, contained in this publication.

Rockmelon and Honeydew Information Kit. Agrilink, your growing guide to better farming guide

Each Agrilink kit has been designed to be both comprehensive and practical. As the kits are arranged to answer questions of increasing complexity, they are useful references for both new and experienced producers of specific crops. Agrilink integrates the technology of horticultural production with the management of horticultural enterprises. REPRINT INFORMATION - PLEASE READ! For updated information please call 13 25 23 or visit the website www.deedi.qld.gov.au (Select: Queensland Industries - Agriculture link) This publication has been reprinted as a digital book without any changes to the content published in 1997. We advise readers to take particular note of the areas most likely to be out-of-date and so requiring further research: see detailed information on first page of the kit. Even with these limitations we believe this information kit provides important and valuable information for intending and existing growers. This publication was last revised in 1997. The information is not current and the accuracy of the information cannot be guaranteed by the State of Queensland. This information has been made available to assist users to identify issues involved in the production of Rockmelon and Honeydew. This information is not to be used or relied upon by users for any purpose which may expose the user or any other person to loss or damage. Users should conduct their own inquiries and rely on their own independent professional advice. While every care has been taken in preparing this publication, the State of Queensland accepts no responsibility for decisions or actions taken as a result of any data, information, statement or advice, expressed or implied, contained in this publication.

Capsicum and Chilli Information Kit. Agrilink, your growing guide to better farming guide.

Each Agrilink kit has been designed to be both comprehensive and practical. As the kits are arranged to answer questions of increasing complexity, they are useful references for both new and experienced producers of specific crops. Agrilink integrates the technology of horticultural production with the management of horticultural enterprises. REPRINT INFORMATION - PLEASE READ! For updated information please call 13 25 23 or visit the website www.deedi.qld.gov.au (Select: Queensland Industries – Agriculture link) This publication has been reprinted as a digital book without any changes to the content published in 1999. We advise readers to take particular note of the areas most likely to be out-of-date and so requiring further research: see detailed information on first page of the kit. Even with these limitations we believe this information kit provides important and valuable information for intending and existing growers. This publication was last revised in 1999. The information is not current and the accuracy of the information cannot be guaranteed by the State of Queensland. This information has been made available to assist users to identify issues involved in the production of capsicum and chilli. This information is not to be used or relied upon by users for any purpose which may expose the user or any other person to loss or damage. Users should conduct their own inquiries and rely on their own independent professional advice. While every care has been taken in preparing this publication, the State of Queensland accepts no responsibility for decisions or actions taken as a result of any data, information, statement or advice, expressed or implied, contained in this publication.

Cashew Information Kit. Agrilink, your growing guide to better farming guide

Each Agrilink kit has been designed to be both comprehensive and practical. As the kits are arranged to answer questions of increasing complexity, they are useful references for both new and experienced producers of specific crops. Agrilink integrates the technology of horticultural production with the management of horticultural enterprises. REPRINT INFORMATION - PLEASE READ! For updated information please call 13 25 23 or visit the website www.deedi.qld.gov.au (Select: Queensland Industries – Agriculture link) This publication has been reprinted as a digital book without any changes to the content published in 1999. We advise readers to take particular note of the areas most likely to be out-of-date and so requiring further research: see detailed information on first page of the kit. Even with these limitations we believe this information kit provides important and valuable information for intending and existing growers. This publication was last revised in 1999. The information is not current and the accuracy of the information cannot be guaranteed by the State of Queensland. This information has been made available to assist users to identify issues involved in the production of cashews. This information is not to be used or relied upon by users for any purpose which may expose the user or any other person to loss or damage. Users should conduct their own inquiries and rely on their own independent professional advice. While every care has been taken in preparing this publication, the State of Queensland accepts no responsibility for decisions or actions taken as a result of any data, information, statement or advice, expressed or implied, contained in this publication.

Custard Apple Information Kit. Agrilink, your growing guide to better farming guide

Each Agrilink kit has been designed to be both comprehensive and practical. As the kits are arranged to answer questions of increasing complexity, they are useful references for both new and experienced producers of specific crops. Agrilink integrates the technology of horticultural production with the management of horticultural enterprises. REPRINT INFORMATION - PLEASE READ! For updated information please call 13 25 23 or visit the website www.deedi.qld.gov.au (Select: Queensland Industries – Agriculture link) This publication has been reprinted as a digital book without any changes to the content published in 1998. We advise readers to take particular note of the areas most likely to be out-of-date and so requiring further research: see detailed information on first page of the kit. Even with these limitations we believe this information kit provides important and valuable information for intending and existing growers. This publication was last revised in 1998. The information is not current and the accuracy of the information cannot be guaranteed by the State of Queensland. This information has been made available to assist users to identify issues involved in the production of custard apples. This information is not to be used or relied upon by users for any purpose which may expose the user or any other person to loss or damage. Users should conduct their own inquiries and rely on their own independent professional advice. While every care has been taken in preparing this publication, the State of Queensland accepts no responsibility for decisions or actions taken as a result of any data, information, statement or advice, expressed or implied, contained in this publication.

Strawberry Information Kit. Agrilink, your growing guide to better farming guide

Each Agrilink kit has been designed to be both comprehensive and practical. As the kits are arranged to answer questions of increasing complexity, they are useful references for both new and experienced producers of specific crops. Agrilink integrates the technology of horticultural production with the management of horticultural enterprises. REPRINT INFORMATION - PLEASE READ! For updated information please call 13 25 23 or visit the website www.deedi.qld.gov.au (Select: Queensland Industries – Agriculture link) This publication has been reprinted as a digital book without any changes to the content published in 1997. We advise readers to take particular note of the areas most likely to be out-of-date and so requiring further research: see detailed information on first page of the kit. Even with these limitations we believe this information kit provides important and valuable information for intending and existing growers. This publication was last revised in 1997. The information is not current and the accuracy of the information cannot be guaranteed by the State of Queensland. This information has been made available to assist users to identify issues involved in the production of strawberries. This information is not to be used or relied upon by users for any purpose which may expose the user or any other person to loss or damage. Users should conduct their own inquiries and rely on their own independent professional advice. While every care has been taken in preparing this publication, the State of Queensland accepts no responsibility for decisions or actions taken as a result of any data, information, statement or advice, expressed or implied, contained in this publication.

Tomato Information Kit. Agrilink, your growing guide to better farming guide

Each Agrilink kit has been designed to be both comprehensive and practical. As the kits are arranged to answer questions of increasing complexity, they are useful references for both new and experienced producers of specific crops. Agrilink integrates the technology of horticultural production with the management of horticultural enterprises. REPRINT INFORMATION - PLEASE READ! For updated information please call 13 25 23 or visit the website www.deedi.qld.gov.au (Select: Queensland Industries – Agriculture link) This publication has been reprinted as a digital book without any changes to the content published in 1998. We advise readers to take particular note of the areas most likely to be out-of-date and so requiring further research: see detailed information on first page of the kit. Even with these limitations we believe this information kit provides important and valuable information for intending and existing growers. This publication was last revised in 1998. The information is not current and the accuracy of the information cannot be guaranteed by the State of Queensland. This information has been made available to assist users to identify issues involved in the production of Tomatoes. This information is not to be used or relied upon by users for any purpose which may expose the user or any other person to loss or damage. Users should conduct their own inquiries and rely on their own independent professional advice. While every care has been taken in preparing this publication, the State of Queensland accepts no responsibility for decisions or actions taken as a result of any data, information, statement or advice, expressed or implied, contained in this publication.

Tropical Banana Information Kit. Agrilink, your growing guide to better farming guide

Each Agrilink kit has been designed to be both comprehensive and practical. As the kits are arranged to answer questions of increasing complexity, they are useful references for both new and experienced producers of specific crops. Agrilink integrates the technology of horticultural production with the management of horticultural enterprises. REPRINT INFORMATION - PLEASE READ! For updated information please call 13 25 23 or visit the website www.deedi.qld.gov.au (Select: Queensland Industries – Agriculture link) This publication has been reprinted as a digital book without any changes to the content published in 1998.. We advise readers to take particular note of the areas most likely to be out-of-date and so requiring further research: see detailed information on first page of the kit. Even with these limitations we believe this information kit provides important and valuable information for intending and existing growers. This publication was last revised in 1998. The information is not current and the accuracy of the information cannot be guaranteed by the State of Queensland. This information has been made available to assist users to identify issues involved in the production of tropical bananas. This information is not to be used or relied upon by users for any purpose which may expose the user or any other person to loss or damage. Users should conduct their own inquiries and rely on their own independent professional advice. While every care has been taken in preparing this publication, the State of Queensland accepts no responsibility for decisions or actions taken as a result of any data, information, statement or advice, expressed or implied, contained in this publication.