Jeger M J
Department of Plant Pathology and Microbiology, Texas Agricultural Experiment Station, The Texas A & M University System, College Station, TX 77843, USA.
New Phytol. 1987 Oct;107(2):459-478. doi: 10.1111/j.1469-8137.1987.tb00197.x.
Including root growth and inoculum density as variables in a simple model of disease progress of a monocyclic root pathogen often leads to a sigmoid curve. If the product of root density and inoculum density is constant, then a monomolecular curve (without an inflexion point) results. When the product is a function of time, then either an asymptotic exponential or a sigmoid curve results, depending upon the parameter values. Where the product of root density and inoculum density increases exponentially, then a Gompertz function in the incidence of surviving plants results. Where root growth is fast relative to the reduction in inoculum through infection, then an asymptotic value of disease less than 1.0 is predicted. Detailed models of dynamics of root infection, incorporating root extension and loss of inoculum due to infection, and cases without and with lesion expansion, lead to the following conclusions: (1) increase in lesion numbers without lesion expansion, does not constrain or provide an upper limit to root growth; (2) where there is no root growth, then the proportion of root surface covered by lesions approaches an asymptote strictly less than 1.0 in the case without lesion expansion, but approaches 1.0 in the case with lesion expansion; (3) where the rate of infection is greater than the rate of root extension (without lesion expansion), then there is an upper limit to lesion surface area on roots; otherwise both root surface area and lesion numbers increase without limit; (4) where the rate of lesion expansion is greater than the rate of root extension, then the proportion of root surface area covered by lesions approaches 1.0 asymptotically. Explicit solutions giving the healthy root area as a function of time are obtained. Analysis of the dynamics of root infection indicates that root disease control strategies should aim to reduce pathogen density, maintain a low rate of root extension relative to root infection and restrict lesion expansion.
在单循环根部病原体疾病进展的简单模型中，将根系生长和接种体密度作为变量通常会导致S形曲线。如果根系密度和接种体密度的乘积是常数，那么就会得到单分子曲线（没有拐点）。当该乘积是时间的函数时，根据参数值的不同，会得到渐近指数曲线或S形曲线。当根系密度和接种体密度的乘积呈指数增长时，存活植物发病率的Gompertz函数就会出现。当根系生长速度相对于因感染导致的接种体减少速度较快时，预计疾病的渐近值小于1.0。结合根系延伸和因感染导致的接种体损失以及有无病斑扩展情况的根部感染动态详细模型，得出以下结论：（1）病斑数量增加但无病斑扩展，不会限制根系生长或为根系生长提供上限；（2）在没有根系生长的情况下，在无病斑扩展的情况下，被病斑覆盖的根表面积比例接近一个严格小于1.0的渐近线，但在有病斑扩展的情况下接近1.0；（3）当感染速率大于根系延伸速率（无病斑扩展）时，根上病斑表面积存在上限；否则根表面积和病斑数量都会无限制增加；（4）当病斑扩展速率大于根系延伸速率时，被病斑覆盖的根表面积比例渐近地接近1.0。得到了将健康根面积表示为时间函数的显式解。对根部感染动态的分析表明，根部病害控制策略应旨在降低病原体密度，相对于根部感染保持较低的根系延伸速率，并限制病斑扩展。
