A growth model for plants attacked by nematodes

Abstract

The relation between small and medium initial population densities and the relative total plant weight was derived as cross sections at right angles to the time axis of a growth model with three dimensions: time after planting t, relative total plant weight Y and relative growth rate r _p /r ₀ . The relative growth rate is the (constant) ratio between the growth rate r _p of plants of a certain weight at a nematode density P and the growth rate r ₀ of (younger) plants of the same weight without nematodes. Therefore, the ratio between the time after planting that plants need to reach a certain weight in the absence of nematodes and at nematode density P, t ₀ /t _p = r _p /r ₀ (2).

The relative growth rate r _p /r _o = k + (1 - k)0.95^P/T-1 for P > T and = 1 for P ≤ T (3). Formally, k is the minimum relative growth rate as P → ∞. As a result the arbitrary equation y = m + (1 - m)0.95^p/T-1 for P > T and = 1 for P ≤ T(6)also applies to the relation between small and medium initial population densities and relative total plant weight. T is the tolerance limit, below which growth and yield are not reduced by nematodes; m is the relative minimum yield.

The relations between small and medium initial population densities of potato cyst nematodes and relative tuber weight of potatoes can be derived from the growth model in an analogous way. However, there is one complication: tuber initiation does not start at the same haulm weight in plants with and without nematodes, but at the smaller haulm weight the larger the nematode density. As a consequence, tuber weights of plants with a certain total weight at nematode density P are not equal to those of plants with the same total weight without nematodes, but r _p Δt units of weight larger, Δt being the difference between the actual time of tuber initiation and the time total plant weight becomes the same as that of plants without nematodes at the initiation of tuber formation.

Relative total and tuber weights of plants with ‘early senescence’ and at large nematode densities are smaller than estimated by the model and Eq. 2. This indicates that at large initial population densities growth reducing mechanism(s) become active that were not operating at smaller densities.