The possibility of sustainable pest management by introducing bio-diversity: simulations of pest mite outbreak and regulation

Abstract

Since the late 1980s, spider mite pests have caused serious damage to many moso bamboo (Phyllostachys pubescens) forests in China’s Fujian province. The culms of this plant are an essential component of the building and handicraft industries, and the shoots are a prized food item in many Asian countries. Furthermore, bamboo forests play an important soil conservation role in mountainous areas. We examined pest mite outbreaks in several moso bamboo plantations in Fujian, and could show that a change in cultivation style from polyculture (a kind of mixed forest) to monoculture (all plants other than bamboo were removed) was primarily responsible for the local extinction of an important predaceous mite species. This phenomenon is due to the periodic shedding of leaves by the bamboo, which forces the predator mites occurring on bamboo to switch to prey mite species that occur on other plants. We then tried to elucidate the factors that resulted from such a cultivation change. Adopting a computer simulation approach, we could successfully show that at least two plants, moso bamboo and Chinese silvergrass, are necessary to maintain stable predator–prey interactions in moso forests. That is, systems consisting of one common predator and two host-specific pest mites on different host plant species frequently became stable when the pest mites were at low density. This finding indicates clearly that bio-diversity, even when it consists of only two plants and three mite species as in this study, is necessary for the sustainable regulation of large-scale forests, such as moso bamboo plantations.

Appendices

Appendix 1: Functions used to determine parameter values

The number of captured preys per day, dispersal rate, and so on are defined as below (Fig. 8).

Fig. 8

Functions used to determine parameter values

Appendix 2: Mathematical description

The model was defined by difference equations as follows:

$$ X_{i1} \left( {t + 1} \right) = \left( {1 - A_{i1} (t)} \right)\left( {1 - d_{i} (t)} \right)X_{i1} (t) + F_{i} \left( {X_{p2} ,X_{m2} } \right)\left( {1 - A_{i2} (t)} \right)B_{i} (t) $$

$$ X_{i2} \left( {t + 1} \right) = \left( {1 - A_{i1} (t)} \right)d_{i} (t)X_{i1} (t) + F_{i} \left( {X_{p2} ,X_{m2} } \right)\left( {1 - A_{i2} (t)} \right) $$

$$ Y_{i1} (t + 1) = \left( {Y_{i1} (t) - P_{i1} (t) - L_{i1} (t)X_{i1} (t)} \right)\left( {1 - d'_{i} (t)} \right) + \left( {Y_{i2} (t) - P_{i2} (t)} \right)\left( {1 - a_{i2} '(t)} \right)b_{i} '(t) $$

$$ Y_{i2} (t + 1) = \left( {Y_{i1} (t) - P_{i1} (t) - L_{i1} (t)X_{i1} (t)} \right)d'_{i} (t) + \left( {Y_{i2} (t) - P_{i2} (t)} \right)\left( {1 - a'_{i2} (t)} \right) $$

$$ F_{p} \left( {X_{p2} ,X_{m2} } \right) = \left( {1 - E_{p} (t)} \right)X_{p2} (t) + m_{m} (t)E_{m} (t)X_{m2} (t) $$

$$ F_{m} \left( {X_{p2} ,X_{m2} } \right) = \left( {1 - E_{m} (t)} \right)X_{m2} (t) + m_{p} (t)E_{p} (t)X_{p2} (t) $$

$$ E_{i} (t) = {\frac{{e^{{20X_{i2} (t)/\left( {Y_{i1} /3 + Y_{i2} } \right) - 4}} }}{{50 + e^{{20X_{i2} (t)/\left( {Y_{i1} /3 + Y_{i2} } \right) - 4}} }}} $$

$$ L_{i1} (t) = 10r_{i1} u_{i1} {\frac{{e^{{0.5((Y_{i1} - P_{i1} )/X_{i1} - n_{i1} ) - 6}} }}{{1 + e^{{0.5((Y_{i1} - P_{i1} )/X_{i1} - n_{i1} ) - 6}} }}} $$

$$ L_{i2} (t) = 20r_{i2} u_{i2} {\frac{{e^{{0.3((Y_{i1} + 3Y_{i2} )/F_{i} (X_{p2} ,X_{m2} ) - n_{i2} ) - 4}} }}{{2 + e^{{0.3((Y_{i1} + 3Y_{i2} )/F_{i} (X_{p2} ,X_{m2} ) - n_{i2} ) - 4}} }}} $$

$$ P_{ij} (t) = {\frac{{Y_{ij} (t)}}{{Y_{i1} (t) + 3Y_{i2} (t)}}}\;L_{i2} (t)F_{i} \left( {X_{p2} ,X_{m2} } \right) $$

$$ A_{i1} (t) = \left\{ {\begin{array}{ll} { - 0.014\,L_{i1} (t) + 0.14} & {\text{if}}\quad {L_{i 1} (t) < 10} \\ 0& {\text{if}}\quad{L_{i 1} (t) > 10} \\ \end{array} } \right. $$

$$ A_{i2} (t) = \left\{ {\begin{array}{ll} { - 0.0034\,L_{i2} (t) + 0.095} & {\text{if}} \quad {L_{i2} (t )< 20} \\ { 0. 0 2 7} & {\text{if}} \quad {L_{i2} (t )> 20} \\ \end{array} } \right. $$

$$ B_{i} (t) = \left\{ {\begin{array}{lll} 0 & {\text{if}} \quad {L_{i2} (t ) { < 0} . 4 5} \\ {0.427\,L_{i2} (t) - 0.192} & {\text{if}} \quad {0.45 < L_{i2} (t) < 4.22} \\ {1.61} & {\text{if}} \quad {L_{i2} (t)>4.22} \\ \end{array} } \right. $$

where i = p (i = m) was on PP (MP), and j was age stage (1 or 2). Variables are defined in Table 1. A detailed flow diagram of PP subsystem model (MS subsystem is almost the same other than the parameter symbols in Table 1) is shown in Fig. 9.

Fig. 9

Flow diagram of PP subsystem model