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Theory and Modern Applications

Table 1 Parameters in the system of difference equations ( 1 )-( 7 )

From: Effect of increased global temperatures on biological control of green lacewings on the spread of mealybugs in a cassava field: a simulation study

Parameter

Definition

\(\boldsymbol{t=25^{\circ}}\mathbf{C}\)

\(\boldsymbol{t=27^{\circ}}\mathbf{C}\)

\(\boldsymbol{t=30^{\circ}}\mathbf{C}\)

• Mealybugs

\(\alpha_{1}\)

The fraction of mealybug’s eggs that develop into instar mealybugs in one time step

0.1075

0.1163

0.1493

\(\alpha_{2}\)

The fraction of instar mealybugs that develop into adult mealybugs in one time step

0.0435

0.0482

0.0388

\(\alpha_{3}\)

The natural death rate of adult mealybugs

0.0612

0.0665

0.0596

\(\alpha_{4}\)

The fraction of female adult mealybugs in the reproductive period

0.4591

0.4991

0.4468

\(r_{1}\)

The survival rate of mealybug’s eggs that develop into instar mealybugs

0.8900

0.8700

0.9120

\(r_{2}\)

The survival rate of instar mealybugs that develop into adult mealybugs

0.7737

0.6079

0.6589

\(r_{3}\)

The fraction of female adult mealybugs

0.7400

0.7200

0.8500

\(v_{1}\)

The average number of eggs laid by a female adult mealybug in one time step

40.0000

36.5300

2.9126

• Green lacewings

\(\gamma_{1}\)

The fraction of green lacewing’s eggs that develop into larva green lacewing in one time step

0.1639

0.2222

0.2703

\(\gamma_{2}\)

The fraction of larva green lacewings that develop into pupa green lacewing in one time step

0.0521

0.0585

0.00625

\(\gamma_{3}\)

The fraction of pupa green lacewings that develop into adult green lacewings in one time step

0.0714

0.0885

0.1053

\(\delta_{2}\)

The natural death rate of adult green lacewings

0.0227

0.0175

0.0206

\(s_{1}\)

The survival rate of green lacewing’s eggs that develop into larva green lacewing

0.8040

0.8210

0.8170

\(s_{2}\)

The survival rate of larva green lacewing that develop into pupa green lacewing

0.9191

0.9629

0.7938

\(s_{3}\)

The survival rate of pupa green lacewing that develop into adult green lacewings

0.9586

0.9614

0.7402

\(s_{4}\)

The fraction of female adult green lacewings

0.5400

0.5500

0.4850

\(v_{2}\)

The average number of eggs laid by a female adult green lacewings in one time step

7.2789

5.8237

2.3876