Table 1.

Cereal aphid models simulating aphid movement or timing of arrival in crops

Model characteristics	Aim	Country	Scale	Phase(s) of the transport process included	Reference
Turbulent advection simulation/Lagrangian stochastic	To investigate aerial density profiles in relation to simplified aphid behaviours	UK	Long distance migration	Transport in Atmosphere	[64]
Atmospheric trajectory model of dispersal	To estimate migration pathways	Finland	Long distance migration	Transport in Atmosphere	[95]
Trajectory	Modelling aphid migration from source to sink	Illinois, USA	Long distance migration	Transport in Atmosphere	[13, 31, 106]
Trajectory coupled to cohort-based population dynamics	Mechanistic simulation of aphid population dynamics at source and factors leading to take-off, coupled to wind a trajectory simulation model to estimate potential long distance movement risk from irrigated pastures to crops.	South-western Australia	Long distance migration	Source, Transport in Atmosphere, Initial Distribution	[126]
Large-scale: Diffusion–advection-reaction equations	To simulate the landing rate of Sitobion avenae in crop fields across landscapes. Explores landing behaviours and responses to landscape (e.g. wavelengths).	France	Landscape (multi-scale)	Initial Distribution	[123]
Small-scale: cellular automata incorporating behavioural rules.
Hierarchical Bayesian	Driven by field observations to gain knowledge on processes such as insect landing and mortality	Germany	Within-field	Initial Distribution	[55]. See also [125, 128, 129]
Analytical regression	Prediction of the timing of migration into crops from primary host (holocyclic populations only)	Denmark/Scandinavia	Within-field	Initial Distribution	[130, 131]
Analytical regression	Prediction of the timing of migration into crops from primary host (holocyclic populations only) – requires suction trap data	Sweden	Within-field	Initial Distribution	[132]
Analytical regression	Prediction of the timing of migration into autumn crops – requires suction trap data	Wales	Within-field	Initial Distribution	[92]
Analytical regression	Prediction of the timing of migration into autumn crops – requires suction trap data	UK	Within-field	Initial Distribution	[133]
Analytical regression	Prediction of the timing of migration into spring crops – requires suction trap data	UK	Within-field	Initial Distribution	[134, 135]
Individual-based	Stochastic wind-driven dispersal model to examine difference in dispersal and population dynamics depending on pesticide regime	UK	Small landscape	Local Movement	[76]
Cohort-based population dynamics model (STELLA)	Population dynamics model that simulates immigration from a ‘background’ source population. Spatial variation in immigration at the regional scale driven by differences in soil moisture levels.	South-western Australia	Within-field	Initial Distribution (from local source)	[136]
Analytical mathematical model	Estimation of the percentage of plants infected with BYDV, given the number of aphids per plant. Distinction between alate migrant transmission and apterous transmission.	UK	Within-field	Initial Distribution, Local Movement	[137]
Cohort-based	Aphid population dynamics, local dispersal and virus sub-models.	UK	Within-field/small landscape	Local Movement	[138]. See also [69, 139]
Cellular Automata	Rate of spread of BYDV from an origin cell, based on probabilities of infection transferring to the next cell (combined with field observations).	UK	Within-field	Local Movement	[140]
Individual-based	Simplified model of aphid population dynamics and virus transmission from plant to plant. Focus on computing methods rather than ecology.	UK	Within-field/small scale	Local Movement	[141, 142]
Analytical probabilistic model and Markov chain model of disease transmission. Individual-based aphid movement through field.	Examines aspatially the implications of vector preference for diseased or healthy hosts on the spread of BYDV. A Markov chain model and a stochastic individual-based model examine disease transmission and the effects of spatial patchiness.	USA	Non-spatial (analytical) and spatial within-field (Markov chain).	Local Movement	[143] see also [144]
Artificial Neural Networks and multiple regression	Aphid autumn flight timing/numbers. No BYDV.	New Zealand	Autumn flight	Source	[145]
Analytical linear and probit models	Soybean aphid early season colonisation of fields from overwintering hosts.	Canada	Spring flight. Within-field.	Source, Local Movement	[146]