Overview¶

Purpose and patterns¶

The purpose of the model is to explore landscape management and agricultural practices' scenarios that promote pest regulation and limit the spread of a virus-borne disease. To do so, the model simulates the spatio-temporal dynamics of Myzus persicae (Hemiptera: Aphididae), an aphid pest, in relation to the agricultural landscape dynamics and agricultural practices. M. persicae is a vector to yellowing viruses of sugar beet, inducing important yield losses. The landscape composition (amount and diversity of crops and semi-natural habitats) and configuration (spatial arrangement) affects both the aphid and its natural enemies dynamics. Their habitat availability (crop rotation, presence of semi-natural habitats) and quality (crop phenology) vary through time, influencing aphid dynamics and natural enemies density, thus their biocontrol efficiency on the aphid. The model gives the possibility to explore the effect of landscape composition (crop mosaic, quantity and type of semi-natural habitats (SNH)) and configuration (field size, fragmentation of SNH), interacting with agricultural practices (sowing dates and pesticide treatments), on the tri-trophic system sugar beet, aphid, natural enemy and ultimately on the spread of yellow viruses in sugar beet fields.

Entities, variables and scales¶

Landscape¶

The landscape is composed of a grid of 100 \(\times\) 100 meter cells. It is characterized by a daily mean temperature, governing several biological processes, a daily abundance of migrating aphids (aphid rain), an aphid and natural enemies’ status (wintering or active).

Spatial units¶

The landscape is composed of agricultural parcels and semi-natural habitats.

Parcel: a specific spatial entity that represents an agricultural field, composed of cells, each of them containing a certain amount of cultivated area. Each parcel has a crop sequence, that defines the crops being cultivated throughout the simulation. The phenology of crops is modeled considering the sum of degree-days since sowing, that will influence aphid growth and dispersion, as well as the virus' spread. Agricultural practices are also defined at the parcel scale, with a delay from base sowing date (number of days), a number of aphicide sprays and time since last treatment.
Semi-natural habitats: spatial elements (vector) that overlaps the cells, and are either "woody" (forest, hedgerow) or "grassy" (flower or grassy strip).

Grid cells¶

Cells are elementary spatial units representing a square portion of the landscape, and may belong to a parcel. They are defined by an area (100x100m), a position in the landscape, an amount of cultivated area, an amount of semi-natural habitats (woody or grassy), and an edge density, corresponding to the length of interface between cultivated areas and between cultivated and non-cultivated areas, in km/ha. Grid cells each contain a stock of aphids, that changes with aphid growth, migration, dispersion and mortality due to natural enemies and pesticide treatments. Cells containing no area devoted to cultivated crops have an aphid stock set to zero, as well as cells covered by crops that are not host for M. persicae. The stock of aphids is described with a number of individuals, and has the ability to increase (due to aphid growth and immigration) and decrease (effect of biocontrol action of natural enemies, winter lethal temperatures, emigration and pesticide treatments). Cells have a yellows virus infection level (proportion of plants that are infected; constraint to zero except for cells occupied by sugar beet) and a natural enemy density for each family which is computed depending on the surrounding landscape composition and configuration.

Time scale¶

A step is a day, and the model can run for several years.

Spatial scale¶

The landscape extent can be adjusted, considering that it is wide enough to represent the landscape well while keeping computation resources reasonable. Each square grid cell represents 1 ha. During the model development, simulated landscapes represented approx. 100 km\(^2\). Natural enemies densities are computed depending on the surrounding landscape in a 2-km radius. Therefore, while the agricultural dynamics are simulated in the whole landscape, aphid dynamics are not simulated in the 2-km border of the landscape.

Entities and variables of the model

Entity	Variable	Description	Type	Units
Landscape	Area	Total area of the landscape	float, static	km²
	Temp	Mean daily temperature	float, dynamic	°C
	Aphid_rain	Daily abundance of migrating aphids	float, dynamic	number
Parcel	myCells	Cells belonging to the parcel	list of cells, static	Unitless
	listCropSeq	Crop sequence	list of string, static	Unitless
	delay_practice	Number of days delay for sowing and harvesting	integer, dynamic	number
	nb_spray	Number of pesticide treatments	integer, dynamic	number
	compt_practice	Time since last pesticide treatment	integer, dynamic	number
Cell	myParcel	Parcel to which the cell belongs	parcel, static	Unitless
	area_crop	Area covered by cultivated crops	float, static	m²
	area_SNH	Proportion of area covered by semi-natural habitats	float, static	Unitless (0-1)
	crop	Crop grown the current year	string, dynamic	Unitless
	myAphid	Aphid stock	aphid, static	Unitless
	my_NE	List of natural enemies densities	list of float, dynamic	number
	infect_degree	Proportion of infected plants	float, dynamic	Unitless (0-1)
	latency_prop	Proportion of infected plants in latency	float, dynamic	Unitless (0-1)
Aphid stock	myCell	Cell to which the stock belongs	cell, static	Unitless
	nb_ind	Number of individuals	float, dynamic	number
	winged_dev	Number of developing winged morphs	float, dynamic	number

Process overview and scheduling¶

Landscape update¶

The first process is the update of the daily mean temperature. Then, environment executes the updateCropParcel model, which manage the sowing and harvesting of crops in the agricultural parcels, as well as the update of plant phenology.

Crop development¶

Crops develop daily depending on the mean temperature. Plant development stage is computed depending on the sum of degree-days above a base temperature from the day of sowing. Depending on the crop, the base and maximum temperatures are different.

Aphid and natural enemies status¶

When daily mean temperatures reaches the defined threshold, during the appropriate time window, the environment variable AphStatus at the end of winter goes from "wintering" to "active" (or the other way around at the beginning of winter). The environment also manages natural enemies activity (test_NEactive model) depending either on the daily mean temperatures, the sum of degree-days from a certain day or the date, depending on input data on natural enemies biology.

Natural enemies densities¶

The densities of natural enemies is computed at initialization, and updated every 1\(^{st}\) of August, using the get_NE_density model, in every dynamic cell of the landscape. The densities are also updated after pesticide treatments in localized plots.

Seasonal changes in simulated processes¶

Agricultural plots dynamics are simulated throughout the whole year. Conversely, the model simulates the aphid dynamics during winter, spring and summer until sugar beet plants are totally resistant to the virus inoculation. Aphid dynamics and disease spread are therefore not simulated from the time when all beet plants are resistant to inoculation, to the start of aphid wintering.

Aphid wintering¶

When aphids are wintering, the environment executes the winter_survival model, which updates aphid stocks' number of individuals depending on the daily mean temperature.

Aphid dispersion¶

Aphids will disperse to other cells of the landscape when the nutritional quality of the host plant decreases (with plant development). When aphids detect the presence of natural enemies close by, they will produce winged progenies that will be able to disperse when they reach the developmental stage required for take-off (ie. the adult stage). Each day, if the temperature threshold is reached, the model executes the aphid_dispersion model.

Aphid migration¶

During spring, aphids take-off and fly passively over medium to long distances carried by the winds. Aphids can thus migrate into the landscape. Number of aphids migrating into the landscape is given as input data. Aphids that land on a cell from migration do not disperse on the same time step, but contribute to the stock growth and disease spread.

Aphid growth and biocontrol¶

When set on a suitable host, aphid stock grows at a daily rate that depend on the host plant family, the mean temperature and the development stage of the crop. Different families of natural enemies are present in the cells, and increase aphid mortality (ie. decrease stocks) during their period of activity. The model represent both specialist (parasitoids) and generalist families. SimBAL will first decrease a cell's aphid stock depending on parasitoids attack rates, then all generalist predators will contribute to the aphid stock decrease in a random order.

Pesticide treatments¶

When the aphid density in a cell of a parcel reaches the threshold, if the delay after the last treatment is passed and the maximum number of treatment has not been reached, the parcel is treated, which affects immediately decreases the cells' aphid stock and natural enemies densities, as well as the number of arriving aphids during the efficiency period.

Disease spread¶

Viruliferous aphids carry the disease to plants, and healthy aphid acquire the virus when feeding on an infected plant. At each time step, migrating and dispersing aphids introduce the virus to a cell (primary infection), while local aphids walking from plant to plant spread the virus within the cell (secondary infection). SimBAL takes into account a latency period during which an inoculated plant is not yet infectious. At each time step a defined proportion of plants in the latency state will become infectious.