Aphidisperse
Spray it before the aphids invade!
Spray it before the aphids invade!
The main vector for the Beet Yellows Virus (BYV) is the aphid Myzus persicae. Cap’siRNA offers a targeted treatment to this virus, with maximized efficiency during the early stages of plant contamination. The best case scenario would therefore be to treat the Beets a few days prior to the field being invaded by aphids, preventing them from transmitting the virus initially. The problematic here is therefore to be able to predict the time of arrival of the aphids in Beet plantations. Migration modelling for M. persicae is not a novel problem, and models were published in the literature in 2004 by Aiming Qi et al. [1] and 2023 by M. Lucquet et al. [2]. While being the most efficient models developed to this day, they do not include accessible GUIs for farmers to use and base their treatments on. It is to tackle this issue that we developed Aphidisperse, a Python framework using an agent-based model combined with a lattice visualization to provide insight on possible migration of Myzus persicae for the upcoming year.
Myzus persicae is a resistant, highly adaptable r-strategist pest (i.e. short life cycle/expectancy, huge growth rate) [3]. It is the privileged host of more than 100 different phytoviruses, making it a dangerous vector for plant diseases in more than thirty major cultures [4,5]. As an aphid, its complex life cycle alternates sexual (just before winter) and asexual reproduction (mostly during summer), but also oviparous (during winter) and viviparous cycles (during summer) [4]. Myzus persicae migration is mostly realized by winged individuals, obtained exclusively from sexual reproduction. This reproduction mode occurs massively before winter to increase the odds of finding a suitable host for winter; however, it also occurs during summer at peak reproduction rate, when the aphid’s population density on a plant becomes too important. When this happens, alate specimens are produced to migrate and create populations on other plants, and the cycle starts again. Therefore, one of the most important migration variables for a population of aphids is population density in a given location [4]. Another important element to factor in is that M. persicae only hibernate in hosts of the genus Prunus spp., which are therefore the starting point of the summer migration [4].
One of the key factors to model M. persicae dispersion is to determine the most probable date of the first migration post-wintering. The development temperature threshold in literature is 4.3°C on average. M. persicae development needs at least 16 added degree-days to develop completely [3]. Below this, there is no development of the aphids [4]. However, for take-off to occur, the temperature has to be at least between 14 to 16 degrees [3,6]. Therefore, the onset date of aphid migration corresponds to regions where the average temperature does not drop too often below the average of 4.3°C (i.e., not too many freezing events) and at some point during the year, the average daily temperature reaches 14 to 16 degrees.
Aphid actual migration highly depends on the climate conditions. Distance and duration depend mostly on windspeed and consistency: airstreams as weak as 2 m/s are strong enough to trigger a migration flight [3]. A migration lasts for 30 minutes to 3 hours on average and occurs only once in a lifetime [7,8,9]. Therefore, an estimate of the distance has been proposed by Parry, H.R. et al. [3] with distance = windspeed * duration. Thus, windspeed data is crucial in deriving a function giving the mean distance traveled by M. persicae from a given point. Windspeed changes with altitude, and aphids have an average flight height of 12.2m, although specimens have been found up to 1km high [3,10].
Many other variables impact aphid flight: rainfall, plant concentration, terrain topography, predators, chemicals, etc. [13]. In short, aphid flight is a complex multivariate behavior, requiring significant amounts of data to obtain reliable results. Finally, the most important factor for migration to happen, as mentioned earlier, is the local population density, and therefore, modeling the population growth dynamics of M. persicae is a key element in modeling global migration.
In population dynamics, a population’s number of individuals can be modeled using either the intrinsic rate of increase usually called r. It describes the theoretical maximum rate of growth of a population per individual and per day [5]. Thus the following differential equation can be used to describe a population dynamics:
$$\frac{dN}{dt} = rN$$
With:
However, for easier computation and understanding, we will use the finite rate of increase of a population to model Myzus persicae populations, in order to express it as a rate of increase per day λ. We can therefore obtain the expression of a population at a time t:
Nt = λtN0
With N0 the starting population size and Nt the population size at a time t. In the literature studying Myzus persicae population dynamics, we can find:
| Parameter | Hong F. et al. [12] | [12] | [12] | [12] | [12] | Williams CT [13] | Özgökçe MS et al. [14] |
|---|---|---|---|---|---|---|---|
| r (d−1) | 0.3831 | 0.3422 | 0.3616 | 0.3595 | 0.3595 | 0.1189 | 0.2748 (std = 0.03) |
| λ (d−1) | 1.4669 | 1.408 | 1.4356 | 1.4327 | 1.3781 | 1.1262 | 1.31606 (std = 0.04) |
| Culture temperature | 23° | 23° | 23° | 23° | 23° | 11° | 25° |
| Country | China | China | China | China | China | United Kingdom | Brazil |
| Plant | Vicia faba | Capsicum annuum | Raphanus sativus | Nicotiana tabacum | Brassica campestris | Beta vulgaris | Capsicum annuum |
The table and the literature used to build it [12,13,14] allow us to strongly advocate considering temperature as the most important factor for aphid population growth rate. Given that the climate in France is more similar to that of the UK compared to the climates of China and Brazil, we will consider a weighted average of the λ values as follows:
$$\lambda_{\text{France}} = \frac{\sum \lambda_{\text{China}} + \lambda_{\text{UK}} \cdot k + \lambda_{\text{Brazil}}}{n_{\lambda} + k} = 1.16576\ \text{d}^{-1}$$
Avec k = nλ = 7 ici pour simuler une importance égale entre la valeur de l’échantillon du Royaume-Uni et les 6 autres échantillons.
The goal of Aphidisperse is to build a framework modeling M. persicae flight behavior. However, time constraints and data availability severely restrict the possibility of implementing the model with enough thoroughness to be built upon by future iGEM teams or ourselves if we were to improve the model later on. Consequently, for the model version presented here, we make several assumptions and omissions to propose a baseline model that can be easily built upon (and typically adapted without problems to other species):
While these assumptions make the model presented here unapplicable, the program is built so that once the quantitative effects of the variables are determined, they can be easily implemented once the lacking data has been gathered and processed. It is also important to note that there are no “verification data” summarizing the date of arrival of aphids in France at given locations based on empirical observations for a few years that would allow verification of the model’s correctness, or a Machine Learning-based approach.
The model combines a lattice with an agent-based model. The lattices are rectangles of 30x50 km. This parameter can be changed if needed; however, squares this big were chosen to accommodate the unequal distribution of the 3,511 meteorological stations from which temperature data was collected. Below is a display of all stations in France. Data obtained from Meteo France.
Despite the number of stations and the size of the lattice, the stations’ uneven distributions led to gaps in data for several years without information on temperature in some cases. To correct this data, we apply a region growing method on these squares. Let u = {px1y1, ..., pxnyn} be the subset of n pixels with coordinates (x,y) where weather data is insufficient. Let V(pxy) = {vi1j1, ..., vinjn} be a subset of size m, containing all the valid neighbors vij of a pixel pxy. Finally, let σv be the standard deviation of the temperature between a pixel and its neighbors. We have therefore:
$$\forall p_{xy} \in u, T(p_{xy}) = \overline{V(p_{xy})} + \sigma_v$$
To determine the value of σv we look at the graph of the temperature difference (ΔT) distribution of the neighbors toward the center pixel:
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Figure 2a : ΔT distribution of neighbors relative to their central pixel. 
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Figure 2b : Scheme of a pixel P with missing data around its neighbor with working data. 
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The distribution resembles a normal distribution, thus the value σv follows a normal distribution of parameters μ and σσ, with $\mu = \overline{V-T}$ the average temperature difference between a central pixel and its neighbor:
$$T(p_{xy}) = \overline{V(p_{xy})} + \biggl[\sigma_v \thicksim \mathcal{N}(\mu,\ \sigma_{V-T}^2)\biggr]$$
Every square on the map has been attributed an average daily temperature, based on meteorological data or approximated thanks to their neighbors, from 2000 to 2022, totaling 8400 values for each of the 477 squares.
Now we would like to determine the date at which the aphids will be able to take off. The temperature threshold is 4.3 degrees, but to minimize false positives we take 5 degrees as the threshold for development. The onset for aphid take-off is the day when the derived accumulated degree-days are over 16 degrees ([Σ(dailyaveragetemperatures–5°C)]) AND the average temperature is over 16 degrees. From 2000 to 2022, we determine the date of flight onset this way.
The idea now is to derive a function to estimate the approximate onset date of aphid migrations. To do this, we use regression-based approaches as shown in the figures below. Precision is calculated based on Root Mean Squared Error (RMSE).
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Figure 3a : Linear regression estimate of flight onset. 
RMSE = 24.4 days |
Figure 3b : Sinusoidal regression estimate of flight onset. 
RMSE = 19.6 days |
We implemented a Grid Search parameter optimization to find the best possible parameters for the sinusoidal regression to predict the flight onset date. This program is run prior to the model, and the parameters for the sinus function are stored for each square, which will be used afterward to determine the onset date for a given year.
As previously mentioned, Aphidisperse is an agent-based model: an agent here represents an aphid population of relative density. The density of this population (the agent) increases over time based on the equation (N_t = ^t N_0) with (= 1.16576 d^{-1}). Once density reaches a fixed threshold, winged aphids are produced and will migrate. As noted earlier, we assume equiprobability of direction, so the offspring will migrate in the 8 possible cardinal directions (North, North-East, North-West, South, South-West, South-East, West, East). The lattice each day displays the total density of populations in it, as shown in Figure 5a and 5b:
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Figure 5a : Example of aphid population starting state on an empty lattice. 
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Figure 5b : Example of aphid population reaching maximum density and migrating to other squares at state n+1. 
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Figure 7 :
Video displaying the aphid migration on the
map.
Ref intro:
