Table 1.
Summary of species targeted by sterile insect technique (SIT) programs: Location represents where SIT has been implemented; Polyandry? indicates whether the species is polyandrous (multiple matings) or not (single mating per female); Date indicates the date or approximate time frame for the initial study on the implementation of SIT for the species; Reference cites key studies.
Fig 1.
Flow diagram of the population dynamics model (Eq 1).
The compartments (and color code) correspond to larvae L (red), wild males M (green), sterilized males S (pink), unmated females FU (purple), fertilized females FF (blue) and infertile females FI (orange). Solid arrows correspond to flows, dotted arrows to matings. Sterilized males are released at rate . Reproduction is represented by the egg-laying rate
, the larvae hatching rate
, the proportion of males among offspring p and the proportion of successfull matings
. Finally, all compartments are affected by specific mortality rates
.
Table 2.
Model parameters estimated for Drosophila suzukii.
Fig 2.
Bifurcation diagram showing the larval density at equilibrium L* as a function of the sterilized male release rate .
The equilibria of system (Eq 2) correspond to the intersection points between the function (Eq 8) (blue, First scenario = Without MM, when
, or orange, Last scenario, when
and
) and the
constant. Stability is represented by solid lines, and unstable equilibria are shown by dashed lines. The eradication thresholds for each case are also shown (blue or orange dotted lines). The diagram was generated by setting the parameters to the values listed in Table 2.
Fig 3.
Flowchart describing the steps of the agent-based model.
The top black rectangle outlines the general model framework, beginning with the initialization phase: (1) input of data (biological data linked to the life cycle, release quantity), (2) creation of counters to track population densities, (3) implementation of the scheduler, (4) creation of agents at the initial time step (four types): sterilized males, wild males, larvae, and females, and (5) parametrization of the data collector to specify the data to be recorded at each step. The subsequent steps, executed at each time step, include: advancing the simulation time, releasing sterilized males (creating new sterilized male agents), performing agent-specific steps for each category, collecting data, and repeating the cycle with the next time step. The bottom rectangle illustrates, in algorithmic diagrams, the specific steps for each type of agent: sterilized males (pink), wild males (green), larvae (red), and females (purple). These diagrams summarize the sequence of decisions and events for each agent category. The agent-based model is described in further details in Section 2.2.
Fig 4.
Simulations of larval density L over time, obtained by numerically simulating the system of equations in (Eq 2), for different initial infestation levels and sterilized male release rates ().
(A) shows a high initial infestation level (initial conditions: L = 30,000, M = 100,000, FI = 0, FF = 100,000, , population almost at the no-SIT equilibrium), while (B) shows a low initial infestation level (initial conditions: L = 100, M = 300, FI = 0, FF = 300,
) at the beginning of the SIT treatment. The black curves represent no sterilized male releases (
). Blue curves show the First sperm use scenario (
), and orange curves show the Last scenario (
and
). Line styles distinguish the different release rates: solid lines correspond to
(below the eradication thresholds in Fig 2), dashed lines to
(between the eradication thresholds in Fig 2), and dotted lines to
(above the eradication thresholds in Fig 2).
Fig 5.
Heatmap showing the difference in larval density reduction between the Last and First scenarios, relative to a no-SIT situation (WR), across time (days, horizontal axis) and sterilized male release rates (vertical axis).
Positive values (orange tones) indicate greater reduction in the Last scenario; negative values (blue tones) indicate better performance of the First scenario. Simulations were run over 3000 days under a high-infestation setting (initial conditions: L = 30,000, M = 100,000, FI = 0, ). Parameters as in Table 2.
Fig 6.
Heatmaps of the eradication threshold (Eq 4) as a function of (A) refractory rates (x-axis) and
(y-axis) and (B) the competitiveness of sterilized males
(x-axis) and the refractory rate of females mated with sterilized males
(y-axis).
Default parameter values are represented by white crosses on heatmpas. (A) The parameter is fixed at 0.6, as listed in Table 2, and the white dashed line represents the scenario of equal re-mating (
). The top-left region corresponds to
, while the bottom-right region corresponds to
. (B) The parameter
is fixed at 0.12, as detailed in Table 2. The eradication threshold was capped at one million; values exceeding this limit are included in the yellow area of the heatmap.
Fig 7.
Dynamics of larval densities (A-B-C) and percentage reduction in areas under the curves (D-E-F) for different sperm bias and three sterilized male release rates : (A-D)
, (B-E)
, (C-F)
.
(A–B–C) Mean larval density over time across 100 simulations, with shaded areas representing standard deviation. The color code for sperm use scenarios is as follows: WR (black) represents the reference case Without Release (no sterilized males released), First (dark blue) corresponds to females using sperm from the first male they mated with, Last (orange) represents females using sperm from the last male they mated with, Mixed (pink) assumes a proportional use of fertile sperm linked to the proportion of eggs laid, and Preference reflects female preference for a specific sperm category, with three subcases: Preference W (gray) indicates total preference for fertile sperm, Preference I (light blue) indicates intermediate preference for fertile sperm, and Preference S (yellow) indicates total preference for sterilized sperm.
(D-E-F) Histograms showing the percentage reduction in areas under the curves for the sperm use scenarios described in A-B-C, relative to the reference scenario WR without release, over a 100-day period. The error bars in these graphs represents the 95% confidence interval (CI 95%). Simulations were conducted under the same initial conditions: 1000 wild males, 1000 females, and 0 larvae. Results are based on 100 simulations performed with the agent-based model described in Section 2.2.
Fig 8.
Graph showing the percentage reduction in areas under the curve (AUC) over a 100-day period, for different sperm use scenarios, relative to the reference scenario WR without release (no sterile insect technique applied) as a function of sterile male released rates.
Simulations were conducted under the same initial conditions: 1000 wild males, 1000 females, and 0 larvae. Each point is the average over 100 simulations performed with the agent-based model described in Section 2.2.