Table 1.
Parameter abbreviations, values, descriptions and units of the DEB model.
Fig 1.
Schema of the schedule of the model of zebrafish population dynamics.
Schema of food sub-model was issued from Li and Yakupitiyage [61] and schema of the dynamic energy budget (DEB) model was issued from Kooijman [21]. An arrow before an action denotes that action was realized in random order by fish agents one after another in swift succession.
Table 2.
Parameter abbreviations, values, descriptions and units of the food sub-model.
Table 3.
Parameter abbreviations, values, descriptions and units of the IBM.
Fig 2.
Mean of the DEB model sensitivity analysis results for length equations (A) and reproduction equations (B).
Parameters are ordered according to the Sobol’s first order indices (light gray). Dark gray indices are the Sobol’s total indices. First order (Si) and total Sobol’ sensitivity indices (STi) were estimated at 25, 50, 75, 100, 200, and 400 dpf for length prediction and at 100, 200, and 400 dpf for the reproduction prediction.
Fig 3.
Morris’ global index (A), mean of the elementary effects (B) and standard deviation of the elementary effects (C) determined for the IBM of the zebrafish population dynamics.
Presented indices were the mean of the indices determined for the total number of fish, the frequency of adult/juvenile, the mean length of adults and juveniles at 1095, 1156, 1217, 1277, 1339, 1400 days from the beginning of the simulations. Sensitivity analysis indices were calculated on the mean of 30 model repetitions for each parameter combination. "Dummy" is a parameter with no influence on the model outputs. The other parameters are presented Tables 1, 2 and 3.
Fig 4.
DEB model simulations against observed length for fish from various literature experiments.
All lengths are presented as standard length (mm). Circles and crosses represent observations, lines represent model predictions. Panel A represents dataset from Lawrence et al. [31], experimental temperature (Texp) of 28.5°C, estimated ingestion level (f) of 0.54 (circles) and f = 0.80 (crosses). Panel B represents dataset from Gòmez-Requeni et al. [33], Texp = 28°C, f = 0.96. Panel C represents dataset from Schilling [30], Texp = 28°C, f = 0.52. Panel D represents dataset from Bagatto et al. [29], Texp = 25°C, f = 0.47. Panel E represents dataset from Eaton and Farley [28], Texp = 25.5°C, f = 0.86. Panel F represents dataset from Best et al. [32], Texp = 25°C, f = 0.87
Fig 5.
DEB model simulations compared to the experimental data produced in this study.
All lengths are presented as standard length (mm). Points represent observations (mean ± SD for length data), lines represent model predictions. (A) Length data, experimental temperature (Texp) of 27°C, estimated ingestion level (f) of 0.70 (circles), 0.81 (squares), and 0.93 (triangles). (B) Median of the cumulated number of eggs, Texp = 26°C, f = 0.48 (points) and Texp = 29°C, f = 0.93 (triangles); Error bars represent the first and third quartiles (C) Model predictions against observed length data for males (black circles and solid line) and females (grey squares and dashed line). Texp = 27°C, f = 0.76. (D) Model predictions against observed length data for males (black circles and solid line) and females (grey squares and dashed line). Texp = 27°C, f = 0.99.
Fig 6.
Probabilistic distributions of the length frequency predicted by the model length compared to frequency distributions observed in [17].
Circles, crosses and triangles represent the length frequency distribution of the three observed populations. Full lines represent the median length frequency distribution of the simulated populations. Colour level represents the frequency of simulated populations (n = 1,000) having a given percentage of individuals for a given class length. Frequency inferior to < 1e-05 was represented in white. The length class was one millimetre. The frequencies in the populations of the length class frequencies was calculated using class of 0.01.
Fig 7.
Zebrafish length distributions predicted compared to the length observed by Spence et al. [24].
(A) Predicted length distributions of all fish. (B) Predicted length distributions of fish > 15 mm. Black full lines represent the median length, purple dotted lines represent the first and third quartile of the fish length, and blue lines represent the limits of 95% of the fish length. Bar plot represent the distribution of the length of the fish sampled by Spence et al. [24] (sample of 120 fish).
Fig 8.
Zebrafish population dynamics predicted through three years.
(A) zebrafish biomass, (B) frequencies of the different fish stages (excluding eggs-larvae), (C) mean length of the different zebrafish stages, and (D) food dynamic state variables.