Table 1 List of model parameters
From: Inferring the energy cost of resistance to parasitic infection and its link to a trade-off
Parameter | Definition | Value | Source |
|---|---|---|---|
Parasites development | |||
\({\mu }_{LI}\); \({\mu }_{LE}\); \({\mu }_{Am}\); \({\mu }_{{Af}_{NL}}\); \({\mu }_{{Af}_{L}}\) | Mortality rates [per day] of LI, LE, and of Am, AfNL, AfL | 0.18; 0.01; 0.015 | [35] |
\({{p}_{A}}_{m}\) | Proportion of LE that are males (the remaining proportion 1—\({{p}_{A}}_{m}\)are females) | 0.5 | assumed |
\({k}_{{E}_{0}}\); \({k}_{{F}_{0}}\) | Maximum transition rates from LI to LE (establishment), and from AfNL to AfL (fecundity) | 2; 0.3 | assumed |
\({k}_{A}\) | Constant transition rate from LE to Am and AfNL | 0.62 | assumed |
\({\tau }_{LI}\);\({\tau }_{LE}\) | Minimum time delay (in days) from ingestion to establishment site, and from establishment to emergence | 2; 15 | [35] |
\({F}_{0}\) | Maximum fecundity rate per capita (number of eggs per day and per adult female) | 7000 | [36] |
\({\omega }_{LE}\); \({\omega }_{Am}\); \({\omega }_{{Af}_{NL}}\); \({\omega }_{{Af}_{L}}\) | Loss in HE per capita for parasite categories LE, Am, AfNL, and AfL, respectively | (× 1e−5) 15; 50; 50; 110 | [37] |
Host immune response | |||
\({I}_{{E}_{0.5}}\); \({I}_{{F}_{0.5}}\) | Levels of IE and IF at which kE and kF respectively, are reduced of 50% | 5 | assumed |
\(\alpha {k}_{E}\); \(\alpha {k}_{F}\) | Shape factors of immune effects on kE and kF | 3 | assumed |
\({\varphi }_{{I}_{E}}\); \({\varphi }_{{I}_{F}}\) | Per capita replication rates of IE and IF, respectively | assumed to vary between individuals; estimated (individual level) | |
\(\alpha {I}_{E}\) | Shape factor of parasite effect (LI) on IE replication | 3 | assumed |
\({LI}_{0.5}\) | Level of LI at which IE replication is at 50% of its maximum | 3000 | assumed |
\({I}_{{E}_{0}}\); \({I}_{{F}_{0}}\) | Baseline levels of IE and IF | 1 | assumed |
\({\beta }_{{I}_{E}}\); \({\beta }_{{I}_{F}}\) | Per capita loss rates of IE and IF, respectively | 0.05 | assumed |
Host energy budget | |||
\({\alpha }_{{P}_{m}}\) | Scaling exponent of\({P}_{m}\) | 0.27 | |
\({P}_{m}\) | Protein weight at maturity [kg] | assumed to vary between individuals; estimated (individual level) | |
\({L}_{m}\) | Lipid weight at maturity [kg] | ||
\({\beta }_{P}\) | Relative protein growth rate from birth to maturity [\({\text{kg}}^{{\alpha }_{{P}_{m}}}\).day−1] | ||
\({\beta }_{P}^{*}\) | Relative protein growth rate during infection [\({\text{kg}}^{{\alpha }_{{P}_{m}}}\).day−1] | ||
\({\beta }_{Wool}\) | Relative wool growth rate [day−1] | ||
\({e}_{growth}\); \({e}_{maint}\); \({e}_{dep}\); \({e}_{mob}\) | Unitary energy costs (in MJ/kg) of protein growth, protein maintenance, lipid deposition, and lipid mobilization, respectively | 56; 1.63; 50; 39.6 | |
\({e}_{{I}_{E}}\); \({e}_{{I}_{F}}\) | Unitary energy costs (in MJ/unit) of immune responses IE and IF, respectively | estimated (population level) | |
Observed host traits | |||
\({HE}_{0}\) | Baseline level of\(HE\)[%] | assumed to vary between individuals; estimated (individual level) | |
\({\beta }_{HE}\) | Per loss rate of HE not due to infection | 0.16 | assumed |
\({\gamma }_{Ash}\); \({\gamma }_{Water}\) | Fixed ratio Ash:P and Water:Pm, respectively | 0.211; 3.25 | |
\({\alpha }_{Water}\) | Scaling factor of protein maturity determining the proportion of body water | 0.815 | |
\({a}_{Gut\_Fill}\); \({b}_{Gut\_Fill}\) | Coefficients to predict Gut_Fill from Feed_Energy | 11; 0.467 | [39] |
\({a}_{BFT}\); \({b}_{BFT}\); \({c}_{BFT}\) | Coefficients to predict BFT | −4.01; 0.56; 1.52 | [40] |
\({DMC}_{Feces}\) | Dry matter content of the feces | 0.35 | assumed |
Diet characteristics | |||
\({DMC}_{Feed}\) | Dry matter content of the feed | 0.88 | known inputs |
\({DMD}_{Feed}\) | Dry matter digestibility of the feed | 0.76 | |
\({MEC}_{Feed}\) | Metabolizable energy content of the feed (MJ/kg of DM) | 7.7 | |