CalcCAMPVrnRates
A function in APSIM Next Generation that calculates vernalisation (Vrn) expression rate parameters for a given genotype, using observed final leaf number (FLN) data and controlled environment parameters. It forms a core part of the CAMP (Cereal Apical Meristem Phenology) model and supports simulation of genotype-specific developmental responses to photoperiod and vernalisation cues.
Overview
CalcCAMPVrnRates is used to derive the coefficients that govern how vernalisation and photoperiod affect the expression rates of vernalisation genes in the CAMP model. It operates on FLN observations from controlled environment studies with defined photoperiod and temperature treatments. The outputs are rate parameters that quantify the rate and phase transitions of Vrn expression in different photothermal regimes, enabling genotype-specific simulation of phenological development.
This function is critical for enabling APSIM NG to simulate genotype-by-environment interactions in crop phenology, particularly for cereal crops where vernalisation and photoperiod sensitivity genes such as Vrn1, Vrn2, and Vrn3 play a pivotal role.
Inputs
This function requires the following inputs:
FinalLeafNumberSet FLNset: A dataset containing FLN values under different photoperiod and vernalisation treatments:LV– Long photoperiod with vernalisationLN– Long photoperiod without vernalisationSV– Short photoperiod with vernalisationSN– Short photoperiod without vernalisation
FLNParameterEnvironment EnvData: The environmental parameters under which FLN was observed:VrnTreatTemp: Vernalisation treatment temperature (°C)VrnTreatDuration: Duration of vernalisation treatment (days)TreatmentPp_L: Long-day photoperiod (hours)TtEmerge: Thermal time from sowing to emergence (°Cd)
In addition, it links to:
basePhyllochron: A child model function that returns the phyllochron (thermal time per leaf)camp: The ancestor CAMP model, which provides helper methods and constants
Methodology
The CalcCAMPVrnRates function estimates vernalisation rate parameters using:
FLNset: a set of final leaf number parametersEnvData: controlled environment data used to measure final leaf number
The function performs the following steps:
- Convert Emergence Duration from Thermal Time to Phyllochrons
- Base phyllochron duration of vernalisation treatment
- Estimate Haun Stage at Terminal Spikelet
- Calculate Minimum Vernalisation Saturation to Terminal Spikelet
- Calculate the accumulated phyllochrons at vernalisation saturation for each treatment
- Calculate Vernalisation Rates and Photoperiod Sensitivities
- Calculate Maximum Vrn2 Expression Under Long Photoperiods
- Calculate Cold-Induced Upregulation of Vrn1 Expression
Convert Emergence Duration from Thermal Time to Phyllochrons
The duration from sowing to emergence is first expressed in phyllochrons (\(Ph_\text{emergence}\)) using the base phyllochron value (\(Ph_\text{base}\)):
\[ Ph_\text{emergence} = \frac{TT_\text{emergence}}{Ph_\text{base}} \]
Where:
- \(TT_\text{emergence}\) is the thermal time from sowing to emergence (°C·days),
TtEmergein FLNParameterEnvironment.qmd, - \(Ph_\text{base}\) is the base phyllochron duration.
Base phyllochron duration of vernalisation treatment
The base phyllochron duration of the vernalisation treatment (\(Ph_\text{vern}\)) is calculated as: \[ Ph_\text{vern} = \frac{T_\text{vern} \times D_\text{V}}{Ph_\text{base}} \]
Where:
- \(T_\text{vern}\) is the vernalisation treatment temperature (°C),
VrnTreatTempin FLNParameterEnvironment.qmd, - \(D_\text{V}\) is the vernalisation treatment duration (days),
VrnTreatDurationin FLNParameterEnvironment.qmd, - \(Ph_\text{base}\) is the base phyllochron duration.
Estimate Haun Stage at Terminal Spikelet
The Haun Stage at terminal spikelet for each environment \(i\) (e.g., LV, LN, SV, SN) is calculated following the method of Brown et al. (2013):
\[ \text{HS}_{TS}(i) = \left( \text{FLN}(i) - 2.85 \right) \times 1.1 \]
Where:
- \(\text{FLN}(i)\) is the final leaf number observed under environment \(i\).
Calculate Minimum Vernalisation Saturation to Terminal Spikelet
The minimum vernalisation saturation at terminal spikelet (\(\text{VS}_{TS,\ min}\)) is estimated as:
\[ \text{VS}_{TS,\ min} = \min\left( \text{HS}_{TS,\ LV} - 1.1,\ 3 \right) \]
Where:
- \(\text{HS}_{TS,\ LV}\) is the Haun Stage at terminal spikelet in the long-day vernalised (LV) treatment,
- 1.1 is the earliest Haun Stage at which vernalisation saturation can begin,
- 3 is the maximum stage for vernalisation saturation, based on Lincoln controlled environment data (CRWT153).
Calculate the accumulated phyllochrons at vernalisation saturation for each treatment
The accumulated phyllochron at vernalisation saturation is estimated for each photoperiod × vernalisation treatment. These values are expressed in phyllochrons and are derived relative to the Haun Stage at terminal spikelet (\(\text{HS}_{TS}\)) and the previously calculated minimum duration between vernalisation saturation and terminal spikelet (\(\text{VS}_{TS,\text{min}}\)).
Long-day Vernalised (LV) Environment
For the LV treatment, vernalisation saturation is assumed to occur exactly \(\text{VS}_{TS,\text{min}}\) before terminal spikelet:
\[ \text{VS}_{LV} = \text{HS}_{TS,\ LV} - \text{VS}_{TS,\text{min}} \]
Where:
- \(\text{HS}_{TS,\ LV}\) is the Haun Stage at terminal spikelet for the LV treatment,
- \(\text{VS}_{TS,\text{min}}\) is the minimum vernalisation saturation to terminal spikelet.
This forms the baseline timing of saturation under conditions without vernalisation and photoperiod impacts.
Long-day Non-vernalised (LN) Environment
For LN, the vernalisation saturation timing is constrained by Haun Stage of LN at terminal spikelet (\(\text{HS}_{TS,\ LN}\)) and cannot occur earlier than in the LV treatment:
\[ \text{VS}_{LN} = \max(\text{HS}_{TS,\ LN} - \text{VS}_{TS,\text{min}},\ \text{VS}_{LV}) \]
Where:
- \(\text{HS}_{TS,\ LN}\) is the Haun Stage at terminal spikelet for the LN treatment,
- \(\text{VS}_{LV}\) is the vernalisation saturation timing for the LV treatment,
- \(\text{VS}_{TS,\text{min}}\) is the minimum vernalisation saturation to terminal spikelet.
This ensures the LN environment does not reach vernalisation saturation before LV.
Short-day Vernalised (SV) Environment
For the SV treatment, the vernalisation saturation timing is constrained by Haun Stage of LN at terminal spikelet (\(\text{HS}_{TS,\ SV}\)) and cannot occur earlier than in the LV treatment:
\[ \text{VS}_{SV} = \max(\text{HS}_{TS,\ SV} - \text{VS}_{TS,\text{min}},\ \text{VS}_{LV}) \]
Where:
- \(\text{HS}_{TS,\ SV}\) is the Haun Stage at terminal spikelet for the SV treatment,
- \(\text{VS}_{LV}\) is the vernalisation saturation timing for the LV treatment,
- \(\text{VS}_{TS,\text{min}}\) is the minimum vernalisation saturation to terminal spikelet.
This ensures the SV environment does not reach vernalisation saturation before LV.
Short-day Non-vernalised (SN) Environment
For the SN environment, saturation is constrained by Haun Stage of LN at terminal spikelet (\(\text{HS}_{TS,\ SN}\)) and cannot occur earlier than in the LV treatment:
\[ \text{VS}_{SN} = \max(\text{HS}_{TS,\ SN} - \left( \text{HS}_{TS,\ SV} - \text{VS}_{SV} \right),\ \text{VS}_{LV}) \]
Where:
- \(\text{HS}_{TS,\ SN}\) is the Haun Stage at terminal spikelet for the SN treatment,
- \(\text{HS}_{TS,\ SV}\) is the Haun Stage at terminal spikelet for the SV treatment,
- \(\text{VS}_{SV}\) is the vernalisation saturation timing for the SV treatment,
- \(\text{VS}_{LV}\) is the vernalisation saturation timing for the LV treatment.
This ensures the SV environment does not reach vernalisation saturation before LV.
Calculate Vernalisation Rates and Photoperiod Sensitivities
The base and maximum rates of vernalisation progression during the vegetative and early reproductive phases are estimated, along with the photoperiod (Pp) sensitivity factors.
Base Vernalisation Rate During Vegetative Phase
Base vernalisation rate during vegetative phase (\(\Delta V_{\text{base, veg}}\), BaseDVrnVeg in CultivarRateParams) assumes vernalisation starts at sowing and proceeds linearly until saturation in the SN treatment (which is short-day and non-vernalised treatment and lacks vernalising temperature and long photoperiod upregulation), the base rate is:
\[ \Delta V_{\text{base, veg}} = \frac{1}{\text{VS}_{SN} + Ph_{\text{emergence}}} \]
Where:
- \(\text{VS}_{SN}\) is the phyllochron at vernalisation saturation for the SN treatment,
- \(Ph_{\text{emergence}}\) is the phyllochron duration from sowing to emergence.
Maximum Vernalisation Rate During Vegetative Phase
The fastest rate of vernalisation during vegetative phase (\(\Delta V_{\text{max, veg}}\), MaxDVrnVeg in CultivarRateParams) is assumed to occur in the SV treatment (i.e. short-day with vernalisation), where the rate is maximised at the minimum vernalisation saturation to terminal spikelet:
\[ \Delta V_{\text{max, veg}} = \frac{1}{\text{VS}_{SV} + Ph_{\text{emergence}}} \]
Where:
- \(\text{VS}_{SV}\) is the phyllochron at vernalisation saturation for the SV treatment,
- \(Ph_{\text{emergence}}\) is the phyllochron duration from sowing to emergence.
Base Vernalisation Rate During Early Reproductive Phase
The base vernalisation rate during early reproductive phase (\(\Delta V_{\text{base, ER}}\), BaseDVrnER in CultivarRateParams) is calculated as:
\[ \Delta V_{\text{base, ER}} = \frac{1}{\text{HS}_{TS,\ SN} - \text{VS}_{SN}} \]
Where:
- \(\text{HS}_{TS,\ SN}\) is the Haun Stage at terminal spikelet for the SN treatment,
- \(\text{VS}_{SN}\) is the phyllochron at vernalisation saturation for the SN treatment.
Maximum Vernalisation Rate During Early Reproductive Phase
The maximum vernalisation rate during early reproductive phase (\(\Delta V_{\text{max, ER}}\), MaxDVrnER in CultivarRateParams) is calculated as:
\[ \Delta V_{\text{max, ER}} = \frac{1}{\text{VS}_{TS,\ min}} \]
Where:
- \(\text{VS}_{TS,\ min}\) is the minimum vernalisation saturation to terminal spikelet, calculated earlier.
Photoperiod Sensitivity Factor During Early Reproductive Phase
The photoperiod sensitivity factor during early reproductive phase (\(F_{\text{Pp, Vrn3, ER}}\), PpVrn3FactER in CultivarRateParams) is calculated as: \[
F_{\text{Pp, Vrn3, ER}} = \left( \frac{\Delta V_{\text{max, ER}}}{\Delta V_{\text{base, ER}}} - 1 \right) + 1
\]
Where:
- \(\Delta V_{\text{max, ER}}\) is the maximum vernalisation rate during early reproductive phase,
- \(\Delta V_{\text{base, ER}}\) is the base vernalisation rate during early reproductive phase.
This factor quantifies how much faster vernalisation proceeds under long photoperiod compared to the baseline.
Photoperiod Sensitivity Factor During Vegetative Phase
The photoperiod sensitivity factor during vegetative phase (\(F_{\text{Pp, Vrn3, veg}}\), PpVrn3FactVeg in CultivarRateParams) is calculated as: \[
F_{\text{Pp, Vrn3, veg}} = \left( \frac{1 / \text{VS}_{LN}}{\Delta V_{\text{max, veg}}} - 1 \right) + 1
\]
Where:
- \(\text{VS}_{LN}\) is the phyllochron at vernalisation saturation for the LN treatment,
- \(\Delta V_{\text{max, veg}}\) is the maximum vernalisation rate during vegetative phase.
To ensure consistency, this factor is constrained to be no less than the early reproductive sensitivity:
\[ F_{\text{Pp, Vrn3, veg}} = \max(F_{\text{Pp, Vrn3, veg}},\ F_{\text{Pp, Vrn3, ER}}) \]
Where:
- \(F_{\text{Pp, Vrn3, veg}}\) is the photoperiod sensitivity factor during vegetative phase,
- \(F_{\text{Pp, Vrn3, ER}}\) is the photoperiod sensitivity factor during early reproductive phase.
Calculate Maximum Vrn2 Expression Under Long Photoperiods
The maximum vernalisation repressor (Vrn2) expression under long photoperiod conditions without vernalising temperatures (\(V_{\text{max, Vrn2}}\), , MaxVrn2 in CultivarRateParams) is estimated as:
Before vernalisation saturation (VS) is reached under long photoperiod without vernalisation, Vrn1 expression is influenced by both baseline and Vrn3-induced pathways. The effective rate of Vrn1 expression is:
\[ \Delta V_{\text{Vrn1} \times \text{Vrn3}} = \max\left( \frac{1}{VS_{\text{LN}}},\ \Delta V_{\text{base, veg}} \times F_{\text{Pp, Vrn3, veg}} \right) \]
Where:
- \(\frac{1}{VS_{\text{LN}}}\) is the rate assuming linear accumulation from sowing to saturation without upregulation,
- \(\Delta V_{\text{base, veg}}\) is the base Vrn1 rate,
- \(F_{\text{Pp, Vrn3, veg}}\) is the photoperiod (Vrn3) sensitivity factor in the vegetative phase.
Duration of Effective Vrn1 × Vrn3 Expression Phase
The time (in Haun stages) needed to reach saturation at the above rate is:
\[ H_{\text{Vrn1} \times \text{Vrn3}} = \frac{1}{\Delta V_{\text{Vrn1} \times \text{Vrn3}}} \]
Where:
- \(\Delta V_{\text{Vrn1} \times \text{Vrn3}}\) is the effective rate of Vrn1 × Vrn3 expression,
- \(H_{\text{Vrn1} \times \text{Vrn3}}\) is the duration of effective Vrn1 × Vrn3 expression in Haun stages.
This represents the duration over which the effective Vrn1 × Vrn3 expression occurs in the absence of vernalisation.
Haun Stage When Vrn2 Expression Ends
Vrn2 expression is assumed to end just before Vrn1 × Vrn3 takes effect. This occurs \(H_{\text{Vrn1} \times \text{Vrn3}}\) stages prior to saturation:
\[ \text{EndVrn2}_{\text{LN}} = \max\left(0,\ VS_{\text{LN}} - H_{\text{Vrn1} \times \text{Vrn3}} \right) \]
Where:
- \(\text{EndVrn2}_{\text{LN}}\) is the Haun stage when Vrn2 expression ends in the LN treatment,
- \(VS_{\text{LN}}\) is the phyllochron at vernalisation saturation for the LN treatment,
- \(H_{\text{Vrn1} \times \text{Vrn3}}\) is the duration of effective Vrn1 × Vrn3 expression in Haun stages.
This value is constrained to be non-negative.
Maximum Vrn2 Expression Under Long Photoperiods
The total Vrn2 expression is assumed to accumulate linearly from emergence to the end of Vrn2 activity under baseline Vrn1 expression:
\[ V_{\text{max, Vrn2}} = \left( \text{EndVrn2}_{\text{LN}} + Ph_{\text{emergence}} \right) \times \Delta V_{\text{base, veg}} \]
Where:
- \(\text{EndVrn2}_{\text{LN}}\) is the Haun stage when Vrn2 expression ends in the LN treatment,
- \(Ph_{\text{emergence}}\) is the phyllochron duration from sowing to emergence,
- \(\Delta V_{\text{base, veg}}\) is the base Vrn1 expression rate during the vegetative phase.
This value represents the maximum repressive effect of Vrn2 that must be overcome before Vrn3-mediated acceleration of Vrn1 expression can begin.
Calculate Cold-Induced Upregulation of Vrn1 Expression
The effect of cold treatment on persistent (methylated) upregulation of Vrn1 expression in the LV (long photoperiod + vernalisation) environment (\[C_{\text{Vrn1}}\], ColdVrn1Fact in CultivarRateParams) is estimated as:
Baseline Vrn1 Expression up to VS in the LV Treatment
The total amount of Vrn1 expressed under baseline conditions in the LV treatment from sowing to vernalisation saturation is:
\[ V_{\text{base, LV}} = (Ph_\text{emergence} + VS_{\text{LV}}) \times \Delta V_{\text{base, veg}} \]
Where:
- \(Ph_\text{emergence}\) is the phyllochron duration from sowing to emergence,
- \(VS_{\text{LV}}\) is the phyllochron at vernalisation saturation for the LV treatment,
- \(\Delta V_{\text{base, veg}}\) is the baseline rate of Vrn1 expression during the vegetative phase.
This reflects the cumulative Vrn1 expression in the absence of cold-specific upregulation.
Amount of Cold-Induced Persistent Vrn1 Expression
Cold upregulation of Vrn1 (assumed to lead to methylation and memory) is calculated as:
\[ V_{\text{cold, LV}} = V_{\text{threshold}} + V_{\text{max, Vrn2}} - V_{\text{base, LV}} \]
Where:
- \(V_{\text{threshold}}\) is the saturation threshold for Vrn1 (typically 1),
- \(V_{\text{max, Vrn2}}\) is the maximum Vrn2 repressive expression,
- \(V_{\text{base, LV}}\) is the amount of Vrn1 expressed at baseline up to VS.
Methylation Threshold
The methylation threshold (\(\theta_{\text{meth}}\), MethalationThreshold in CultivarRateParams) (i.e., amount of Vrn1 needed for full persistent response) is assumed to be equal to the cold-induced Vrn1 amount:
\[ \theta_{\text{meth}} = V_{\text{cold, LV}} \]
This assumption is based on findings by Brooking and Jamieson that the lag before methylation equals the duration of vernalisation response.
Effective Duration of Vernalisation
The duration (in Haun stages) over which vernalisation is active is:
\[ H_{\text{vern, LV}} = \min(Ph_\text{vern},\ Ph_\text{emergence} + VS_{\text{LV}}) \]
Where: - \(Ph_\text{vern}\) is the phyllochron duration of the vernalisation treatment, - \(Ph_\text{emergence}\) is the phyllochron duration from sowing to emergence, - \(VS_{\text{LV}}\) is the phyllochron at vernalisation saturation for the LV treatment.
Cold-Induced Vrn1 Expression Rate During Treatment
The total rate of Vrn1 expression under cold treatment is:
\[ \Delta V_{\text{cold, LV}} = \frac{V_{\text{cold, LV}} + \theta_{\text{meth}}}{H_{\text{vern, LV}}} \]
Where:
- \(V_{\text{cold, LV}}\) is the amount of cold-induced Vrn1 expression,
- \(\theta_{\text{meth}}\) is the methylation threshold,
- \(H_{\text{vern, LV}}\) is the effective duration of vernalisation in Haun stages.
Maximum Cold-Induced Expression Rate at 0°C
Assuming an exponential temperature effect, the maximum rate of Vrn1 expression under cold is:
\[ \Delta V_{\text{cold, max}} = \frac{\Delta V_{\text{cold, LV}}}{\exp(k \cdot T_{\text{cold}})} \]
Where:
- \(\Delta V_{\text{cold, LV}}\) is the cold-induced Vrn1 expression rate during the vernalisation treatment,
- \(k\) is the temperature coefficient for vernalisation (typically -0.17),
- \(T_{\text{cold}}\) is the vernalisation treatment temperature,
VrnTreatTempin FLNParameterEnvironment.
Cold-Induced Vrn1 Upregulation Factor
The cold upregulation factor (\(F_{\text{cold, vrn1}}\), ColdVrn1Fact in CultivarRateParams) is calculated as the ratio of cold-enhanced Vrn1 expression to baseline expression:
\[ F_{\text{cold, vrn1}} = \frac{\Delta V_{\text{cold, max}}}{\Delta V_{\text{base, veg}}} \]
Where:
- \(\Delta V_{\text{cold, max}}\) is the maximum cold-induced Vrn1 expression rate at 0°C,
- \(\Delta V_{\text{base, veg}}\) is the baseline Vrn1 expression rate during the vegetative phase.
This factor quantifies the enhancement in Vrn1 expression due to cold during vernalisation.
Events
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Properties
Configurable and Reportable Properties
No configurable properties are available for this function.
Read-Only Reportable Properties
No read-only properties are available for this function.
User Interface
Not typically user-configurable through the UI. It is populated by the
CalcCAMPVrnRatesfunction based on genotype-specific FLN observations.
Practical Example
No practical example is available for this function.
See Also
- Source code: CalcCAMPVrnRates.cs on GitHub