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Time‑invariance of the fitness weighting factor k1

Determine whether the fitness weighting factor k1 in the three-dimensional impulse–response model is constant over time, or whether k1 changes due to physiological ceilings or saturation effects during prolonged training.

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Background

Classical Banister-type models often treat the fitness gain coefficient (k1) as a constant. The present work raises the possibility that k1 could change over time due to biological limits or saturation, which would affect the accuracy of model-based performance forecasts.

Clarifying whether k1 is time-invariant or time-varying is necessary to properly parameterize and apply the three-dimensional impulse–response model, especially across long training periods and near physiological ceilings.

References

Number 3 is unknown but possibly false, as there likely is some maximum to physiological qualities that cannot respond further by infinite increases in the stimulus - but whether this maximum is often approached in practice is uncertain.

— The three-dimensional impulse-response model: Modeling the training process in accordance with energy system-specific adaptation (2503.14841 - Kontro et al., 19 Mar 2025) in Section V. Limitations of the Model (Assumption 3)