General information on the DEBkiss-tox package
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GENERAL WARNING: This package has not extensively been tested yet. I hope that in the near future, more (and more interesting) data sets will become available. Therefore, this version of the package should be seen as experimental.
This package contains three sets of closely-related model equations, all based on DEBkiss. These models are derived and described in detail in version 2.0 of the DEBkiss e-book (https://leanpub.com/debkiss_book). Version 3.0 of this package is consistent (in terms of models and symbols) with version 2.0 of the e-book. This implies that the models are phrased as 'reduced models', using scaled damage as the central property driving toxicity, and a rate constant designated as a 'dominant rate constant'. In this way, the model formulation differs from the classical DEBtox models (e.g., Jager & Zimmer), but is in line with the developments of GUTS (see the GUTS e-book: https://leanpub.com/guts_book). The 'Making sense' e-book has, in version 2.0) also been updated to reflect a central role for damage.
For those familiar with classic DEBtox models, there are a few general things to note:
1) Damage is central, so there is no scaled internal concentration anymore. However, in reduced models, these two metrics play a similar role. Difference is that damage is not necessarily diluted by growth or affected by the animal's surface to volume ratio. Therefore, several options for the TK/damage module have been implemented to try out.
2) The tolerance concentration has been replaced by an effect strength (which is equivalent to 1/cT). This is done to bring the model for sub-lethal effects more in line with that for lethal effects (the killing rate is also an effect strength).
3) The TK/damage module allows incorporation of losses with reproduction. This requires an additional parameter (KRV). KRV=1 is a useful starting point, which implies that eggs receive the same chemical concentration as the mother had at the time of egg production. This value is fixed in derivatives.m as there is little point in trying to fit it on data for effects.
4) Model type 1 and 2 (see below) have the possibility to calculate initial body size from the egg size (which is also needed as an input). In model 1, this is done in the examples provided in its directory. For model 2, this is not done, and would require some additional code in call_deri.m.
5) The model formulations in this package standardly contain a few extras, namely the possibility to include a size-dependent food limitation in model 1 and 2 (as e.g., used for nematodes), and a lag time. This latter is used for the Capitella case study in the directory for model 1.
Three model types that are included in this package. This was done to support the discussions on the 'most-appropriate DEB-based model' for environmental risk assessment.
1) complete_model. This is the full DEBkiss model, specified in primary parameters (e.g., maximum surface-specific assimilation rate and specific maintenance rate).
2) compound_model. This is the full DEBkiss model, specified in compound parameters (e.g., maximum body length and von Bertalanffy growth-rate constant). The user thus interacts with easy-to-understand parameters, that are internally translated into the primary ones. After that translation, the model calculations are exactly the same as for the previous model.
3) simple_model. This is the DEBkiss model translated into compound parameters. This leads to a very compact (though slightly abstract) set of model equations (as in the original DEBtox of Kooijman & Bedaux).
Model 3 has the advantage that it can be entirely identified using data on growth and reproduction; there is no need to settle on conversion factors (e.g., shape correction) or yield factors (e.g., the yield of structure on assimilates). Exception is when one likes to includes losses with reproduction in the TK/damage module; in that case, the relative egg dry weight is needed. Disadvantage is that this model version cannot deal with starvation in a consistent manner. Starvation occurs when when food availability varies over time, but can also be induced by toxic stress on assimilation and maintenance (especially under time-varying exposure). The model will calculate something, but the mass/energy balance is broken.
Model 2 has easy-to-understand parameters that are fitted to data. However, it additionally requires that several general parameters for the animal are defined: shape-correction factor, dry-weight density, yield factors (DEBkiss offers defaults that should be fine), and egg weight. This allows for a consistent starvation module (which will likely also be species dependent). Downside is that these additional parameters are difficult to derive, which is troublesome for risk assessment as it raises questions on the consequences of these settings for the model output. Since the model can be simplified to *not* include these parameters, it should be clear that they generally have no effect whatsoever on the model output. Their *only* effect is on model behaviour under starvation. This model version also allows modification to produce additional outputs such as respiration rates or feeding rates, in a consistent manner. It is therefore more future proof than Model 1.
Main open questions:
1) The most appropriate feedbacks from the life-history traits to the TK/damage module requires further investigation. That this moment, this package includes 4 options, and it is unclear which one is most relevant (for which situations). The classical DEBtox models simply used growth dilution and scaling with the surface:volume ratio for all cases (ignoring losses with reproduction). However, since damage dynamics may be dominant, this is not a good idea in general. This aspect requires dedicated testing.
2) Few studies have dealt in detail with starvation effects in DEB models, and none have looked at toxicant effects on starvation. Since starvation may be induced by (time-varying) exposure to toxicants, this is not a trivial matter. In this version of the model, animals will shrink at some point, which leads to the reverse of growth dilution: 'shrinking concentration'. This is a positive feedback mechanism that will rapidly lead to runaway model behaviour. It needs to be investigated whether 'shrinking concentration' actually happens.
3) Starvation could also increase the probability to die. This is not considered at the moment, due to a lack of suitable information on this issue.