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Ipimar Palestra Modelling uptake and clearance dynamics: how do we figure out what is really going on? Modelling uptake and clearance dynamics: how do we figure out what is really going on? Bill Silvert Emeritus Research Scientist Bedford Institute of Oceanography 4If you want to learn about stock assessment, you are in the wrong room!

Introductory Remarks 4This PowerPoint presentation is based on the seminar I gave at IPIMAR on , and is for people who had to miss the talk. 4It is a bit disorganised, since I just threw together some additional material to fill in the spaces between the original slides.

What Kinds of Models? 4Models can be descriptive or interpretive. 4Descriptive models are of limited value in situations that do not repeat the past. 4Interpretive models can be top-down or bottom-up. 4Top-down models work from the data to structure, and do not stop at description.

Description or Understanding? 4We can choose between models that describe the data and those which give us some understanding of the system. 4Descriptive models (statistical, empirical, phenomenological) can be used to describe situations which recur in similar patterns, but are of limited value in extreme or novel cases.

Interpretive Modelling 4There are two basic ways of interpretive modelling, top-down and bottom-up. 4Top-down modelling starts from the output, namely the data to be modelled, and works toward the structure (not just a description) of the model. 4Bottom-up modelling starts from assumed model structure and translates it into a model on reductionist principles.

Top-Down Modelling My preferred approach is a variant of top- down modelling. Start from a very simple model structure that represents the basic known structure of the system, and build up a model that reflects our understanding about the processes involved in the context of the data. Try to avoid making assumptions that do not fit the data.

Top-Down Toxin Modelling Modelling of phycotoxin kinetics is a good example of this top-down modelling variant. We have a good basic starting point in the uptake & clearance model, but there are many processes and pathways that are poorly understood for which we can try to find models that fit the data in a meaningful way.

Basic Equation for Fluxes [rate of change] = [uptake] – [loss] dC/dt = aX – bC Change

Problems with Modelling 4Grazing rates In this figure you can see how several sets of parameter values were used to fit the model output to the data, but it is very difficult to match the peak toxicity values that were observed.

Simpler Flux Equation – [loss] [rate of change] = [uptake] – [loss] – bC dC/dt = aX – bC Change

Grazing Rate Problem Even when we assume that all toxin is retained dC/dt = aX …… and use the maximum a we cannot reach the maximum.

This time series of PSP data for mussels will be used to illustrate several modelling problems.

Problems with Modelling 4Grazing rates 4Aliasing errors FMissing toxic blooms Because we can only sample the water column at discrete intervals, we can miss significant events, e.g., pulses of toxic algae that can cause high levels of shellfish toxicity.

How can we explain toxicity in the mussels before there is toxicity in the water column, other than as aliasing error?

Problems with Modelling 4Grazing rates 4Aliasing errors FMissing toxic blooms FExaggerating toxic events We can also overestimate the importance of very short pulses of toxic algae that happen to coincide with our sampling.

This simulated peak is due to a single observation of a toxic algal patch.

Problems with Modelling 4Grazing rates 4Aliasing errors FMissing toxic blooms FExaggerating toxic events 4Multiple compartments

Two-Compartment Models There are lots of clues that can indicate the existence of multiple compartments within a system (i.e., within a shellfish). We have to look at things the right way. For example, if we plot the uptake and clearance from an experiment like this:

Concentration vs. Time Here is a hypothetical experiment...

Two-Compartment Models But if we plot the uptake and clearance from the same experiment on a semi-log scale we can see that the decay is not a straight line and therefore cannot be a simple exponential:

Concentration vs. Time Semi-Log plot of same “data”...

Two-Compartment Models in Real Time Series When we look at a real time series we may see evidence that some of the toxin is moving more slowly than the rest, which shows up as lag effects in the data. If we add a second compartment to the model we can often explain these lag effects very effectively.

This cluster of persistent toxicity suggests a second compartment.

Including a second compartment improves the agreement

What the Second Compartment Does The role of the second compartment can be seen in the following figure. It takes time to move toxin into the second compartment, and it leaves more slowly, so it lags behind the main compartment.

System Identification for Multi-Compartment Models Viscera A single-compartment model is easy to visualise:

System Identification for Multi-Compartment Models Viscera Even a two-compartment model adds lots of complexity! Other

Problems in Data Analysis 4Lab data may not apply to field results. 4Discrete sampling of continuous variables can lead to aliasing errors. 4Not all of the processes to be modelled can be measured directly. 4It is difficult to identify what compartments exist and what the flows are beween them.

Basic Conclusions 4Start with simple models and refine them as you go along. 4Define your models in such a way that you can relate them to the biology. 4You may not be able to determine exact model structure.

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