I think response of @Mariel Gullian Klanian settles your first question. As for forecasting heavy metal concentration in other species using model results, presumably of another species, I think it may be possible but a bit tricky. Tricky because different species assimilate heavy metals differently. I think it is possible to do this within congenerics. It may be tricky and complex if you want to cross genus.

I agree with Mariel's answer. RDA is an appropriate analysis. However, I am thinking about the regression models. I will be informed you ASAP.

Dear Mariel Gullian Klanian and Omid Safari

Thank you very much for your answer. Definitely CCA or RDA would be a great option if the aim of study is to find blind relationship between just to matrix. But my main goal is to find a pathway between heavy metal concentration in sediment, water and fish body and model it. In other words, we want to know if we have time series X amount heavy metal concentration in sediment, Y amount in water and Z amount in fish body; what is the relationship between X, Y and Z and how we can model the time series.

I would try a growth model coupled with a tissue replacement model. Although I can't remember off the top of my head. Look up literature and theses associated with tissue replacement. There has been some great work done with respect to mercury concentrations in fish - e.g., yellow perch at the Experimental Lakes Area, Ontario Canada, and the University of Manitoba. I suggest you check it out, its really good work on how fish uptake and replenish tissue with respect to a heavy metal that has been added experimentally to the environment.

Dear @ John M. Plumb

Thank you so much for your answer.

What is tissue replacement model actually? Is it a mathematical model or a method or protocol for assessing the concentration of heavy metals in fish tissue?

Mohammad, I'm not very familiar with tissue replancement models myself, but they are basically an adaptation to fish growth models, but I am aware of them. Like I said, check out the mercury/contaminants literature - e.g., some work by Madenjian et al. with lake trout etc. Its not my expertise by I am aware of them.

JP

Thanks JP. It helped a lot.

Dear Dr. Gerami,

I think that you must decide if you will try to model this problem using an statistical or mathemathical approach. If you decide by the statistical approach you can use an adaptation of the models mentioned by @Mariel Gullian Klanian called collectively RLQ analysis. Those methods are direct gradient analysis adapted to analyse the relationship of three matrices X, Y and Z as you wish, in this methods they are called R, L and Q matrices.

But if there are theory to model this with a mathemathical mechanistic approach, you can use diferential equations to build a dynamic model and use your data to validate your model.

Best regards,

GCC

Dear @ Gilson Correia Carvalho

Thanks for your answer.

Cheers

Mohammad

Dear Mohammad Hasan Gerami

Both Redundancy analysis (RDA) or Canonical correspondence analysis (CCA) are quite okay based on the comments of the experts. More over still you have sediment data which could be used along with bivalve tissue concentration you can find out ecological risk indices like pollution load index, enrichment factor, Potential Ecological Risk index (PERI). Many refernces in indian waters are available.

Dear Mohammad Hasan Gerami,

I agree with J.M. Plumb: Mathematical relationships between metal body and environmental concentrations must be related with metabolic activity and growth.

There are some simple index that can guide you before being involved in complex models:

· -Coefficient condition in fishes is an example: J.E. Williams, 2000: The coefficient of condition of fish. Chapter 13 in Manual of fisheries survey methods II. Michigan Dept. Natl. Resources. Fisheries Special Report 25, Ann Arbor

· -Relationship between carapace length and weight is also used in bivalves.

Dear Mohan Dhandapani and Iñigo Legórburu

Thanks for your valuable points..