http://www.ncbi.nlm.nih.gov/pubmed/12832159#

This paper is about environmental half-life of some radionuclides produced during nuclear explosion. It may help you.

The actual biological effects of dispersed radionuclides can only be estimated through the employment of dispersion models taking into account the whole decay scheme for the analised radionuclides. One specific, and also disputed case, is the tritium example (with a good article about it at https://www.researchgate.net/profile/M_Unterweger/publication/251782904_Comprehensive_Review_and_Critical_Evaluation_of_the_Half-Life_of_Tritium/links/004635295f2943e2a4000000.pdf) but the biologica effects are less considered.

In my opinion, the ecological impact can only be estimated through extensive knowledge of the ecosystem and the employment of radionuclide aware dispersion models. 

I hope this helps you but the question is a generic one. If you have a specific case in mind please let me know and maybe I will be able to give you more detailed info.

Article Comprehensive Review and Critical Evaluation of the Half-Lif...

Dear Guilherme,

for me it is rather interesting question. Biological half-life issues from the models of a body as the open system in steady state, i.e. superposition of the effective decrease of radionuclide concentration due to its decay rate and the physiological release from the system. By analogy, first such open subsystem of environment should be defined in which average concentration (specific activity) of radionuclide can be reliably monitored, and then establish kinetics of this value: it should not follow first-order rate apriori, because of natural perturbancies, you correctly mentioned condition of quasi-equilibrium (or better a steady-state)! Also the methodological problems concerning sampling are on the hand: may I refer to my paper in JRNC 2000 you can find at https://www.researchgate.net/profile/Fedor_Macasek/contributions ?

Conclusion: In  my opinion, the selection of well-monitored radionuclide in a well-defined and not too much heterogeneous subsystem(s) - sea, lake, river, virgin soil, trees, mushrooms ..(?) -is the key to success.  And it is rather long work ahead!

Best regards,

Fedor

https://www.researchgate.net/profile/Fedor_Macasek/contributions

Hello,

IAEA TECDOC 1616 may be helpful to get an overview about present knowledge and gaps.

Yours, Helmut

http://www-pub.iaea.org/MTCD/publications/PDF/te_1616_web.pdf

Dear Guilherme,

I will try to summarise here my point of view.

The radionuclide ecological half-life concept is based on the assumption that, following the introduction into a given ecosystem of a radionuclide, once the introduction has ceased, the concentration of contaminant in each component of the ecosystem after a sufficiently long period of time tends to decrease on time and that the concentration data over time can be fitted to an exponential decay function. This assumption is not definitely true for any ecosystem and any circumstance. Indeed it is possible that some effects like seasonal behaviours give rise to decay curves that show characteristics not rigorously exponential. However, if we consider the concentrations averaged over certain period of time (for instance one year in the case of seasonal effects) we can assume that the time behaviour of the radionuclide concentration can be approximately fitted to an exponential decay curve.

Further we should remember that the decay curve generally can be fitted to a series of exponential decay components depending on the range of time we are analysing (short term, medium term, long term). I should recognise that this subdivision can be somewhat arbitrary or, to be more precise, uncertain. At any rate, I assume that the decomposition into exponential components can bes performed by well known and well founded mathematical techniques.

What is extremely important to note is that the ecological half-time is an empirical concept and that such a concept is useful when  the value of the relevant parameter (the half-life, I mean) depends only on the ecosystem component  and on the considered ecosystem and is independent of the way the radionuclide is introduced in the ecosystem.

In conclusion, when you speak of ecological half-life you should define: the radionuclide, the ecosystem, the compartment, the range of time you considered (I think that this is the reason you spoken of a myriad of methodology; however, the methodology is only one: the decomposition of the curve into exponential components).

Note that the ecological half-life is a very useful parameter to suggest the span of time necessary for the concentration of radionuclide in a given compartment reaches values below certain limit levels (for instance the level for banning the consumption of food).

The compartment model can give a justification for the theoretical foundation of the concept of half-life. Indeed, it is well known that the function representing the time behaviour of  the concentration of a radionuclide in each compartment, after a sufficiently long period of time, once the introduction of a radionuclide into the ecosystem is ceased, becomes  the sum a certain number of exponential decay components. Each of these components is dominant during a certain time range and corresponds to the ecological half-life relevant to the specific period of time. Further, the half-life for each compartment corresponds to a given decay time rate that, being one of the eigenvalues of the system of differential equations controlling the time behaviour of the radionuclide concentration in the considered ecosystem, does not depend on the input characteristics.

You can find a discussion of the above concept in the VAMP report you can find at IAEA website or, probably, somewhere at researchgate site (VAMP= VAlidation of Model Predictions, a project organised by IAEA). In the report you will find examples relevant to the ecological half-life of 137Cs in fish. Such an example can be useful to elucidate the difference existing between the ecological and the biological half-life of radionuclides in fish species. Specifically, the ecological half-life depend on the ecosystem structure (for instance the food-web) whereas the biological half-life depends on the biological metabolism of a radionuclide in the fish organism.

Dear all, 

Thank you very much for all the replies. I'm sure it is a quite interesting subject and your answers will help others to better understand such an important concept.

Dear Luigi,

Thank you very much for the lesson! It made everything much more clear for me! Indeed if we consider the outstanding complexity of an ecosystem there would be very challenging not only to draw clear lines around the concept of ecological half-life, but also to measure/estimate such parameter. But it makes more sense, as you and Dr. Macasek  pointed out, to define the context or sub-system (radionuclide, ecosystem, compartment, time span) for this concept.

Please, let me see if I got it right:

Given a punctual input of an specific activity in a defined ecosystem, ceteris paribus, the loss of such activity over time by a given compartment of the ecosystem (e.g. an earth-worm population, the soil, the canopy,  I don't know, just wondering), not the whole ecosystem, may fit empirically to an exponential decay curve, and the empirical half-life of such fitting will be called the ecological half-life. (?)

I think that your explanation is a good and concise summary of what I think. Of course you should account for the occurrence that you can find more than one exponential component depending on the time horizon.