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Logistic growth modelling in plants

Discussion of the distribution and abundance of living organisms and how these properties are affected by interactions between the organisms and their environment

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Logistic growth modelling in plants

Postby JAP1st » Mon Nov 10, 2008 12:18 am

Hi everyone, I hope someone can help me with this doubt I have (and if I'm mistaken in something please let me know).

As far as I can tell, growth of measurable morphological traits in individual organisms (in this specific case: height, basal diameter and ' leaf cover' in plants) could be represented by a logistic growth model, in which the early years are more fast-paced than the later years. However, according to the dendrochronology discipline, growth in trees is heavily influenced both by external and internal factors, such as year seasons, climatological and hydrological factors of an specific area, forest fires, plagues, etc.

Thus, taking into account all these possible factors (in a theoretical way), my question is: what could be a more appropriate model for representing morphological growth in plants: a logistic growth model or a bi- or multi-logistic one (considering that it is highly possible to exist several growth pulses throughout an individual's life or even within a year)? And if you believe a multi-logistic model should be used, how could it be represented?

Here is the specific context: in my bachelor thesis research I have obtained measures of height, basal diameter, leaf cover (I am not sure if it is the right term in English) and age for individual pine saplings (max age = 10 years) belonging to natural regeneration and plantation populations. My objective is to compare the growth performance of these two treatments, but since the populations are not coetaneous, there would be a great bias in the comparison. And since I only have one measure in time (retrospective study), I found best to determine the calculated growth rates (based only on the last measure and the age of the individual) in order to overcome this bias.

Now, in order to perform the proper statistical analyses, I am trying to develop a model suitable for these data (considering that the data do not meet the ANOVA assumptions, not even when log-transformed) in which I take into account a proper growth model for these pines, and thus the question about a single- or multi-logistic growth model.

Another question comes to my mind: is it appropriate to determine this 'calculated growth rates' by means of a simple [measure/age] division or should I use some sort of specific formula? (I got this doubt when looking at a formula for an exponential growth model: r = ln (pf / pi) / n , where pf and pi are the final and initial measures [or extreme values] of the variable for every variate - but let us remember that I do not have any initial value). And how would you call this 'calculated growth rate'?

I would really appreciate if someone could help me with this, thanks in advance.
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Postby mith » Mon Nov 10, 2008 10:22 pm

I don't know much about trees but wouldn't it make sense to use a couple of models and then note the standard error, perhaps then do some extrapolation to test it out.
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Postby JAP1st » Mon Nov 10, 2008 10:43 pm

Do you mean as to evaluate each model with standard values and the extrapolate it to my data? 0k, I will try that, though I am not very right-handed with statistics and mathematical models. Thanks Mith.

And now, would a logarithmic transformation be suitable if my data seem to correspond to a logistic distribution? or what kind of transformation should I perform? I have tried looking for help in two statistic forums, but in statistics.com I get no response and in talkstats.com I cannot register.
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Postby mith » Mon Nov 10, 2008 11:14 pm

Well, I mean if you already have the data, you can fit a curve to them and then compare the standard errors. If you happen to acquire more data, you can compare that to extrapolated data. If you prefer, you can also split the data sets first ,say into 10 random groups to lessen the effects of overfitting and generate models based 9 groups and test against the 10th.
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Postby JAP1st » Mon Nov 10, 2008 11:34 pm

Ah, I get it now. Yes, I have already fitted a distribution to my 'height estimated rate' (Hr) variable and it appears to be log-normally distributed, so everything is fine for that variable, ungrouped.

The issue now is that I plan to compare the values of this variable for two treatments (N and P) and Hr(N) follows the same distribution, which I cannot say for Hr(P), as the log(Hr[P]) is significantly different from a normal distribution. I think I will have to perform some discriminate outlier removal...

Thanks for everything Mith.
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