Try to model the concentrations of the chemicals depending on species and time (possibly on other well-known influential factors that may vary over time or between stands). The error model should be chosen depending on the characteristic of the response (the conc. of the chemicals). I would guess that a gamma-model with log-link might be appropriate. If the concentrations are all high and show little variation, a normal model might be ok.

Your research questions can then be answered from the fitted coefficients of the model. The details depend on the particular model (very simple, probably too simple: straight-line models, where the differences between slopes can be inferred).

Such data can be messy, a reasonable model can be difficult to find, and it will need some experience to set a model up correctly and interpret it correctly (when it is not a simple additive straight-line model). You might consider consulting a statistician.

Dear Gregory,

If I did not misunderstand, you have two (or more) simultaneous time-series of compositional character. This means that your series are made of several chemical species at each observation time, probably recorded as parts per million or mg/liter or other concentration units. This kind of data are called compositional data an require special treatment to avoid the undesired effect of spurious correlation (K. Pearson 1896, J. Aitchison, 1986). The values of the time series are defined, explicitly or implicitly, in a simplex (constant sum vectors). There are several transformations to translate concentrations, proportions or vectors of percentages into real variables. From my point of view, log-ratio transformations are the most appropriate (J. Aitchison 1982,1986). A feasible recipe is to transform your time series into real time series is to apply the so-called isometric log-ratio transformation (ilr) (Egozcue et al. 2003, Egozcue and Pawlowsky-Glahn, 2011). Once this is done, the test of equal intercepts (means) or more involved parameters (different slopes) can be carried out using regression techniques and the associated battery of hypothesis testing.

Some references follow (Latex format):

@ARTICLE{Pea1897,

author = {Pearson, Karl},

title = {{{M}athematical contributions to the theory of evolution. {O}n a

form of spurious correlation which may arise when indices are used

in the measurement of organs}},

journal = {Proceedings of the Royal Society of London},

year = {1897},

volume = {LX},

pages = {489--502},

}

@BOOK{Ait1986,

title = {The Statistical Analysis of Compositional Data},

publisher = {Chapman \& Hall Ltd., London (UK). (Reprinted in 2003 with additional

material by The Blackburn Press)},

year = {1986},

author = {Aitchison, John},

series = {{Monographs on {S}tatistics and {A}pplied {P}robability}},

address = {London (UK)},

note = {416 p},

isbn = {0-412-28060-4}

}

@ARTICLE{Ait1982,

author = {Aitchison, John},

title = {{{T}he statistical analysis of compositional data (with discussion)}},

journal = {Journal of the Royal Statistical Society, Series B (Statistical Methodology)},

year = {1982},

volume = {44},

pages = {139--177},

number = {2}

}

@ARTICLE{EPMB2003,

author = {Egozcue, Juan Jos{\'e} and Pawlowsky-Glahn, Vera and Mateu-Figueras,

Gloria and Barcel{\'o}-Vidal, Carles},

title = {{{I}sometric logratio transformations for compositional data analysis}},

journal = {Mathematical Geology},

year = {2003},

volume = {35},

pages = {279--300},

number = {3},

issn = {0882-8121},

}

@BOOK{EP2011,

AUTHOR = {Egozcue, J. J. and Pawlowsky-Glahn, V.},

TITLE = {Basic concepts and procedures},

PUBLISHER = {In: Pawlowsky-Glahn, V. and Buccianti A. (eds.),

\emph{Compositional Data Analysis: Theory and Applications}, Wiley, Chichester UK},

YEAR = {2011},

isbn = {0-470-71135-3},

}

@ARTICLE{Par++2013,

AUTHOR = {Parent, S. E. and Parent, L. E. and Egozcue, J. J. and Rozane, D. E. and Hernandes, A. and Lapointe, L. and H\'ebert-Gentile, V. and

Naess, K. and Marchand, S. and Lafond J. and Mattos, D. Jr.

Barlow, P. and Natale, William},

TITLE = {The plant ionome revisited by the nutrient balance concept},

JOURNAL = {Frontiers in Plant Science},

YEAR = {2013},

volume = {4},

number = {art. 39},

pages = {1--10},

month = {March},

}