Re: Relational "Space" - Ulanowicz works

[Dan Fiscus <***>]

Tim,

Some replies...great questions...

Tim Gwinn wrote:

> Dan,
> One thing I find very counter-intuitive in the paper is the number R, of the
> 'roles' or functions. To me, Figure 2 shows ALOT of functions occuring, not
> just R=1 as stated in the paper. The more interactions something is having
> with other things, the more roles or functions are involved, it seems to me.
> Can you help me out with this? Its a conceptual stumbling-block for me.
Well "roles" as a term, concept is kinda new to me also.
Bob has told me it's OK to think of roles as trophic
levels. In the Zorach + Ulanowicz paper they say that of
Fig. 2 that none of the components/nodes/agents is doing
anything unique - each node receives from all other nodes
and gives to all other nodes. And "One can think of the
nodes as distinct agents playing the same role." In
contrast, an autotroph or plant is distinct from a herbivore
heterotroph - plants can only "eat" or receive as an input
sunlight, CO2, inorganic nutrients, water, etc. and
herbivores can only eat or receive as input plants, O2,
water. And carnivores are distinct again because they
can receive as input herbivores, which neither plants nor
herbivores can do. So these three roles are unique and
they would show up as such in a network diagram based
on qualitative, topological differences in where the input
and output arrows can connect for each role = trophic
or functional type.

> Secondly, in these weighted networks, where flows are assigned specific
> weight numbers which indicate a measure of how large each flow rate is,
> don't the fixed weights represent a network with an entirely fixed and
> stable dynamical situation? This would seem unlikely in a real ecosystem. It
> would seem that in a real ecosystem, each weight (flow rate) would have
> dependencies on other parts of the network that lead to all sorts of
> variatins or oscillations. Or, perhaps ecosystems really are this stable, or
> are these flow rates supposed to be representative of "smoothed" numbers
> over some period of time?
Yes - these are snapshots or annual averages or monthly
averages, etc. In this sense this approach is akin to the
atemporal approach you mention below. And there is
also some smoothing or balancing that Bob and others
who use network analytical software/code do to make
flows balance to approximate a steady state, which is
required for some of the math related to cycling and
indirect effects, etc. So you are right that no two
snapshots would ever look exactly the same - not for
links nor for weights. But having done enough snapshots
I think Bob can fairly convincingly say that no matter
when you grab the numbers and topology, no matter
how long a time you pick for your averaging, you are
going to get very similar topologies and network indices.
Because the things that do not change - that are
atemporal and even aspatial (and also don't change that
much with energy or matter measures either and thus
are great candidate dimensions in that "relational space"
we talk about) - are 1) nodes must remain connected
to other nodes of living functional types (at least two
roles) and 2) nodes remain connected to the
environment. So these essential relations - between life
and life and between life and environment - are not
going to change much, and I think Bob's indices and
quantitative measures are great for showing this and
bringing out more details in what does and does not
change.

> The other thing I see is that I think we can take the networks diagrams and
> their flows, and convert them to Rosennean atemporal relational diagrams,
> with nodes replaced by categories and flow arrows replaced by functorial
> relations. I'm not sure where that could lead, I just wanted to mention the
> possibility.
I think this translation or conversion would be awesome
to develop and do, as I think the functional/relational
diagrams you/Rosen describe could be even more
general than the network analysis methods for
ecosystems. With a bridge to more general diagrams
and analyses, we could test for similar constancy of
relational and topological factors in other networks
besides ecosystems - like social, economic, power grid,
internet, science publications/citations, genetic,
metabolic, etc. etc. networks. And people do do these
via various routes and network methods. I have come
to think that everything can be described in a network
model. Not completely and this is not enough, but it
does seem a good and general and robust model at a
time when the world is ostensibly the most
"interconnected" it may ever have been and may ever
be.

Happy weekend,

Dan