Posted by
Russell Standish on
URL: http://friam.383.s1.nabble.com/Diversity-and-Stability-in-Food-Webs-tp520801p520804.html
On Wed, Nov 09, 2005 at 06:31:06PM +0100, Jochen Fromm wrote:
>
> Does increasing diversity affect the stability in
> ecosystems and food-webs? If so, is the effect positive
> or negative, i.e. does increasing diversity lead to
> stability or fragility of the system ? Common sense
> says that systems with low diversity (for instance artificial
> monocultures) have low stability and are vulnerable
> to parasites, infections and diseases.
>
> Yet does declining diversity ultimately lead to reductions
> in food-chain length and ecosystem stability ? The relation
> between diversity, food-chain length and ecological processes
> seens to be complex. Ecosystems do not contain only linear
> food-chains, they consist of complex recurrent food-webs.
There are many different notions of stability used in ecosystems, and
one needs to keep this in mind to unravel the debate. The 3 I've
mainly used are:
1) linear stability - this is _the_ mathematical notion of stability
of an equilibrium point. Robert May proved increased diversity lead
to a decrease in stability of the interior equilibrium point for a
randomly assembled L-V ecosystem. Whilst not proven (to my
knowledge), it is widely assume to hold for general ecosystems.
2) persistence - the absence of extinctions in the future of the
ecosystem. This is not the same as stability, as the ecosystem need
not be at equilibrium (the classic 2 species L-V limit cycle is an
example). Some results are known about this - eg the determinant of
the interaction matrix must be positive for persistence to hold in
L-V systems. This in turn implies that positive feedback loops must
be dominated by the negative feed back loops - I've got a comment
about this in my paper "Ecolab, Webworld and self-organisation",
which is available from my website below.
3) resilience - resistance to invasion by another species. Not so much
is known about resilience. Ted Case has done some work on
this. Obviously it is very easy for one species to invade a simple
ecosystem - eg you parasite above, but for complex systems it is
not known whether the general effect is resilience to invasion, or
fragility (being disrupted by invading species) (at least to my knowledge).
> If I remember it correctly, even in simple Lotka-Volterra
> equations with more than 2 dimensions chaotic structures can
> arise (in 2 dimensions with 2 species there is the usual
> predator-prey limit cycle, but in 3 dimensions there are
> also strange attractors possible. I have read it somewhere,
> but I can't remember where).
This is a well known result from dynamical systems. 2D systems can
only have stable point attractors, or limit cycles - no strange
attractor. A Mexican chap whose name escapes me for the present proved
this in the 1980s.
>
> Insights in this ongoing diversity-stability debate
> could be useful, because consumer-producer or
> predator-prey relations can be found in many complex
> systems. The SFI has an interesting site with
> many links about it at
http://discuss.santafe.edu/paleofoodwebs/> for example the following:
>
> (a)
> The diversity-stability debate
> Kevin Shear McCann, Nature 405 (2000) 228-233
>
http://discuss.santafe.edu/files/paleofoodwebs/McCann2000Nature.pdf>
> (b)
> The long and short of food-chain length
> David M. Post, Trends in Ecology & Evolution Vol.17 No.6 June (2002) 269-277
>
http://discuss.santafe.edu/files/paleofoodwebs/Post2002TREE.pdf>
> (c)
> Stability in Real Food Webs: Weak Links in Long Loops
> Anje-Margriet Neutel et al., Science 296 (2002) 1120-1123
>
http://discuss.santafe.edu/files/paleofoodwebs/Neuteletal2002Science.pdf>
> (a) is a nice review, (b) argues that the food-chain length is
> influenced by many factors, ecosystem size and age, degree of
> ecological isolation, natural resource availability, and
> predator-prey interactions, and (c) says that "trophic loops",
> i.e. closed food-chains, add stability to the system, esp.
> the particularly long ones which contain many weak links.
> They found that "loop weights" of the longer loops were low
> in real systems.
>
See above - they add "stability" ie persistence really provided there
are more negative feedback loops than positive one. May's result
(complexity begets instabily) holds because randomly assembled
ecosystems tend to have more positive feedback loops that negative
ones. The determinant result mentioned above would seem to indicate a
50-50 chance of a persistent system (ie a random determinant is as
likely to be +ve ad -ve) but remember this is a necessary result
only, not sufficient. No -ve determinant ecosystem can be persistent,
but not all +ve ones are either.
> -J.
>
>
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