It is going to take a while for this to come together. I'm currently reading Kauffman's "Reinventign the Sacred" which is a frustrating, annoying, and challenging book. I'll leave the book review for another time. The section I'm reading now talks about "non-ergodic" systems -- systems that have so many possible states that they will not repeat themselves in the history of the universe. He also talks about systems that develop novel features that then affect the future state of the system. His example is swim bladders in fish. By his telling, swim bladders originated as a primitive lung for surviving in low oxygen water. They subsequently became adapted to controlling buoyancy, and once that function was established it permitted a new radiation of fishes. He distinguishes the behavior of these systems from systems with dynamical chaos, because in principle the chaotic system is predictable if its initial state is perfectly known. The appearance of novel features makes the system unpredictable because we can't anticipate which novelties will become adopted, and in what new form (how can you know, in advance, that a lung sac will become a swim bladder, or how the emergence of a swim bladder will alter the trajectory of the system?)
Another feature of complex systems Kauffman describes is criticality. In his models, systems can be chaotic or ordered. The area of transition between the two he terms critical. It is this kind of dynamic system that seems to behave much as biololgical and other complex systems behave. I don't entirely trust this result, and especially not the parameters he finds produce critical systems, because his models are oversimplified in an important way -- the nature of interactions between system components are fixed, and George Mpitsos observes that, in simple nervous systems, the nerves are constantly adjusting their interactions. this seems like a more realistic scenario for systems based on organisms (as opposed to chemicals or genes).
I'm trying to apply this to near-shore ocean ecosystems. We have the idea of non-repeatability and criticality. The first is based on the number of possible interactions being much greater than the number of interacting components, and on the time available for interactions to occur. Criticality (in Kauffman's models) is a property dependent on the number of elements each system component interacts with, and the total number of components. Can we predict future states of an ocean ecosystem? The quick answer is no.We may be able to predict future abundances of individual components with some, short-term, skill. But we can't describe how the components interact, much less predict future interactions. John Field has spent a lot of time building trophic models of the near-shore Pacific, and he will tell you how speculative they are. Can we predict the effects of fishing removals on the ecosystem? No. Changes in wind patterns? No. Benthic disturbance by trawls? No. Marine reserves? No. I submit that the ecosystem is inherently unpredictable in this sense.
What we may be able to do is describe the kind of dynamics we expect the system to show. We can do this if we can define the system in relation to Kauffman's criticality. If the system is near the criticality threshold it should have a predictable set of behaviors (number of stable states, time scales of response ...). If it is ordered or chaotic these behaviors will be different. Extrapolating from Kauffman's models is risky, but it is a place to start, and it provides a context for a more applicable set of theoretical models.
That's enough for now!
Saturday, September 27, 2008
Thursday, September 25, 2008
More specific thoughts
I've been trying to focus my thinking into a relevant and do-able project.It is way easy to get washed away in the sea of complexity and feel like you have real insights without having any way to verify or test them. So, I would like to test the proposition that:
Natural populations in dynamic equilibrium with their environment incorporate variability in their [genomes, epigenetic responses, plasticity, life history variation] that reflects (incorporates information about) environmental variability.
This informed or structured variability results in a more rapid response to system perturbations.
Questions of scale (as usual!): Are we talking about variability within an individual, or in a population. If we are at the population level then we have to invoke some sort of group selection.
Are we talking about responses within the lifetime of the fish (plasticity, epi-genetic) or in a few generations (evolutionary). Or both?
How can we use George M's models, or models like them, to explore these ideas? On a practical note, can we come up with $$ to hire a programmer who knows how to do this stuff?
More later...
Natural populations in dynamic equilibrium with their environment incorporate variability in their [genomes, epigenetic responses, plasticity, life history variation] that reflects (incorporates information about) environmental variability.
This informed or structured variability results in a more rapid response to system perturbations.
Questions of scale (as usual!): Are we talking about variability within an individual, or in a population. If we are at the population level then we have to invoke some sort of group selection.
Are we talking about responses within the lifetime of the fish (plasticity, epi-genetic) or in a few generations (evolutionary). Or both?
How can we use George M's models, or models like them, to explore these ideas? On a practical note, can we come up with $$ to hire a programmer who knows how to do this stuff?
More later...
Tuesday, September 23, 2008
The original proposal
Complex systems self-organize. Stuart Kaufman has simulated simple classes of complex systems and formally described how they tend to form low-order organized networks. George Mpistos has applied the same ideas to neural systems and found that, even with minimal increases in complexity system behavior becomes more realistic in simulations, but mathematically intractable. George Sugihara's analysis suggests that natural systems have complex dynamical behaviors that render their behavior nearly impossible to predict. If we are to truly understand natural systems beyond the equilibrium assumptions almost universal in the field (Lotka-Volterra, Ricker, Beverton-Holt, Hardy-Weinberg just for starters) we must consider the nature of complexity and apply its general properties to specific examples.
One of Mpitsos' intriguing findings relates to the behavior of neural networks. He simulated three neural nets; one without noise, one with noise, and one with noise and interactive nodes (is this right, George?). The noisy networks learned much faster than the un-noisy net. More interesting, when perturbed the un-noisy net behaved exactly as it did initially, while the noisy nets responded more quickly than they had the first time. George's explanation is that the state of the noisy nets incorporated information about the error structure of the process. As long as the perturbation did not greatly affect the error structure, the noisy nets started with a great deal of information they did not have to re-discover. Therefore they could more quickly arrive at a good solution.
I propose that this has direct relevance to natural populations. Over time, natural populations evolve and adapt to find a good solution to surviving in a noisy environment. This adaptation is embedded in their genome and in cultural or other epigenetic phenomena. They are analogous to George's neural nets with noise. When their environment experiences natural perturbations these populations can respond rapidly to find a new good solution. However, if the population's natural adaptive state is disturbed by simplifying the genome, reducing or eliminating behavioral variability, or introducing novel, unadapted genotypes then the ability of the population to respond to perturbation is reduced. This translates, in conservation biology lingo, to lower resilience. The explanation is that, by simplifying, information about the error structure of the system is lost. (There may also be other properties of neural networks that we can invoke related to behaviors with different numbers of nodes as an analog to simplified genome).
Another way the well-adapted population can be rendered less resilient is if the error structure of the system is changed. This can occur through rapid habitat alteration, changes in predation patterns, or rapid changes in environmental forcing factors (i.e., climate change).
I would like to explore this idea using salmon as a model system (any other suggestions for more tractable systems?). We could compare relatively undisturbed systems (Bristol Bay sockeye) with severely disturbed systems (Central Valley Chinook). We could look at newly established populations (Glacier Bay coho?) with populations believed to be in equilibrium with their environment (where?). Can we find indexes of variability for genetics, life cycle, habitat, climate? We can do simulations using some of the methodologies George M. has developed.
If these principles are truly common to all complex dynamical systems it could provide important insight for conservation planning of all sorts. It could help explain forest dynamics, population dynamics, ecosystem dynamics, dynamics of exploited populations. It would not predict specific outcomes, but might provide an index of risk or vulnerability, and suggest restoration measures. It might also give insight into how long it may take (generations) for resiliency to become reestablished once lost due to perturbation of either the population or the environment. It could also give insight into what may happen when (as is happening) both the population and the environment are being perturbed simultaneously.
One of Mpitsos' intriguing findings relates to the behavior of neural networks. He simulated three neural nets; one without noise, one with noise, and one with noise and interactive nodes (is this right, George?). The noisy networks learned much faster than the un-noisy net. More interesting, when perturbed the un-noisy net behaved exactly as it did initially, while the noisy nets responded more quickly than they had the first time. George's explanation is that the state of the noisy nets incorporated information about the error structure of the process. As long as the perturbation did not greatly affect the error structure, the noisy nets started with a great deal of information they did not have to re-discover. Therefore they could more quickly arrive at a good solution.
I propose that this has direct relevance to natural populations. Over time, natural populations evolve and adapt to find a good solution to surviving in a noisy environment. This adaptation is embedded in their genome and in cultural or other epigenetic phenomena. They are analogous to George's neural nets with noise. When their environment experiences natural perturbations these populations can respond rapidly to find a new good solution. However, if the population's natural adaptive state is disturbed by simplifying the genome, reducing or eliminating behavioral variability, or introducing novel, unadapted genotypes then the ability of the population to respond to perturbation is reduced. This translates, in conservation biology lingo, to lower resilience. The explanation is that, by simplifying, information about the error structure of the system is lost. (There may also be other properties of neural networks that we can invoke related to behaviors with different numbers of nodes as an analog to simplified genome).
Another way the well-adapted population can be rendered less resilient is if the error structure of the system is changed. This can occur through rapid habitat alteration, changes in predation patterns, or rapid changes in environmental forcing factors (i.e., climate change).
I would like to explore this idea using salmon as a model system (any other suggestions for more tractable systems?). We could compare relatively undisturbed systems (Bristol Bay sockeye) with severely disturbed systems (Central Valley Chinook). We could look at newly established populations (Glacier Bay coho?) with populations believed to be in equilibrium with their environment (where?). Can we find indexes of variability for genetics, life cycle, habitat, climate? We can do simulations using some of the methodologies George M. has developed.
If these principles are truly common to all complex dynamical systems it could provide important insight for conservation planning of all sorts. It could help explain forest dynamics, population dynamics, ecosystem dynamics, dynamics of exploited populations. It would not predict specific outcomes, but might provide an index of risk or vulnerability, and suggest restoration measures. It might also give insight into how long it may take (generations) for resiliency to become reestablished once lost due to perturbation of either the population or the environment. It could also give insight into what may happen when (as is happening) both the population and the environment are being perturbed simultaneously.
Another experiment
As a way to facilitate discussion on the complexity idea I'd like to see if a blog is a good way to share ideas. So here it is, using the good services of Google, once again.
I come to this through my long-time dissatisfaction with deterministic pop dy models and my conviction that variability is as much a part of natural systems as central tendency. By treating systems as averages with deterministic behaviors plus a random error term we are leaving out, perhaps the most important part of their makeup. I believe the error term is not random, and cannot all be explained by adding more variables or substantially reduced by improving measurement precision and accuracy. As long as we concentrate our science on central tendencies we will be missing what may be the central wellspring conferring resiliency – variability conditioned and shaped through generations of interaction with the natural environment. This is not random variability, it is informed variability, informed by the context of a population's history in a particular place and time. It need not have any formal statistical structure, and probably is not stationary, but constantly tracks environmental changes.
One difficulty is in arriving at a formal definition of this variability. For starters, I would like to look at George's neural nets and understand (1) how noise in the incoming signal was incorporated. From there we would try to see (2) how the network responded to that noise. These would be analogs to (1) environmental variability and (2) genetic or other response.
Another difficulty is that it is probably impossible to observe or characterize (2) in natural systems. Perhaps we can say “if (2) has certain properties then we expect (some system behavior or response).
I come to this through my long-time dissatisfaction with deterministic pop dy models and my conviction that variability is as much a part of natural systems as central tendency. By treating systems as averages with deterministic behaviors plus a random error term we are leaving out, perhaps the most important part of their makeup. I believe the error term is not random, and cannot all be explained by adding more variables or substantially reduced by improving measurement precision and accuracy. As long as we concentrate our science on central tendencies we will be missing what may be the central wellspring conferring resiliency – variability conditioned and shaped through generations of interaction with the natural environment. This is not random variability, it is informed variability, informed by the context of a population's history in a particular place and time. It need not have any formal statistical structure, and probably is not stationary, but constantly tracks environmental changes.
One difficulty is in arriving at a formal definition of this variability. For starters, I would like to look at George's neural nets and understand (1) how noise in the incoming signal was incorporated. From there we would try to see (2) how the network responded to that noise. These would be analogs to (1) environmental variability and (2) genetic or other response.
Another difficulty is that it is probably impossible to observe or characterize (2) in natural systems. Perhaps we can say “if (2) has certain properties then we expect (some system behavior or response).
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