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'''Darwin's arrow of time versus the 2nd law'''
Life on earth is subject to constant energy input from the sun. The 2nd law of thermodynamics, that entropy should increase, is for a closed system. So it seems it is not even really relevant for thinking about life on earth.
'''Definitions of irreversibility'''
One key definition of irreversibility we discussed is that if you reversed time the process would look strange—abiological. Can we make that definition more quantitative? Perhaps we mean simply that it would be going against changes predicted by the selective regime or expected population dynamics? Can we make that definition accommodate degrees of irreversibility, e.g. looking backwards involves changes less likely to happen? This fits in with what Priyanga talked about with adaptation to colder being easier than adaptation to warmer due to the shape of the relationship between the performance and temperature.
''BUT is this definition too broad?'' Any system with an equilibrium point is irreversible in this sense, because if you reversed a time series of it approaching its equilibrium it would not make physical/biological sense?
So do we really need to add something more to that definition, perhaps to include the idea that some environmental variable is being changed in time and we are watching the response to it, and asking if the system would go back if we changed the environment back? In that case our definition of irreversibility is the presence of hysteresis?
Is another definition of irreversibility that the system changes in a way that impacts its future potential changes or response to change in the environment? Or maybe this is just something often associated with irreversibility, as it is not the same as asking about a reversal of time, but instead whether there is path dependency in the system? Is this question of path dependency related to Gould’s question about whether replaying the tape of life would lead to the same outcome?
An example of this idea of the change in the system impacting potential response to future change is the case of competitive cluster formation (see below). If one assembles the community under one environmental filter, and then the environmental filter changes, community biomass may go down and never achieve what it was before or could have been under new environmental regime if assembled that way in the first place. The idea is that the change in environmental filter may not have be strong enough to overcome competitive footholds species have in the community.
'''Drift and selection, and is drift reversible?'''
Two key processes in ecology and evolution are drift and selection (among species or among alleles). Is drift in a sense a force creating more disorder? If so, we would think it would increase entropy in a sense and lead to irreversible changes? (Note there has been one paper by Sella and Hirsh in 2005 in PNAS trying to think about drift as something increasing entropy and more broadly a "free fitness" function like a "free energy" function, summarizing the role of selection and drift in the state of the population.) But we discussed it yesterday as reversible. Can we be more quantitative about why we think about it as reversible?
''Further, is drift really reversible?'' Drift can prevent a system from reaching another fitness peak, by causing loss of advantageous, neutral, or disadvantageous alleles when they are rare. (Recall the stochastic tunnelling examples Stephen Proulx talked about for how evolution may overcome this however.) So it can change the future possibilities for the system. It can also be involved in the somewhat irreversible process of competitive cluster formation (see below). A particular species may gain high abundance by chance (drift) and then have a stronger influence on the the competitive landscape for other species and become abundant in its cluster. Actually if there are no edges and no environmental filter, drift one of the two key ingredients in cluster formation (the other being initial conditions).
'''Key idea related to irreversibility and questions I raised in my talk'''
In my talk I highlighted that the formation of species clusters on trait axes under competition has some degree of irreversibility, in the sense that under strong competitive sorting, once a species dominates a particular cluster it is unlikely to loose its foothold. It would take a strong perturbation in species' abundances, or a change in which species are favored by the environment, to change which species would dominate in each cluster. Further, once certain species have gained a foothold in each cluster, this influence any subsequent assembly or evolution (selection, speciation, extinction) in the community.
The questions I posed about this particular phenomenon of irreversibility are:
1) How is the rate of competitive sorting, i.e. the strength of cluster formation, and hence degree of irreversibility, shaped by the mechanisms of competition? Do clusters emerge for all realistic competition mechanisms?
2) How will cluster formation depend on spatial scale, and how will this be influenced by the strength and scale of dispersal, relative to the scale of any heterogeneity involved in niche differentiation mechanisms?
3) Is the irreversibility of community pattern formation a particular concern for communities that may become isolated? These communities will experience extinction debt, and afterwards their resilience to environmental change may be low (the species that may be favored by the new environment may be gone).