AEBAKER%CSUGREEN@PUCC.PRINCETON.EDU (ann baker biology dept 303 491 5307) (10/21/90)
Gene flow is likely to be asymmetric when there is a large difference in population size between two source populations. The larger population will donate more migrants than the small one usually, though exceptions may exist where very small populations are unstable because they don't have a "critical mass" to make the individuals socially cohesive. The "critical mass" idea is from a very old paper by Gilbert and Singer on Euphydryas butterflies (Am Natur 1960s I think). The asymmetry idea is from simulations I do with Len Nunney on t haplotypes and on my unpublished analyses of the rate of dispersal as a function of the rate of population growth (house mice only). Equilibrium seems to be what theoretical popgeneticists use as a stopping point for their simulations. It removes the influence of the initial starting conditions, but I have a problem with this: in house mice living in barns or homes, the habitat is often changing at the whim of the economics (price of corn, hay, eggs etc): the barn is cleaned out, the chickens or corn are sold etc: often these cleaning out periods occur every year (about 4 generations?) in house mice (Petras and Topping 1979? JMamm for example). Can equilibrium occur that quickly? No. Yet we run simulations for 200 generations or so until the equilibrium is reached. I don't know a way around this problem: the equilibrium is easily defined, the other stuff is not, though the other stuff may be a more realistic reflection of house mouse populations near human habitation. ann eileen miller baker biology department colorado state university fort collins 80523 aebaker@csugreen
manderse@orion.oac.uci.edu (Mark Andersen) (10/22/90)
In article <9010210525.AA06820@genbank.bio.net> AEBAKER%CSUGREEN@PUCC.PRINCETON.EDU (ann baker biology dept 303 491 5307) writes: > >Equilibrium seems to be what theoretical popgeneticists use as a >stopping point for their simulations. It removes the influence of >the initial starting conditions, but I have a problem with this: >in house mice living in barns or homes, the habitat is often changing >at the whim of the economics (price of corn, hay, eggs etc): the >barn is cleaned out, the chickens or corn are sold etc: often these >cleaning out periods occur every year (about 4 generations?) in house >mice (Petras and Topping 1979? JMamm for example). Can equilibrium >occur that quickly? No. Yet we run simulations for 200 generations >or so until the equilibrium is reached. I don't know a way around >this problem: the equilibrium is easily defined, the other stuff is >not, though the other stuff may be a more realistic reflection of >house mouse populations near human habitation. > >ann eileen miller baker >biology department >colorado state university >fort collins 80523 >aebaker@csugreen Ann, you've identified an important problem, namely the importance of transient dynamics (i.e., what happens between the initial conditions and equilibrium) in both demography and population genetics. The problem is recognized, I think, by both theoretical ecologists and pop'n geneticists. Recognized, but underappreciated, or at least not given its due in studies by theorists. This problem affects empiricists as well. Since they see little mention of transient dynamics in (accessible) theoretical works, they fail to recognize what they observe in the field or lab as transient dynamics. I try to look at transient dynamics in my own theoretical work, but the results one gets are seldom clear-cut. It's much simpler to find a fixed point for a system, and determine conditions for its stability; the techniques for doing so are standard, even for very sophisticated mathematical models. For example, just this weekend I was using local linearization techniques to look at the stability of systems of integrodifference equations; these are some hairy mathematical beasts that can easily be tamed with simple analytical methods. I welcome discussion from anyone on how theorists can emphasize the importance of transient dynamics in their work. Poor communication between theorists and empiricists slows progress. Mark Andersen manderse@orion.oac.uci.edu Dept. of Ecology and Evolutionary Biology UC Irvine, Irvine, CA, 92717
wcalvin@milton.u.washington.edu (William Calvin) (10/23/90)
Rapid fluctuations in mammalian populations are likely to occur from the
abrupt climate changes that have been recently documented from ice-core
records of North Atlantic climate. Its minor fluctuations a thousand years
ago were responsible for why Iceland was not named Greenland and vice versa
(by the time that the coast of Greenland was settled by explorers from
Iceland, things had warmed somewhat). Then came the Little Ice Age which
wiped out the non-Inuit settlements on Greenland. Yet neither such changes of
the last millennium, nor the occasional multiyear drought, is what is meant by
*abrupt* climate change. The most recent abrupt episode was the Younger
Dryas: in the midst of the rising CO2 and the general warming trend that
melted the ice sheets of the last glaciation, there was a "cold spike" that
lasted about 800 years, extremely sharp in both onset and release.
It caused European forests to die within a decade or two; they were
replaced with Arctic-adapted plants such as Dryas. It caused Scotland's
glaciers to form once again. Because this happened when northern hemisphere
summer sunshine was near its astronomical maximum, it served to alert
climatologists that there was more to ice advance than just the familiar
Milankovitch cycles. A good time for rapidly melting all that ice in the
northern hemisphere is, just as Milankovitch predicted, when the earth's axial
tilt is maximal and the earth's closest approach to the sun occurs in June --
but there appears to be something else going on that can occasionally override
this general pacemaker of the ice cycles (probably a mode-switching change in
ocean currents associated with a big "sink" near Iceland).
Apropos speed, the Younger Dryas cooling started 11,500 years ago; it
lasted until 10,700 years ago, when it ended even more suddenly than it began.
Thanks to the year-by-year detail in the ice cores of Greenland studied by
Dansgaard et al. (Nature, June '89, is a recent version), we know that
rainfall returned over a 20 year period and, as Europe's land surface warmed
up, the formerly severe winter storms diminished dramatically in that same
two-decade-long period. Cooling episodes are just as rapid (though often with
associated hot-and-cold "whiplash" chattering). Once triggered, mode-
switching climatic "leaps" evidently operate on a far faster time scale than
20,000-to-100,000 year Milankovitch cycles, faster even than the century-long
time scale of the predicted greenhouse warming.
So just within a generation or so (for the larger mammals), there are
enormous stresses on populations -- both crashes and booms. Add to this the
30-year drought cycle in the Sahara (that seems to affect the western side of
the Atlantic as well) and you have a lot of natural selection operating on
boom-and-bust, such as abilities to r-shift a little from K extremes
(increases in twinning, etc.).
This has been of particular interest to me because of how it might have
affected hominid evolution (if you are interested, my book THE ASCENT OF MIND
will be published next month in the US by Bantam) and how it might affect
present-day human populations in Europe. The 500 million people in Europe who
depend on that bonus of winter heat from the North Atlantic Current (perhaps
700 million: the Younger Dryas climate changes reached at least as far east
as the Ukraine) have a considerable interest in preventing such unpleasant
surprises as were experienced by the hunters and gatherers living in Europe
11,500 years ago. The thousand-fold population increase since then causes
Europe to be particularly vulnerable to climatic shocks that arrive with
little warning; the two-decade-long excursion of the proxy climate indicators
should be interpreted to mean that significant changes could occur in several
years. Essentially, a drought would start, get worse -- and then it would be
too late for stockpiling.
William H. Calvin
University of Washington -- Biology NJ-15
Seattle WA 98195
wcalvin@u.washington.edumroussel@alchemy.chem.utoronto.ca (Marc Roussel) (10/24/90)
In article <272321E7.18602@orion.oac.uci.edu> manderse@orion.oac.uci.edu (Mark Andersen) writes: >Ann, you've identified an important problem, namely the importance of transient >dynamics (i.e., what happens between the initial conditions and equilibrium) >in both demography and population genetics. I'm just now starting to become aware of the biological literature due to some new work I'm undertaking. Conversely, I wonder how aware Biologists are of the chemical and physics literatures. Much work has been done by Chemists on transient kinetics. The models are different, but the methods should be extensible. In some ways, the problems of chemical kinetics and population dynamics are the same (and different from those of physics) in that our phase spaces are only physically observable for positive values of the coordinates. Just a thought... Marc R. Roussel mroussel@alchemy.chem.utoronto.ca