How can we be so sure?  Two reasons.  First, there are some basic plant physiological facts that are never mentioned in the extinction-by-global-warming doomsday scenario that mitigate strongly against it ever occurring.  And second, scientists are beginning to uncover more and more evidence which suggests that many plant and animal species have faced this challenge several times before, and that they have done so successfully.

So what are these "plant physiological facts" that are routinely ignored by the climate alarmists?  First and foremost is the fact that when the air's CO2 content rises, so too does the temperature at which plants perform at their optimum.  Cowling and Sage (1998), for example, have shown that plant optimal growth temperature (Topt) can rise by as much as 5°C when the air's CO2 concentration rises from 200 to 380 ppm; while Cowling and Sykes (1999) have described how "increases in CO2 from 350 to 650 ppm are estimated to result in an up to 5°C rise in Topt primarily because of a reduction in rate of photorespiration at high temperatures."

What are the implications of these facts?  They tell us that even if the worst-case scenario of CO2-induced global warming were ever to materialize, there would still be no need for plants to migrate poleward or upward in search of cooler temperatures; for as temperatures increased, so too would the capacities of plants to tolerate those higher temperatures increase concurrently, as the air's rising CO2 content would enable them to adjust their physiology to operate more efficiently when exposed to higher temperatures.

Of course plants could migrate poleward and upward at the poleward and upper bounds of their ranges, as new territories that were too cold for them in the past became more hospitable; but their warm-edge boundaries would not need to change.  Likewise, there would be no need for changes in the warm-edge bounds of the ranges of animals that depend upon specific species of plants for their sustenance.  And, in fact, this is precisely what scientists are discovering where there has been regional warming over the past several decades.

In a study of shifts in the ranges of more than half a hundred European butterfly species over the past century, for example, Parmesan et al. (1999) found that most of them extended the northern boundaries of their ranges further north in response to a regional warming of approximately 0.8°C; but the southern boundaries of their ranges remained unchanged.  Likewise, Thomas and Lennon (1999) studied an equally large number of British bird species from 1970 to 1990, finding that the northern boundaries of species residing in the southern part of Britain shifted northward by an average of 19 km, while the southern boundaries of species residing in the northern part of the country shifted not at all.  Hence, rather than being forced to migrate and being nudged closer to extinction in response to a local increase in temperature during a period of increasing atmospheric CO2 concentration, these many butterfly and bird species actually increased their ranges and became even more protected from the possibility of extinction.

Similar phenomena have been observed in the sea.  In a detailed analysis of benthic foraminifera in the Northeast Pacific, Cannariato et al. (1999) evaluated a sediment core to determine the effects of a number of rapid climatic changes over the course of its 60,000-year record.  They found many periods of rapid temperature change, but no extinctions.  In fact, they determined that the benthic ecosystems they studied "appear to be both resilient and robust in response to rapid and often extreme environmental conditions," concluding that "broad segments of the biosphere are well adapted to rapid climate change."

It has also been determined that shifts in vegetation can occur much faster than has long been believed possible.  In a study of sediment cores obtained from a lake in southern Italy and the Mediterranean Sea that spanned the last 100,000 years, for example, Allen et al. (1999) found that rapid changes in terrestrial vegetation were closely correlated with rapid changes in climate, such that complete shifts in natural ecosystems would sometimes occur over periods of less than two hundred years.  The study's fifteen authors thus concluded that "the biosphere was a full participant in these rapid fluctuations, contrary to widely held views that vegetation is unable to change with such rapidity."

References
Allen, J.R.M., Brandt, U., Brauer, A., Hubberten, H.-W., Huntley, B., Keller, J., Kraml, M., Mackensen, A., Mingram, J., Negendank, J.F.W., Nowaczyk, N.R., Oberhansli, H., Watts, W.A., Wulf, S. and Zolitschka, B.  1999.  Rapid environmental changes in southern Europe during the last glacial period.  Nature 400: 740-743.

Cannariato, K.G., Kennett, J.P. and Behl, R.J.  1999.  Biotic response to late Quaternary rapid climate switches in Santa Barbara Basin: Ecological and evolutionary implications.  Geology 27: 63-66.

Cowling, S.A. and Sage, R.F.  1998.  Interactive effects of low atmospheric CO2 and elevated temperature on growth, photosynthesis, and respiration in Phaseolus vulgaris.  Plant, Cell and Environment 21: 427-435.

Cowling, S.A. and Sykes, M.T.  1999.  Physiological significance of low atmospheric CO2 for plant-climate interactions.  Quaternary Research 52: 237-242.

Parmesan, C., Ryrholm, N., Stefanescu, C., Hill, J.K., Thomas, C.D., Descimon, H., Huntley, B., Kaila, L., Kullberg, J., Tammaru, T., Tennent, W.J., Thomas, J.A. and Warren, M.  1999.  Poleward shifts in geographical ranges of butterfly species associated with regional warming.  Nature 399: 579-583.

Thomas, C.D. and Lennon, J.N.  1999.  Birds extend their ranges northwards.  Nature 399: 213.