A closer look at our research on population extinction |
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The study of extinction is complicated because experimentally causing extinction in natural populations in order to study it is unethical and is counter productive to conservation goals. An alternative approach to the study of extinction is to test extinction theory using model laboratory systems. Griffen and Drake 2008 reviews these laboratory extinction studies and makes several suggestions for areas of emphasis moving forward. My own work on extinction can be conveniently divided into three categories as shown in the figure below. |
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Population trajectories can be divided into the three regions shown in the figure on the left. In the first region a species establishes a new population that grows from small population size up to carrying capacity. In the second region, the population has reached carrying capacity and fluctuates around this steady state for some time. Finally, in the third region, the population will dip below the carrying capacity for the final time and will decline to extinction. My research has explored factors in each of these three regions that may influence extinction risk. Below I describe my work as it focuses on each of these three regions. |
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Region 1: How does initial population size influence time to extinction? |
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New populations are initiated by migrants that establish in new habitats that were not previously inhabited. This may be the result of natural range expansion or may be the result of human-mediated species introductions into new areas. Virtually all populations models predict that the time to population extinction should be a function of initial population size - the more individuals that make up the initial population, the longer the population is expected to persist. This theoretical prediction has been largely supported from data on both natural and introduced populations in the field. However, experimental investigations of this prediction have not found any correlation between initial population size and time to extinction. In a collaborative study with John Drake and Jeff Shapiro (then an undergraduate) at the University of Georgia, we demonstrated that initial population size produces a two-phase extinction hazard. Extinction risk is strongly influenced very early on by initial populations size. However, this initial effect is quickly overcome by population growth and then other factors become much more important. This initial phase is especially short lived under idealized laboratory conditions, which is likely why experimental support for this hypotheses using laboratory experiments has been lacking. The figure on the right is from Drake et al. 2011 and show the results of two separate experiments where very small initial populations had a higher extinction risk early on. Such effects may be relatively hard to detect under laboratory conditions. |
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Region 2: What is the connection between environmental factors that determine carrying capacity, population growth rate, and extinction risk? |
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One of the greatest threats to populations currently is habitat destruction (reductions in habitat size) and habitat degradation (reductions in habitat quality). Habitat size and quality are expected to influence
extinction risk through different causal mechanistic
pathways. Specifically, small habitat size is expected to
influence extinction risk by reducing carrying capacity,
thereby diminishing the buffer that exists between the long-run average population size and extinction. As a result,
populations in smaller habitats are more susceptible to
extinction from demographic stochasticity, which is strongest for small populations. Poor habitat quality, by contrast, is expected to
influence extinction risk in two ways. First, as with small
habitats, poor quality habitats can only support small
populations that are prone to extinction from demographic
stochasticity. Second, poor habitat quality diminishes a
population’s growth rate, delaying the escape from vulnerability when populations are small. I conducted an experiment in which I examined the influence of habitat size and habitat quality (food amount) on population carrying capacity and growth rate and, in turn, the effects on population extinction. |
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Figure from Griffen and Drake 2008 that shows that carrying capacity and population growth rate both increased with habitat size (open symbols: large habitats; closed symbols: small habitats) and with habitat quality (triangles: low food; squares: medium food; circles: high food). Also shows that time to extinction increased with both carrying capacity and with population growth rate. As stated above, the conventional assumption is that habitat size influences extinction via its influence on carrying capacity only. These results show that habitat size has the capacity to influence extinction simultaneously by altering carrying capacity and population growth rate. |
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Region 2: How do migration rate and environmental quality influence population dynamics and thus extinction risk? |
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Ecological theory suggests that several demographic factors influence metapopulation extinction risk, including synchrony in population size between subpopulations, metapopulation size, and the magnitude of fluctuations in population size. Theoretically, each of these is influenced by the rate of migration between subpopulations. Environmental quality can also influence these factors. We conducted an experiment where we manipulated migration rate within metapopulations of the freshwater zooplankton Daphnia magna to examine how migration influenced each of the demographic variables listed above, and subsequent effects on metapopulation extinction. In addition, our experimental procedures introduced unplanned but controlled differences between metapopulations in light intensity, enabling us to examine the relative influences of environmental and demographic factors. |
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The figure to the right is from Griffen and Drake 2009 and shows the results of this experiment. Migration rate was controlled by the area of the holes that provided passage between the subpopulation chambers. Experimental chambers were stacked like pancakes (see picture at top of this page) and the height in the stack influenced the amount of light received by each metapopulation. We found, consistent with ecological theory, that migration rate was positively correlated with subpopulation synchrony, but that migration rate did not influence overall metapopulation fluctuations or metapopulation size. Further, because population synchrony was not correlated with extinction risk, migration rate had no influence on extinction risk (top figure). Instead, environmental factors had an overriding driving influence on extinction risk that was determined by the height in the stack of chambers (bottom figure). This occurred because environment that was as determined by height in the stack of chambers was correlated with overall subpopulation and metapopulation fluctuations and with overall metapopulation size. Each of these three factors were individually correlated with extinction risk. Thus, while migration may clearly influence metapopulation dynamics, overall extinction risk may be more strongly influenced by subtle environmental factors. |
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Region 2: Early warning signs of the final decline to extinction |
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Populations at steady state fluctuate around carrying capacity. At some point, a population destined for extinction will drop below its carrying capacity for the last time and will begin its final decline. Whether a population is growing or declining depends on its population growth rate. When population growth rates exceed 1.0, the population grows. A population growth rate equal to 1.0 indicates no change in population size. While a population growth rate below 1.0 indicates a shrinking population. The shift from a population growth rate greater than 1.0 to a rate less than 1.0 represents a critical transition where the stable state shifts from carrying capacity to extinction. The ability to predict when these critical transitions are approaching would be very helpful in trying to prevent extinctions from happening. Critical transitions are common in many systems, from geological climate regimes, to financial systems, to the firing of neurons. Work from other systems has demonstrated that early warning signs often occur, signaling that these critical transitions are approaching. These early warnings are characterized by a phenomenon known as "critical slowing down", where a system rebounds more and more slowly to perturbations away from steady state as the critical transition approaches. We conducted an experiment in which we forced populations to approach the critical transition as their population growth rate drops below 1.0. We did this by gradually decreasing their food amount, simulating habitat deterioration that is so common in many natural systems today. We then monitored population size at regular intervals and used these to calculate the population growth rate, thus allowing us to determine when the critical transition occurred. |
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The figure on the left comes from Drake and Griffen 2010 and demonstrates the coefficient of variation in population size throughout the experiment. This is one of the early warning signs that we used to detect the critical slowing down (CSD) that provided an 8-generation warning that the critical transition was approaching. We also used three other simple statistics as early warning indicators (skewness, coefficient of autocorrelation, and coefficient of spatial correlation between connected subpopulations). Each of these provided an early warning of the impending decline. This study demonstrated for the first time that detecting critical transitions in populations is possible. The next step is to take this technique and apply it to natural populations in the field. This will be a difficult task because field conditions are much more variable than our laboratory conditions, and because long, high quality time series of population sizes from field populations are relatively rare. Nevertheless, this study provides evidence that early detection of extinction is possible, potentially providing enough time to act to save populations that are at risk. |
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Region 3: Once a population has started its final decline to extinction, how fast will it get there? |
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Once a species has dipped below carrying capacity for the last time and is headed towards extinction, how long do we have to act before it is gone? This is a crucial question for managers of threatened and endangered populations. Ecological theory suggests several scaling rules that should allow the duration of this final decline to be approximated. Specifically, theory predicts that the duration of the final decline should be much shorter than the time that the population spends at carrying capacity before declining, that the final decline should scale with the log of the carrying capacity, and should also scale inversely with population growth rate. These predictions were made for populations under a relatively limited set of conditions (using a ceiling model). In Griffen and Drake 2009 we extended these predictions to a much broader class of conditions using a theta-logistic stochastic population model. We demonstrated that these predictions hold under a wide range of density dependent conditions. We then tested these predictions using population time series of Daphnia populations obtained from experiments described above. Our results provide partial support for these scaling rules. In addition, theory predicts that the speed of the final decline should be equivalent to the speed of initial expansion when a population is initiated (known as equal passage time). In Drake and Griffen 2009 we also tested this counter-intuitive prediction using data from multiple experiments and found that this prediction was indeed supported by our laboratory Daphnia populations under a variety of experimental conditions. These results provide important tests of extinction theory. Given the difficulty of testing extinction under natural conditions, tests of extinction theory will likely continue to benefit from and be honed by tests conducted using laboratory microcosm experiments. |
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