Category Archives: Conservation Biology

On the Loss of Large Mammals

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The loss of large mammals and birds in the Pleistocene was highlighted many years ago (Martin and Wright 1967, Grayson 1977, Guthrie 1984 and many other papers). Hypotheses about why these extinctions occurred were flying left and right for many years with no clear consensus (e.g. Choquenot and Bowman 1998). The museums of the world are filled with mastodons, moas, sabre-tooth tigers and many other skeletons of large mammals and birds long extinct. The topic has come up again in a discussion of these extinctions and a prognosis of future losses (Smith et al. 2018). I do not want to question the analysis in Smith et al. (2018) but I want to concentrate on this one quotation that has captured the essence of this paper in the media:

“Because megafauna have a disproportionate influence on ecosystem structure and function, past and present body size downgrading is reshaping Earth’s biosphere.”
(pg. 310).

What is the evidence for this very strong statement? The first thought that comes to mind is from my botanical colleagues who keep reminding me that plants make of 99% of the biomass of the Earth’s ecosystems. So, if this statement is correct, it must mean that large mammals have a very strong effect on plant ecosystem structure and function. And it must also imply that large mammals are virtually immune to predators, so no trophic cascade can occur to prevent plant overgrazing.

I appreciate that it is very difficult to test such a statement since evolution has been going on for a long time before humans arrived, and so there must have been a lot of other factors causing ecosystem changes in those early years. Humans have a disproportionate love for biodiversity that is larger than us. So, we revel in elephants, tigers, bears, and whales, while at the same time we pay little attention to the insects, small mammals, most fish, and plankton. Because of this size bias, we are greatly concerned with the conservation of large animals, as we should be, but much less concerned about what is happening to the small chaps.

What is the evidence that large mammals and birds have a disproportionate influence on ecosystem structure and function? In my experience, I would say there is very little evidence for strong ecosystem effects from the collapse of the megafauna. DeMaster et al. (2006) evaluated a proposed explanation for ecosystem collapse caused by whaling in the North Pacific Ocean and concluded that the evidence was weak for a sequential megafauna collapse caused by commercial whaling. Trites et al. (2007) and Wade et al. (2007) supported this conclusion. Citing paleo-ecological data for Australia, Johnson (2010) and Rule et al. (2012) argued in another evaluation of ecosystem changes that the human-driven extinction of the megafauna in Australia resulted in large changes in plant communities, potentially confounded by climate change and increases in fire frequency about 40K years ago. If we accept these controversies, we are left with trying to decide if the current losses of large mammals are of similar strength to those assigned to the Pleistocene megafauna, as suggested by Smith et al. (2018).

If we define ecosystem function as primary productivity and ecosystem structure as species diversity, I cannot think of a single case in recent studies where this idea has been clearly tested and supported. Perhaps this simply reflects my biased career working in arctic and subarctic ecosystems in which the vast majority of the energy flow in the system rotates through the smaller species rather than the larger ones. Take the Great Plains of North America with and without the bison herds. What aspect of ecosystem function has changed because of their loss? It is impossible to say because of human intervention in the fire cycle and agricultural pre-emption of much of the landscape. It is certainly correct that overgrazing impacts can be severe in human-managed landscapes with overstocking of cattle and sheep, and that is a tragedy brought on by economics, predator elimination programs, and human land use decisions. All the changes we can describe with paleo-ecological methods have potential explanations that are highly confounded.

I think the challenge is this: to demonstrate that the loss of large mammals at the present time creates a large change in ecosystem structure and function with data on energy flow and species diversity. The only place I can see it possible to do this experimentally today would be in arctic Canada where, at least in some areas, caribou come and go in large numbers and with relatively little human impact. I doubt that you could detect any large effect in this hypothetical experiment. It is the little chaps that matter to ecosystem function, not the big chaps that we all love so much. And I would worry if you could do this experiment, the argument would be that it is a special case of extreme environments not relevant to Africa or Australia.

No one should want the large mammals and birds to disappear, but the question of how this might play out in the coming 200 years in relation to ecosystem function requires more analysis. And unlike the current political inactivity over the looming crisis in climate change, we conservation biologists should certainly try to prevent the loss of megafauna.

Choquenot, D., and Bowman, D.M.J.S. 1998. Marsupial megafauna, Aborigines and the overkill hypothesis: application of predator-prey models to the question of Pleistocene extinction in Australia. Global Ecology and Biogeography Letters 7: 167-180.

DeMaster, D.P., Trites, A.W., Clapham, P., Mizroch, S., Wade, P., Small, R.J., and Hoef, J.V. 2006. The sequential megafaunal collapse hypothesis: testing with existing data. Progress in Oceanography 68(2-4): 329-342. doi:10.1016/j.pocean.2006.02.007

Grayson, D.K. 1977. Pleistocene avifaunas and the Overkill Hypothesis. Science 195: 691-693.

Guthrie, R.D. 1984. Mosaics, allelochemics and nutrients: An ecological theory of late Pleistocene megafaunal extinctions. In: Quaternary Extinctions: A Prehistoric Revolution ed by P.S. Martin and R.G. Klein. University of Arizona Press Tucson.

Johnson, C.N. 2010. Ecological consequences of Late Quaternary extinctions of megafauna. Proceeding of the Royal Society of London, Series B 276(1667): 2509-2519. doi: 10.1098/rspb.2008.1921.

Martin, P.S., and Wright, H.E. (eds). 1967. Pleistocene Extinctions; The Search for a Cause. Yale University Press, New Haven, Connecticut. 453 pp.

Rule, S., Brook, B.W., Haberle, S.G., Turney, C.S.M., Kershaw, A.P., and Johnson, C.N. 2012. The aftermath of megafaunal extinction: ecosystem transformation in Pleistocene Australia. Science 335(6075): 1483-1486. doi: 10.1126/science.1214261.

Smith, F.A., Elliott Smith, R.E., Lyons, S.K., and Payne, J.L. 2018. Body size downgrading of mammals over the late Quaternary. Science 360(6386): 310-313. doi: 10.1126/science.aao5987.

Trites, A.W., Deecke, V.B., Gregr, E.J., Ford, J.K.B., and Olesiuk, P.F. 2007. Killer whales, whaling, and sequential megafaunal collapse in the North Pacific: a comparative analysis of the dynamics of marine mammals in Alaska and British Columbia following commercial whaling. Marine Mammal Science 23(4): 751-765. doi: 10.1111/j.1748-7692.2006.00076.x.

Wade, P.R., et al. 2007. Killer whales and marine mammal trends in the North Pacific – a re-examination of evidence for sequential megafaunal collapse and the prey-switching hypothesis. Marine Mammal Science 23(4): 766-802. doi: 10.1111/j.1748-7692.2006.00093.x.

On Detecting Rare Species with Camera Trapping

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If you are a conservation biologist and you wish to save all or as many species as possible, your first problem is detectability. Does the species of concern live in this habitat? If it is present how many are there, and is their abundance changing from year to year? These are fundamental questions in conservation science and there is accordingly a very large literature on how to answer these simple questions for animals in different taxonomic groups. I want to deal briefly here with rare species in which the issue of detectability is most critical.

There is a large array of papers on detection methods in the conservation literature (e.g. Brodie et al. 2018; Crates et al. 2017; Steenweg et al. 2016; Clement et al. 2016, Trolliet et al. 2014). Detection methods vary from live trapping marked individuals, visual sighting of unmarked individuals, camera photos of marked or unmarked individuals, sign data such as tracks or scats in snow, mud or sand, DNA fingerprinting, and many clever natural-history- derived methods to measure detection. These methods are well developed for common animals (Williams et al. 2002).

Rare species are the first problem faced by all these detection methods. Rare species range from those virtually impossible to detect with current technology to those that turn up infrequently in the designated detection device. The conservation challenge of rare species is difficult if they are hard to detect and difficult to study so that we have few natural history parameters to guide conservation actions. For these we can only set aside what we think are suitable areas and conserve them.

The technology of monitoring rare species that can be detected at some reasonable level has greatly improved with the advent of passive-infrared-cameras that can be deployed 24-7 to capture images of whomever walks or swims by. But this technology raises a whole set of methodological issues that must be addressed. The first and most obvious one is the skill of the observer both in setting up the cameras and in looking at the photos to identify correctly the species present. The second and more difficult question is what to count as a detection or ‘hit’. If your question is simply ‘occupancy’ seeing one photograph in the time period of the study provides a + for occupancy. But many ecologists wish to connect the dots from occupancy scores to abundance so that some index of population numbers can arise from these camera data. To make this leap of faith relies heavily on the experimental design of the camera placements, the number of cameras, the make of the cameras (Meek et al. 2014), and the exact placement of cameras on trees or stakes to cover a specific area of habitat. Clearly if cameras are placed too close to one another, the photos from the different cameras are not independent, as most of the models of occupancy assume (Brodie et al. 2018). If bait is used with the cameras the situation becomes even more complex because some species may be attracted while others are repelled by the bait. In general camera detections or ‘hits’ for a particular species are a measure of activity rather than a direct measure of abundance, and so often the assumption is made that activity = abundance, which must be justified. In the extreme case in which a density estimate is needed from camera data, the problem of ‘edge effects’ of the sampled area must be considered just as it does with grid trapping (e.g Thornton and Pekins 2015). New approaches for estimating density from camera data appear almost daily and must be evaluated for accuracy (Nakashima et al. 2018).

We are now in the exponential phase of camera trapping with cameras put up in all sorts of spatial designs for different lengths of time with the hope that someone will have time to look at the photos and some clever statistician can factor out all the potential biases and non-independence of the resulting data. So in a nutshell my simple advice is to use cameras to gather wildlife information but think carefully about what exactly you wish to achieve: occupancy?, an index of abundance?, actual numerical abundance? population density? Or simply beautiful photos of interesting animals? And in the end you may be envious of plant ecologists whose plants do not walk away when you census them.

 

Brodie, J.F., et al. (2018). Models for assessing local-scale co-abundance of animal species while accounting for differential detectability and varied responses to the environment. Biotropica 50, 5-15. doi: 10.1111/btp.12500.

Clement, M. J., J. E. Hines, J. D. Nichols, K. L. Pardieck, and D. J. Ziolkowski. 2016. Estimating indices of range shifts in birds using dynamic models when detection is imperfect. Global Change Biology 22:3273-3285. doi: 10.1111/gcb.13283

Crates, R., L. Rayner, D. Stojanovic, M. Webb, and R. Heinsohn. 2017. Undetected Allee effects in Australia’s threatened birds: implications for conservation. Emu 117:207-221. doi: 10.1080/01584197.2017.1333392

Meek, P.D., et al. (2014). Camera traps can be heard and seen by animals. PLoS ONE 9, e110832. doi: 10.1371/journal.pone.0110832.

Nakashima, Y., Fukasawa, K., and Samejima, H. (2018). Estimating animal density without individual recognition using information derivable exclusively from camera traps. Journal of Applied Ecology 55, 735-744. doi: 10.1111/1365-2664.13059.

Smith, D.H.V. and Weston, K.A. (2017). Capturing the cryptic: a comparison of detection methods for stoats (Mustela erminea) in alpine habitats. Wildlife Research 44, 418-426. doi: 10.1071/WR16159.

Steenweg, R., et al. (2016). Camera-based occupancy monitoring at large scales: Power to detect trends in grizzly bears across the Canadian Rockies. Biological Conservation 201:192-200. doi: 10.1016/j.biocon.2016.06.020

Thornton, D.H. and Pekins, C.E. (2015). Spatially explicit capture-recapture analysis of bobcat (Lynx rufus) density: implications for mesocarnivore monitoring Wildlife Research 42, 394-404. doi: 10.1071/WR15092.

Trolliet, F., et al. (2014). Use of camera traps for wildlife studies. A review. Biotechnology, Agronomy, Society and Environment (BASE) 18, 446-454.

Williams, B.K., Nichols, J.D., and Conroy, M.J. (2002) ‘Analysis and Management of Animal Populations.’ (Academic Press: New York.). 817 pp.

 

Seven Prescriptive Principles for Ecologists

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After three of us put together a paper to list the principles of applied ecology (Hone, Drake, and Krebs 2015), I thought that perhaps we might have an additional set of general behavioural principles for ecologists. We might think of using these seven principles as a broad template for the work we do in science.

  1. Do good science and avoid opinions that are not based on facts and reliable studies. Do not cite bad science even if it is published in Science.
  2. Appreciate and support your colleagues.
  3. Because you disagree with another scientist it is not acceptable to be rude, and it is preferable to decide what experiment can solve the disagreement.
  4. Adulterating your data to remove values that do not fit your hypothesis is not acceptable.
  5. Alternative facts have no place in science. A Professor should not profess nonsense. Nonsense should be the sole prerogative of politicians.
  6. Help your fellow scientists whenever possible, and do not envy those whose papers get published in Science or Nature. Your contribution to science cannot be measured by your h-index.
  7. We have only one Earth. We should give up dreaming about moving to Mars and take care of our home here.

Many of these principles can be grouped under the umbrella of ‘scientific integrity’, and there is an extensive discussion in the literature about integrity (Edwards and Roy 2017, Horbach and Halffman 2017). Edwards and Roy (2017, pg. 53) in a (dis-) service to aspiring young academics quote a method for increasing an individual’s h-index without committing outright fraud. Horbach and Halffman (2017) point out that scientists and policymakers adopt different approaches to research integrity. Scientists discuss ‘integrity’ with a positive view of ‘good scientific practice’ that has an ethical focus, while policy people discuss ‘integrity’ with a negative view of ‘misconduct’ that has a legal focus.

The immediate problem with scientific integrity in the USA involves the current President and his preoccupation with defining ‘alternative facts’ (Goldman et al. 2017). But the problem is also a more general one, as illustrated by the long discussion carried out by conservation biologists who asked whether or not a scientist can also be an advocate for a particular policy (Garrard et al. 2016, Carroll et al. 2017).

The bottom line for ecologists and environmental scientists is important, and a serious discussion of scientific integrity should be part of every graduate seminar class. Scientific journals should become more open to challenges to papers that use faulty data, and maintaining high standards must remain number one on the list for all of us.

Carroll, C., Hartl, B., Goldman, G.T., Rohlf, D.J., and Treves, A. 2017. Defending the scientific integrity of conservation-policy processes. Conservation Biology 31(5): 967-975. doi: 10.1111/cobi.12958.

Edwards, M.A., and Roy, S. 2017. Academic research in the 21st century: Maintaining scientific integrity in a climate of perverse incentives and hypercompetition. Environmental Engineering Science 34(1): 51-61. doi: 10.1089/ees.2016.0223.correx.

Garrard, G.E., Fidler, F., Wintle, B.C., Chee, Y.E., and Bekessy, S.A. 2016. Beyond advocacy: Making space for conservation scientists in public debate. Conservation Letters 9(3): 208-212. doi: 10.1111/conl.12193.

Goldman, G.T., Berman, E., Halpern, M., Johnson, C. & Kothari, Y. (2017) Ensuring scientific integrity in the Age of Trump. Science, 355, 696-698. doi: 10.1126/science.aam5733

Hone, J., A. Drake, and C. J. Krebs. 2015. Prescriptive and empirical principles of applied ecology. Environmental Reviews 23:170-176. doi: 10.1139/er-2014-0076

Horbach, S.P.J.M., and Halffman, W. 2017. Promoting virtue or punishing fraud: Mapping contrasts in the language of ‘scientific integrity’. Science and Engineering Ethics 23(6): 1461-1485. doi: 10.1007/s11948-016-9858-y.

 

Three Approaches to Ecology

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I ask the question here why ecology is not appreciated as a science at a time when it is critical to the survival of the existing world. So the first question we need to answer is if this premise is correct. I offer only one example. A university zoology department has recently produced a discussion paper on its plans for faculty recruitment over the next 15 years. This document does not include the word “ecology” in any of its forward planning. Now it is probably not unusual for biology or zoology departments in major universities to downplay ecology when there is so much excitement in molecular biology, but it is an indicator that ecology is not a good place to put your money and reputation as you await a Nobel Prize. So if we can accept the initial premise that ecology is not appreciated, we might ask why this situation exists, a point raised long ago by O’Connor (2000). Here are a few thoughts on the matter.

There are three broad approaches to the science of ecology – theoretical ecology, empirical ecology, and applied ecology. These three areas of ecology rarely talk to each other, although one might hope that they could in future evolve into a seamless thread of science.

Theoretical ecology deals with the mathematical world that has too often only a tangential concern with ecological problems. It has its own journals and a whole set of elegant discussions that have few connections to the real world. It is most useful for exploring what might be if we make certain mathematical assumptions. It is without question the most prestigious part of the broad science of ecology, partly because it involves elegant mathematics and partly because it does not get involved in all the complexities of real-world ecological systems. It is the physics of ecology. As such it carries on in its own world and tends to be ignored by most of those working in the other two broad areas of ecology.

Empirical ecology has set itself the task of understanding how the natural world works at the level of individuals, populations, communities and ecosystems. In its pure form it does not care about solving practical ecological or environmental problems, but its practitioners assume probably correctly that the information they provide will in fact be useful now or in the future. It seeks generality but rarely finds it because all individuals and species differ in how they play the ecological game of survival. If it has a mantra, it is “the devil is in the details”. The problem is the details of empirical ecology are boring to politicians, business people, and to much of the television generation now operating with a 7 second or 140 character limit on concentration.

Applied ecology is where the action is now, and if you wish to be relevant and topical you should be an applied ecologist, whether a conservation biologist, a forester, or an agricultural scientist. The mantra of applied ecologists is to do no harm to the environment while solving real world problems. Applied ecologists are forced to put the human imprint into empirical ecology, so they are very much concerned with declining populations and extinctions of plants and animals. The main but not the sole impact of humans is on climate change, so much of applied ecology traces back to the impacts of climate change on ecosystems, all added to by the increasing human population with its rising expectations. But applied ecologists are always behind the environmental problems of the day because the issues multiply faster than possible solutions can be evaluated. This ought to make for high employment for applied ecologists but in fact the opposite seems to be happening because governments too often avoid long-term problems beyond their 4-year mandate. If you do not agree, think climate change.

So, the consequence is that we have three independent worlds out there. Applied ecologists are too busy to apply the successful paradigms of empirical ecology to their problems because they are under strict time limits by their line managers who need to suggest immediate action on problems. They must therefore fire off solutions like golf balls in all directions, hoping that some might actually help solve problems. Empirical ecologists may not be helpful for applied ecologists if they are overwhelmed by the details of their particular system of study and are constrained by the ‘publish or perish’ mentality of the granting agencies.

Finally, we lay on top all this a lack of funding in the environmental sciences for investigating and solving both immediate and long-term ecological problems. And I am back to my favourite quote in the ecological literature:

“Humans, including ecologists, have a peculiar fascination with attempting to correct one ecological mistake with another, rather than removing the source of the problem.” (Schindler 1997).

What can we do about this? Three things. Pressure our politicians to increase funding on long-term environmental problems. This will provide the person-power to find and test solutions to our known problems. Vote with your ballot and your feet to improve sustainability. And whether you are young or old strive to do no harm to the Earth. And if all this is too difficult, take some practical advice not to buy a house in Miami Beach, or any house near the beach. Do something for the environment every day.

 

O’Connor, R.J. (2000) Why ecology lags behind biology. The Scientist 14(20):35. (October 16, 2000).

Schindler, D.W. (1997) Liming to restore acidified lakes and streams: a typical approach to restoring damaged ecosystems? Restoration Ecology 5:1-6

 

On Evolution and Ecology and Climate Change

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If ecology can team up with evolution to become a predictive science, we can all profit greatly since it will make us more like physics and the hard sciences. It is highly desirable to have a grand vision of accomplishing this, but there could be a few roadblocks on the way. A recent paper by Bay et al. (2018) illustrates some of the difficulties we face.

The yellow warbler (Setophaga petechia) has a broad breeding range across the United States and Canada, and could therefore be a good species to survey because it inhabits widely different climatic zones. Bay et al. (2018) identified genomic variation associated with climate across the breeding range of this migratory songbird, and concluded that populations requiring the greatest shifts in allele frequencies to keep pace with future climate change have experienced the largest population declines, suggesting that failure to adapt may have already negatively affected population abundance. This study by Bay et al. (2018) sampled 229 yellow warblers from 21 locations across North America, with an average of 10 birds per sample area (range n = 6 to 21). They examined 104,711 single-nucleotide polymorphisms. They correlated genetic structure to 19 climate variables and 3 vegetation indices, a measure of surface moisture, and average elevation. This is an important study claiming to support an important conclusion, and consequently it is also important to break it down into the three major assumptions on which it rests.

First, this study is a space for time analysis, a subject of much discussion already in plant ecology (e.g. Pickett 1989, Blois et al. 2013). It is an untested assumption that you can substitute space for time in analyzing for future evolutionary changes.

Second, the conclusions of the Bay et al. paper rest on an assumption that you have adequate data on the genetics involved in change and on the demography of the species. A clear understanding of the ecology of the species and what limits its distribution and abundance would seem to be prerequisites for understanding the mechanisms of how evolutionary changes might occur.

The third assumption is that, if there is a correlation between the genetic measures and the climate or vegetation indices, one can identify the precise ‘genomic vulnerability’ of the local population. Genomic variation was most closely related to precipitation variables at each site. The geographic area with one of the highest scores in genomic vulnerability was in the desert area of the intermountain west (USA). As far as I can determine from their Figure 1, there was only one sampling site in this whole area of the intermountain west. Finally Bay et al. (2018) compared the genomic vulnerability data to the population changes reported for each site. Population changes for each sampled site were obtained from the North American Breeding Bird Survey data from 1996 to 2012.

The genetic data and its analysis are more impressive, and since I am not a genetics expert I will simply give it a A grade for genetics. It is the ecology that worries me. I doubt that the North American Breeding Bird Survey is a very precise measure of population changes in any particular area. But following the Bay et al. paper, assume that it is a good measure of changing abundance for the yellow warbler. From the Bay et al. paper abstract we see this prediction:

“Populations requiring the greatest shifts in allele frequencies to keep pace with future climate change have experienced the largest population declines, suggesting that failure to adapt may have already negatively affected populations.”

The prediction is illustrated in Figure 1 below from the Bay et al. paper.

Figure 1. From Bay et al. (2018) Figure 2C. (Red dot explained below).

Consider a single case, the Great Basin, area S09 of the Sauer et al. (2017) breeding bird surveys. From the map in Bay et al. (2018) Figure 2 we get the prediction of a very high genomic vulnerability (above 0.06, approximate red dot in Figure 1 above) for the Great Basin, and thus a strongly declining population trend. But if we go to the Sauer et al. (2017) database, we get this result for the Great Basin (Figure 2 here), a completely stable yellow warbler population for the last 45 years.

Figure 2. Data for the Great Basin populations of the Yellow Warbler from the North American Breeding Bird Survey, 1967 to 2015 (area S09). (From Sauer et al. 2017)

One clue to this discrepancy is shown in Figure 1 above where R2 = 0.10, which is to say the predictability of this genomic model is near zero.

So where does this leave us? We have what appears to be an A grade genetic analysis coupled with a D- grade ecological model in which explanations are not based on any mechanism of population dynamics, so that the model presented is useless for any predictions that can be tested in the next 10-20 years. I am far from convinced that this is a useful exercise. It would be a good paper for a graduate seminar discussion. Marvelous genetics, very poor ecology.

And as a footnote I note that mammalian ecologists have already taken a different but more insightful approach to this whole problem of climate-driven adaptation (Boutin and Lane 2014).

Bay, R.A., Harrigan, R.J., Underwood, V.L., Gibbs, H.L., Smith, T.B., and Ruegg, K. 2018. Genomic signals of selection predict climate-driven population declines in a migratory bird. Science 359(6371): 83-86. doi: 10.1126/science.aan4380.

Blois, J.L., Williams, J.W., Fitzpatrick, M.C., Jackson, S.T., and Ferrier, S. 2013. Space can substitute for time in predicting climate-change effects on biodiversity. Proceedings of the National Academy of Sciences 110(23): 9374-9379. doi: 10.1073/pnas.1220228110.

Boutin, S., and Lane, J.E. 2014. Climate change and mammals: evolutionary versus plastic responses. Evolutionary Applications 7(1): 29-41. doi: 10.1111/eva.12121.

Pickett, S.T.A. 1989. Space-for-Time substitution as an alternative to long-term studies. In Long-Term Studies in Ecology: Approaches and Alternatives. Edited by G.E. Likens. Springer New York, New York, NY. pp. 110-135.

Sauer, J.R., Niven, D.K., Hines, J.E., D. J. Ziolkowski, J., Pardieck, K.L., and Fallon, J.E. 2017. The North American Breeding Bird Survey, Results and Analysis 1966 – 2015. USGS Patuxent Wildlife Research Center, Laurel, MD. https://www.mbr-pwrc.usgs.gov/bbs/

On Caribou and Hypothesis Testing

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Mountain caribou populations in western Canada have been declining for the past 10-20 years and concern has mounted to the point where extinction of many populations could be imminent, and the Canadian federal government is asking why this has occurred. This conservation issue has supported a host of field studies to determine what the threatening processes are and what we can do about them. A recent excellent summary of experimental studies in British Columbia (Serrouya et al. 2017) has stimulated me to examine this caribou crisis as an illustration of the art of hypothesis testing in field ecology. We teach all our students to specify hypotheses and alternative hypotheses as the first step to solving problems in population ecology, so here is a good example to start with.

From the abstract of this paper, here is a statement of the problem and the major hypothesis:

“The expansion of moose into southern British Columbia caused the decline and extirpation of woodland caribou due to their shared predators, a process commonly referred to as apparent competition. Using an adaptive management experiment, we tested the hypothesis that reducing moose to historic levels would reduce apparent competition and therefore recover caribou populations. “

So the first observation we might make is that much is left out of this approach to the problem. Populations can decline because of habitat loss, food shortage, excessive hunting, predation, parasitism, disease, severe weather, or inbreeding depression. In this case much background research has narrowed the field to focus on predation as a major limitation, so we can begin our search by focusing on the predation factor (review in Boutin and Merrill 2016). In particular Serrouya et al. (2017) focused their studies on the nexus of moose, wolves, and caribou and the supposition that wolves feed preferentially on moose and only secondarily on caribou, so that if moose numbers are lower, wolf numbers will be lower and incidental kills of caribou will be reduced. So they proposed two very specific hypotheses – that wolves are limited by moose abundance, and that caribou are limited by wolf predation. The experiment proposed and carried out was relatively simple in concept: kill moose by allowing more hunting in certain areas and measure the changes in wolf numbers and caribou numbers.

The experimental area contained 3 small herds of caribou (50 to 150) and the unmanipulated area contained 2 herds (20 and 120 animals) when the study began in 2003. The extended hunting worked well, and moose in the experimental area were reduced from about 1600 animals down to about 500 over the period from 2003 to 2014. Wolf numbers in the experimental area declined by about half over the experimental period because of dispersal out of the area and some starvation within the area. So the two necessary conditions of the experiment were satisfied – moose numbers declined by about two-thirds from additional hunting and wolf numbers declined by about half on the experimental area. But the caribou population on the experimental area showed mixed results with one population showing a slight increase in numbers but the other two showing a slight loss. On the unmanipulated area both caribou populations showed a continuing slow decline. On the positive side the survival rate of adult caribou was higher on the experimental area, suggesting that the treatment hypothesis was correct.

From the viewpoint of caribou conservation, the experiment failed to change the caribou population from continuous slow declines to the rapid increase needed to recover these populations to their former greater abundance. At best it could be argued that this particular experiment slowed the rate of caribou decline. Why might this be? We can make a list of possibilities:

  1. Moose numbers on the experimental area were not reduced enough (to 300 instead of to 500 achieved). Lower moose would have meant much lower wolf numbers.
  2. Small caribou populations are nearly impossible to recover because of chance events that affect small numbers. A few wolves or bears or cougars could be making all the difference to populations numbering 10-20 individuals.
  3. The experimental area and the unmanipulated area were not assigned treatments at random. This would mean to a pure statistician that you cannot make statistical comparisons between these two areas.
  4. The general hypothesis being tested is wrong, and predation by wolves is not the major limiting factor to mountain caribou populations. Many factors are involved in caribou declines and we cannot determine what they are because they change for area to area, year to year.
  5. It is impossible to do these landscape experiments because for large landscapes it is impossible to find 2 or more areas that can be considered replicates.
  6. The experimental manipulation was not carried out long enough. Ten years of manipulation is not long for caribou who have a generation time of 15-25 years.

Let us evaluate these 6 points.

#1 is fair enough, hard to achieve a population of moose this low but possible in a second experiment.

#2 is a worry because it is difficult to deal experimentally with small populations, but we have to take the populations as a given at the time we do a manipulation.

#3 is true if you are a purist but is silly in the real world where treatments can never be assigned at random in landscape experiments.

#4 is a concern and it would be nice to include bears and other predators in the studies but there is a limit to people and money. Almost all previous studies in mountain caribou declines have pointed the finger at wolves so it is only reasonable to start with this idea. The multiple factor idea is hopeless to investigate or indeed even to study without infinite time and resources.

#5 is like #3 and it is an impossible constraint on field studies. It is a common statistical fallacy to assume that replicates must be identical in every conceivable way. If this were true, no one could do any science, lab or field.

#6 is correct but was impossible in this case because the management agencies forced this study to end in 2014 so that they could conduct another different experiment. There is always a problem deciding how long a study is sufficient, and the universal problem is that the scientists or (more likely) the money and the landscape managers run out of energy if the time exceeds about 10 years or more. The result is that one must qualify the conclusions to state that this is what happened in the 10 years available for study.

This study involved a heroic amount of field work over 10 years, and is a landmark in showing what needs to be done and the scale involved. It is a far cry from sitting at a computer designing the perfect field experiment on a theoretical landscape to actually carrying out the field work to get the data summarized in this paper. The next step is to continue to monitor some of these small caribou populations, the wolves and moose to determine how this food chain continues to adjust to changes in prey levels. The next experiment needed is not yet clear, and the eternal problem is to find the high levels of funding needed to study both predators and prey in any ecosystem in the detail needed to understand why prey numbers change. Perhaps a study of all the major predators – wolves, bears, cougars – in this system should be next. We now have the radio telemetry advances that allow satellite locations, activity levels, timing of mortality, proximity sensors when predators are near their prey, and even video and sound recording so that more details of predation events can be recorded. But all this costs money that is not yet here because governments and people have other priorities and value the natural world rather less than we ecologists would prefer. There is not yet a Nobel Prize for ecological field research, and yet here is a study on an iconic Canadian species that would be high up in the running.

What would I add to this paper? My curiosity would be satisfied by the number of person-years and the budget needed to collect and analyze these results. These statistics should be on every scientific paper. And perhaps a discussion of what to do next. In much of ecology these kinds of discussions are done informally over coffee and students who want to know how science works would benefit from listening to how these informal discussions evolve. Ecology is far from simple. Physics and chemistry are simple, genetics is simple, and ecology is really a difficult science.

Boutin, S. and Merrill, E. 2016. A review of population-based management of Southern Mountain caribou in BC. {Unpublished review available at: http://cmiae.org/wp-content/uploads/Mountain-Caribou-review-final.pdf

Serrouya, R., McLellan, B.N., van Oort, H., Mowat, G., and Boutin, S. 2017. Experimental moose reduction lowers wolf density and stops decline of endangered caribou. PeerJ  5: e3736. doi: 10.7717/peerj.3736.

 

On Immigration – An Ecological Perspective

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There is a great deal of discussion in the news about immigration into developed countries like Canada, USA, and Europe. The perspective on this important issue in the media is virtually entirely economic and social, occasionally moral, but in my experience almost never ecological. There are two main aspects of immigration that are particularly ecological – defining sustainable populations and protecting ecosystems from biodiversity loss. These ecological concerns ought to be part of the discussion.

Sustainability is one of the sciences current buzz words. As I write this, in the Web of Science Core Collection I can find 9218 scientific papers published already in 2017 that appear under the topic of ‘sustainability’. No one could read all these, and the general problem with buzz words like ‘sustainability’ is that they tend to be used so loosely that they verge on the meaningless. Sustainability is critical in this century, but as scientists we must specify the details of how this or that public policy really does increase some metric of sustainability.

There have been several attempts to define what a sustainable human population might be for any country or the whole Earth (e.g. Ehrlich 1996, Rees and Wackernagel 2013) and many papers on specific aspects of sustainability (e.g. Hilborn et al. 2015, Delonge et al. 2016). The controversy arises in specifying the metric of sustainability. The result is that there is no agreement particularly among economists and politicians about what to target. For the most part we can all agree that exponential population growth cannot continue indefinitely. But when do we quit? In developed countries the birth rate is about at equilibrium, and population growth is achieved in large part by immigration. Long term goals of achieving a defined sustainable population will always be trumped in the short term by changes in the goal posts – long term thinking seems almost impossible in our current political systems. One elephant in the room is that what we might define now as sustainable agriculture or sustainable fisheries will likely not be sustainable as climates change. Optimists predict that technological advances will greatly relieve the current limiting factors so all will be well as populations increase. It would seem to be conservative to slow our population growth, and thus wait to see if this optimism is justified (Ehrlich and Ehrlich 2013).

Few developed countries seem to have set a sustainable population limit. It is nearly impossible to even suggest doing this, so this ecological topic disappears in the media. One possible way around this is to divert the discussion to protecting ecosystems from biodiversity loss. This approach to the overall problem might be an easier topic to sell to the public and to politicians because it avoids the direct message about population growth. But too often we run into a brick wall of economics even when we try this approach to sustainability because we need jobs for a growing population and the holy grail of continued economic growth is a firm government policy almost everywhere (Cafaro 2014, Martin et al. 2016). At present this biodiversity approach seems to be the best chance of convincing the general public and politicians that action is needed on conservation issues in the broad sense. And by doing this we can hopefully obtain action on the population issue that is blocked so often by political and religious groups.

A more purely scientific issue is the question why the concept of a sustainable population is thought to be off limits for a symposium at a scientific meeting? In recent years attempts to organize symposia on sustainable population concepts at scientific conferences have been denied by the organizers because the topic is not considered a scientific issue. Many ecologists would deny this because without a sustainable population, however that is defined, we may well face social collapse (Ehrlich and Ehrlich 2013).

What can we do as ecologists? I think shying away from these population issues is impossible because we need to have a good grounding in population arithmetic to understand the consequences of short-term policies. It is not the ecologist’s job to determine public policy but it is our job to question much of the pseudo-scientific nonsense that gets repeated in the media every day. At least we should get the arithmetic right.

Cafaro, P. (2014) How Many Is Too Many? The Progressive Argument for Reducing Immigration into the United States. University of Chicago Press, Chicago. ISBN: 9780226190655

DeLonge, M.S., Miles, A. & Carlisle, L. (2016) Investing in the transition to sustainable agriculture. Environmental Science & Policy, 55, 266-273. doi: 10.1016/j.envsci.2015.09.013

Ehrlich, A.H. (1996) Towards a sustainable global population. Building Sustainable Societies (ed. D.C. Pirages), pp. 151-165. M. E. Sharpe, London. ISBN: 1-56324-738-0, 978-1-56324-738-5

Ehrlich, P.R. & Ehrlich, A.H. (2013) Can a collapse of global civilization be avoided? Proceedings of the Royal Society B: Biological Sciences, 280, 20122845. doi: 10.1098/rspb.2012.2845

Hilborn, R., Fulton, E.A., Green, B.S., Hartmann, K. & Tracey, S.R. (2015) When is a fishery sustainable? Canadian Journal of Fisheries and Aquatic Sciences, 72, 1433-1441. doi: 10.1139/cjfas-2015-0062

Hurlbert, S.H. (2013) Critical need for modification of U.S. population policy. Conservation Biology, 27, 887-889. doi: 10.1111/cobi.12091

Martin, J.-L., Maris, V. & Simberloff, D.S. (2016) The need to respect nature and its limits challenges society and conservation science. Proceedings of the National Academy of Sciences, 113, 6105-6112. doi: 10.1073/pnas.1525003113

Rees W.E. &, Wackernagel, M. (2013). The shoe fits, but the footprint is larger than Earth. PLOS Biology 11, e1001701. doi: 10.1371/journal.pbio.1001701

On Defining a Statistical Population

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The more I do “field ecology” the more I wonder about our standard statistical advice to young ecologists to “random sample your statistical population”. Go to the literature and look for papers on “random environmental fluctuations”, or “non-random processes”, or “random mating” and you will be overwhelmed with references and biology’s preoccupation with randomness. Perhaps we should start with the opposite paradigm, that nothing in the biological world is random in space or time, and then the corollary that if your data show a random pattern or random mating or whatever random, it means you have not done enough research and your inferences are weak.

Since virtually all modern statistical inference rests on a foundation of random sampling, every statistician will be outraged by any concerns that random sampling is possible only in situations that are scientifically uninteresting. It is nearly impossible to find an ecological paper about anything in the real world that even mentions what their statistical “population” is, what they are trying to draw inferences about. And there is a very good reason for this – it is quite impossible to define any statistical population except for those of trivial interest. Suppose we wish to measure the heights of the male 12-year-olds that go to school in Minneapolis in 2017. You can certainly do this, and select a random sample, as all statisticians would recommend. And if you continued to do this for 50 years, you would have a lot of data but no understanding of any growth changes in 12-year-old male humans because the children of 2067 in Minneapolis would be different in many ways from those of today. And so, it is like the daily report of the stock market, lots of numbers with no understanding of processes.

Despite all these ‘philosophical’ issues, ecologists carry on and try to get around this by sampling a small area that is considered homogeneous (to the human eye at least) and then arm waving that their conclusions will apply across the world for similar small areas of some ill-defined habitat (Krebs 2010). Climate change may of course disrupt our conclusions, but perhaps this is all we can do.

Alternatively, we can retreat to the minimalist position and argue that we are drawing no general conclusions but only describing the state of this small piece of real estate in 2017. But alas this is not what science is supposed to be about. We are supposed to reach general conclusions and even general laws with some predictive power. Should biologists just give up pretending they are scientists? That would not be good for our image, but on the other hand to say that the laws of ecology have changed because the climate is changing is not comforting to our political masters. Imagine the outcry if the laws of physics changed over time, so that for example in 25years it might be that CO2 is not a greenhouse gas. Impossible.

These considerations should make ecologists and other biologists very humble, but in fact this cannot be because the media would not approve and money for research would never flow into biology. Humility is a lost virtue in many western cultures, and particularly in ecology we leap from bandwagon to bandwagon to avoid the judgement that our research is limited in application to undefined statistical populations.

One solution to the dilemma of the impossibility of random sampling is just to ignore this requirement, and this approach seems to be the most common solution implicit in ecology papers. Rabe et al. (2002) surveyed the methods used by management agencies to survey population of large mammals and found that even when it was possible to use randomized counts on survey areas, most states used non-random sampling which leads to possible bias in estimates even in aerial surveys. They pointed out that ground surveys of big game were even more likely to provide data based on non-random sampling simply because most of the survey area is very difficult to access on foot. The general problem is that inference is limited in all these wildlife surveys and we do not know the ‘population’ to which the numbers derived are applicable.

In an interesting paper that could apply directly to ecology papers, Williamson (2003) analyzed research papers in a nursing journal to ask if random sampling was utilized in contrast to convenience sampling. He found that only 32% of the 89 studies he reviewed used random sampling. I suspect that this kind of result would apply to much of medical research now, and it might be useful to repeat his kind of analysis with a current ecology journal. He did not consider the even more difficult issue of exactly what statistical population is specified in particular medical studies.

I would recommend that you should put a red flag up when you read “random” in an ecology paper and try to determine how exactly the term is used. But carry on with your research because:

Errors using inadequate data are much less than those using no data at all.

—Charles Babbage (1792–1871

Krebs CJ (2010). Case studies and ecological understanding. Chapter 13 in: Billick I, Price MV, eds. The Ecology of Place: Contributions of Place-Based Research to Ecological Understanding. University of Chicago Press, Chicago, pp. 283-302. ISBN: 9780226050430

Rabe, M. J., Rosenstock, S. S. & deVos, J. C. (2002) Review of big-game survey methods used by wildlife agencies of the western United States. Wildlife Society Bulletin, 30, 46-52.

Williamson, G. R. (2003) Misrepresenting random sampling? A systematic review of research papers in the Journal of Advanced Nursing. Journal of Advanced Nursing, 44, 278-288. doi: 10.1046/j.1365-2648.2003.02803.x

 

On Wildlife Management

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There are two global views about wildlife management that are echoed in conservation biology. The first view is that we manage wildlife for the sake of wildlife so that future generations have the ability to see what we see when we go out into the woods and fields. The second view is that we manage wildlife and indeed all of nature for humans to exploit. The second view was elegantly summarized many years ago by White (1967):

“Our science and technology have grown out of Christian attitudes toward man’s relation to nature which are almost universally held not only by Christians and neo-Christians but also by those who fondly regard themselves as post-Christians. Despite Copernicus, all the cosmos rotates around our little globe. Despite Darwin, we are not, in our hearts, part of the natural process. We are superior to nature, contemptuous of it, willing to use it for our slightest whim. The newly elected Governor of California, like myself a churchman but less troubled than I, spoke for the Christian tradition when he said (as is alleged), “when you’ve seen one redwood tree, you’ve seen them all.” (p.1206)

The first view of wildlife is now for ecologists the dominant conservation ethic of our time, the recognition that wildlife and nature in general has intrinsic value (Vucetich et al. 2015). Yet when there are conflicts in environmental management, the second view that humans trump all comes to the fore. Think of examples in your region. When caribou and moose are declining, the shout goes up to shoot the wolves. The golden example of this is perhaps Norway where wolves are nearly all gone and moose are superabundant and fed in winter so that there are plenty for hunters to shoot in the following year. Where domestic and feral cats threaten bird populations, the view typically expressed is that cats are our pets and quite cute, and certainly cannot be regulated or controlled as feral pests.

One of the main defenses of biodiversity conservation during the last 20 years has been the role of ecosystem services. The utilitarian view that ecosystems do things for humans that you can then calculate in dollars has been used to carry conservation forward for those who subscribe to the second global view of nature as something that exists only for our exploitation. Two recent reviews are critical of this approach. Silvertown (2015) argues that the ecosystem services paradigm has been oversold and suggests alternatives. An important critical overview of the conundrum of biodiversity research is presented very clearly in Vellend (2017) and is essential reading for all those interested in environmental management issues and the collision of science and human values expressed in our two global views of biodiversity conservation.

Wildlife managers must operate with the first view in mind to manage wildlife for wildlife but at the same time must act in ways determined by their political masters to adopt the second view of human values over wildlife. Ecologists walk a thin line in this dilemma. A good example is the book by Woinarski et al. (2007) which details the disastrous state of environmental management in northern Australia. There are courageous attempts to resolve these management problems and to bridge the two global views by bringing ecological knowledge into policy development and environmental management (e.g. Morton et al. 2009, Lindenmayer et al. 2015). Many others beginning with Aldo Leopold in North America and many others in Europe have made elegant pleas for the first global view of wildlife conservation. The attempts now to bridge this gap between exploitation and preservation are to bring social sciences into environmental research programs, and these efforts can be increasingly effective. But there is a large contingent of the public that support the second view that humans are the most important species on earth. The increasing collision of rising human populations, resource shortages, and climate change produce a perfect storm of events that place wildlife management and environmental sustainability in a difficult position. Everyone who is able must speak up for the first global view in order to achieve a sustainable society on earth and for wildlife and biodiversity in general to be protected for future generations.

Lindenmayer, D.B.,et al. 2015. Contemplating the future: Acting now on long-term monitoring to answer 2050’s questions. Austral Ecology 40(3): 213-224. doi: 10.1111/aec.12207.

Morton, S.R., et al. 2009. The big ecological questions inhibiting effective environmental management in Australia. Austral Ecology 34(1): 1-9. doi: 10.1111/j.1442-9993.2008.01938.x.

Silvertown, J. 2015. Have Ecosystem Services been oversold? Trends in Ecology & Evolution 30(11): 641-648. doi: 10.1016/j.tree.2015.08.007.

Vellend, M. 2017. The biodiversity conservation paradox. American Scientist 105(2): 94-101.

Vucetich, J.A., Bruskotter, J.T., and Nelson, M.P. 2015. Evaluating whether nature’s intrinsic value is an axiom of or anathema to conservation. Conservation Biology 29(2): 321-332. doi: 10.1111/cobi.12464.

White, L., Jr. 1967. The historical roots of our ecologic crisis. Science 155(3767): 1203-1207.

Woinarski, J., Mackey, B., Nix, H., and Traill, B. 2007. The Nature of Northern Australia: Natural values, ecological processes and future prospects. Australian National University E Press, Canberra. (available at: http://press.anu.edu.au/publications/nature-northern-australia)

On Biodiversity and Ecosystem Function

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I begin with a quote from Seddon et al. (2016):

“By 2012, the consensus view based on 20 years of research was that (i) experimental reduction in species richness, at any trophic level, negatively impacts both the magnitude and stability of ecosystem functioning [12,52], and (ii) the impact of biodiversity loss on ecosystem functioning is comparable in magnitude to other major drivers of global change [13,54].”

The references are to Cardinale et al. (2012), Naeem et al. (2012), Hooper et al. (2012), and Tilman et al. (2012).

The basic conclusion of the literature cited here is that with very extensive biodiversity loss, ecosystem function such as primary productivity will be reduced. I first of all wonder which set of ecologists would doubt this. Secondly, I would like to see these papers analysed for problems of data analysis and interpretation. A good project for a graduate class in experimental design and analysis. Many of the studies I suspect are so artificial in design as to be useless for telling us what will really happen as natural biodiversity is lost. At best perhaps we can view them as political ecology to try to convince politicians and the public to do something about the true drivers of the mess, climate change and overpopulation.

Too many of the graphs I see in published papers on biodiversity and ecosystem function look like this (from Maestre et al. (2012): data from 224 global dryland plots)

There is a trend in these data but zero predictability. And even if you feel that showing trends are good enough in ecology, the trend is very weak.

Many of these analyses utilize meta-analysis. I am a critic of the philosophy of meta-analysis and not alone in wondering how useful many of these are in guiding ecological research (Vetter et al. 2013, Koricheva, and Gurevitch 2014). Perhaps the strongest division in deciding the utility of these meta-analyses is whether one is interested in general trends across ecosystems or predictability which depends largely on understanding the mechanisms behind particular trends.

Another interesting aspect of many of these analyses lies in the preoccupation with stability as a critical ecosystem function maintained by species richness. In contrast to this belief, Jacquet et al. (2016) have argued that in empirical food webs there is no simple relationship between species richness and stability, contrary to conventional theory.

Finally, another quotation from Naeem et al. (2012) which raises a critical issue on which ecologists need to focus more:

“In much of experimental ecological research, nature is seen as the complex, species-rich reference against which treatment effects are measured. In contrast, biodiversity and ecosystem functioning experiments often simply compare replicate ecosystems that differ in biodiversity, without any replicate serving as a reference to nature. Consequently, it has often been difficult to evaluate the external validity of biodiversity and ecosystem functioning research, or how its findings map onto the “real” worlds of conservation and decision making. Put another way, what light can be shed on the stewardship of nature by microbial microcosms that have no analogs in nature, or by experimental grassland studies in which some plots have, by design, no grass species? “ (page 1403)

And for those of you who are animal ecologists, the vast bulk of these studies were done on plants with none of the vertebrate browsers and grazers present. Perhaps some problems here.

Whatever one’s view of these research paradigms, no questions will be answered if we lose too much biodiversity.

Cardinale, B.J., Duffy, J.E., Gonzalez, A., Hooper, D.U., Perrings, C., Venail, P., Narwani, A., Mace, G.M., Tilman, D., Wardle, D.A., Kinzig, A.P., Daily, G.C., Loreau, M., Grace, J.B., Larigauderie, A., Srivastava, D.S. & Naeem, S. (2012) Biodiversity loss and its impact on humanity. Nature, 486, 59-67. doi: 10.1038/nature11148

Hooper, D.U., Adair, E.C., Cardinale, B.J., Byrnes, J.E.K., Hungate, B.A., Matulich, K.L., Gonzalez, A., Duffy, J.E., Gamfeldt, L. & O/’Connor, M.I. (2012) A global synthesis reveals biodiversity loss as a major driver of ecosystem change. Nature, 486, 105-108. doi: 10.1038/nature11118

Jacquet, C., Moritz, C., Morissette, L., Legagneux, P., Massol, F., Archambault, P. & Gravel, D. (2016) No complexity–stability relationship in empirical ecosystems. Nature Communications, 7, 12573. doi: 10.1038/ncomms12573

Koricheva, J. & Gurevitch, J. (2014) Uses and misuses of meta-analysis in plant ecology. Journal of Ecology, 102, 828-844. doi: 10.1111/1365-2745.12224

Maestre, F.T. et al. (2012) Plant species richness and ecosystem multifunctionality in global drylands. Science, 335, 214-218. doi: 10.1126/science.1215442

Naeem, S., Duffy, J.E. & Zavaleta, E. (2012) The functions of biological diversity in an Age of Extinction. Science, 336, 1401.

Seddon, N., Mace, G.M., Naeem, S., Tobias, J.A., Pigot, A.L., Cavanagh, R., Mouillot, D., Vause, J. & Walpole, M. (2016) Biodiversity in the Anthropocene: prospects and policy. Proceedings of the Royal Society B: Biological Sciences, 283, 20162094. doi: 10.1098/rspb.2016.2094

Tilman, D., Reich, P.B. & Isbell, F. (2012) Biodiversity impacts ecosystem productivity as much as resources, disturbance, or herbivory. Proceedings of the National Academy of Sciences 109, 10394-10397. doi: 10.1073/pnas.1208240109

Vetter, D., Rücker, G. & Storch, I. (2013) Meta-analysis: A need for well-defined usage in ecology and conservation biology. Ecosphere, 4, art74. doi: 10.1890/ES13-00062.1