# What do the Data Points Mean?

In Statistics 101 we were told that each data point in a scatter plot should have a precise meaning. Hopefully all ecologists agree with this, and if so I proceed to ask two questions about the ecology literature:

1. What fraction of scatter plots in ecology papers define what the dots on the plot mean? Are they individual measurements, are they means of several measurements? Are they predictions from a mathematical model?
2. Given that we know what the dots are, are we shown confidence limits for the points, or do we assume they are absolutely precise with no possible error?

With these two simple questions in mind I did a short, non-random search of recent ecology journals. Perhaps if a graduate ecology class is reading this blog, they could do a much wider search so that we might even be able to tell some of the editors of our journals how they score on Statistics 101 Quiz # 1. I went through 3 issues of Ecology (2015, issues 4, 5, and 6), 3 issues of the Journal of Animal Ecology (2015, issues 4 to 6), and 3 issues of Ecology Letters (2016, issues 1, 2, and 3). I scored each figure in each paper. The first question above is harder to score, so I divided the answer into three groups: clearly defined in figure legend, not defined in figure legend but clear in the paper itself, and not clearly defined anywhere. I kept the second question above on a simpler scale by asking if there were or were not confidence limits or S.E. on the dots in the scatter diagram. I considered histogram bars as ‘data points’ equivalent to scatter plots and scored these with these same 2 questions. I scored figures with multiple plots in the same figure as just one data source for my survey. I ignored maps, simulation data, and papers with only models. I got these results:

 Data points Confidence Limits or S.E. Journal Number of papers Clearly defined in figure legend Yes No Ecology 80 179 (95%) 98 (50%) 96 (50%) Journal of Animal Ecology 84 195 (98%) 119 (60%) 81 (40%) Ecology Letters 33 64 (94%) 29 (43%) 39 (57%)

The good news is that virtually all the data points in figures that contained empirical data were clearly defined, so the first question was not problematic. The potentially bad news is that around half of the data figures did not contain any measure of statistical precision for the data points.

There could be many reasons why confidence limits could not be applied to data points on graphs in papers. In some cases it would clutter the plot too much. In other cases the data points are completely accurate and have no error although this might be unusual in ecological data. Whatever the reason, some mention of the reason should be given in the text or the figure legend.

There were many limitations to this brief survey. It is clear that some subdisciplines of ecology adhere to Statistics 101 recommendations more carefully than others, but I did not tally these subdisciplines. One could make a thesis out of this sort of tally. Often I could not decipher if the data point was for an experimental unit or for a sampling unit but I have not analyzed for this error here.

So what do we conclude from this non-random survey? The take home message for authors is to make sure that the data points or histograms in their published figures are clearly defined in the figure legend and include if possible some measure of probable error. The message for reviewers and journal editors is to check that data points presented in submitted papers are properly identified and labeled with some measure of precision.

# On Critical Questions in Biodiversity and Conservation Ecology

Biodiversity can be a vague concept with so many measurement variants to make one wonder what it is exactly, and how to incorporate ideas about biodiversity into scientific hypotheses. Even if we take the simplest concept of species richness as the operational measure, many questions arise about the importance of the rare species that make up most of the biodiversity but so little of the biomass. How can we proceed to a better understanding of this nebulous ecological concept that we continually put before the public as needing their attention?

Biodiversity conservation relies on community and ecosystem ecology for guidance on how to advance scientific understanding. A recent paper by Turkington and Harrower (2016) articulates this very clearly by laying out 7 general questions for analyzing community structure for conservation of biodiversity. As such these questions are a general model for community and ecosystem ecology approaches that are needed in this century. Thus it would pay to look at these 7 questions more closely and to read this new paper. Here is the list of 7 questions from the paper:

1. How are natural communities structured?
2. How does biodiversity determine the function of ecosystems?
3. How does the loss of biodiversity alter the stability of ecosystems?
4. How does the loss of biodiversity alter the integrity of ecosystems?
5. Diversity and species composition
6. How does the loss of species determine the ability of ecosystems to respond to disturbances?
7. How does food web complexity and productivity influence the relative strength of trophic interactions and how do changes in trophic structure influence ecosystem function?

Turkington and Harrower (2016) note that each of these 7 questions can be asked in at least 5 different contexts in the biodiversity hotspots of China:

1. How do the observed responses change across the 28 vegetation types in China?
2. How do the observed responses change from the low productivity grasslands of the Qinghai Plateau to higher productivity grasslands in other parts of China?
3. How do the observed responses change along a gradient in the intensity of human use or degradation?
4. How long should an experiment be conducted given that the immediate results are seldom indicative of longer-term outcomes?
5. How does the scale of the experiment influence treatment responses?

There are major problems in all of this as Turkington and Harrower (2016) and Bruelheide et al. (2014) have discussed. The first problem is to determine what the community is or what the bounds of an ecosystem are. This is a trivial issue according to community and ecosystem ecologists, and all one does is draw a circle around the particular area of interest for your study. But two points remain. Populations, communities, and ecosystems are open systems with no clear boundaries. In population ecology we can master this problem by analyses of movements and dispersal of individuals. On a short time scale plants in communities are fixed in position while their associated animals move on species-specific scales. Communities and ecosystems are not a unit but vary continuously in space and time, making their analysis difficult. The species present on 50 m2 are not the same as those on another plot 100 m or 1000 m away even if the vegetation types are labeled the same. So we replicate plots within what we define to be our community. If you are studying plant dynamics, you can experimentally place all plant species selected in defined plots in a pre-arranged configuration for your planting experiments, but you cannot do this with animals except in microcosms. All experiments are place specific, and if you consider climate change on a 100 year time scale, they are also time specific. We can hope that generality is strong and our conclusions will apply in 100 years but we do not know this now.

But we can do manipulative experiments, as these authors strongly recommend, and that brings a whole new set of problems, outlined for example in Bruelheide et al. (2014, Table 1, page 78) for a forestry experiment in southern China. Decisions about how many tree species to manipulate in what size of plots and what planting density to use are all potentially critical to the conclusions we reach. But it is the time frame of hypothesis testing that is the great unknown. All these studies must be long-term but whether this is 10 years or 50 years can only be found out in retrospect. Is it better to have, for example, forestry experiments around the world carried out with identical protocols, or to adopt a laissez faire approach with different designs since we have no idea yet of what design is best for answering these broad questions.

I suspect that this outline of the broad questions given in Turkington and Harrower (2016) is at least a 100 year agenda, and we need to be concerned how we can carry this forward in a world where funding of research questions has a 3 or 5 year time frame. The only possible way forward, until we win the Lottery, is for all researchers to carry out short term experiments on very specific hypotheses within this framework. So every graduate student thesis in experimental community and ecosystem ecology is important to achieving the goals outlined in these papers. Even if this 100 year time frame is optimistic and achievable, we can progress on a shorter time scale by a series of detailed experiments on small parts of the community or ecosystem at hand. I note that some of these broad questions listed above have been around for more than 50 years without being answered. If we redefine our objectives more precisely and do the kinds of experiments that these authors suggest we can move forward, not with the solution of grand ideas as much as with detailed experimental data on very precise questions about our chosen community. In this way we keep the long-range goal posts in view but concentrate on short-term manipulative experiments that are place and time specific.

This will not be easy. Birds are probably the best studied group of animals on Earth, and we now have many species that are changing in abundance dramatically over large spatial scales (e.g. http://www.stateofcanadasbirds.org/ ). I am sobered by asking avian ecologists why a particular species is declining or dramatically increasing. I never get a good answer, typically only a generally plausible idea, a hand waving explanation based on correlations that are not measured or well understood. Species recovery plans are often based on hunches rather than good data, with few of the key experiments of the type requested by Turkington and Harrower (2016). At the moment the world is changing rather faster than our understanding of these ecological interactions that tie species together in communities and ecosystems. We are walking when we need to be running, and even the Red Queen is not keeping up.

Bruelheide, H. et al. 2014. Designing forest biodiversity experiments: general considerations illustrated by a new large experiment in subtropical China. Methods in Ecology and Evolution, 5, 74-89. doi: 10.1111/2041-210X.12126

Turkington, R. & Harrower, W.L. 2016. An experimental approach to addressing ecological questions related to the conservation of plant biodiversity in China. Plant Diversity, 38, 1-10. Available at: http://journal.kib.ac.cn/EN/volumn/current.shtml