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  • Andy Davis

New statistical study shows continued problems during overwintering, yet none during breeding

Greetings everyone,

A new study of eastern monarchs was just published last month, which has some bad news, and some not-so-bad news. Today I’m going to fill you in on this paper. Be warned, there is some statistical lingo discussed here (but in a non-technical way).

The first thing you should know is that the authors of the study, Lorenzo Marini and Myron Zalucki, are established scientists and Zalucki especially is a long-standing monarch scientist with a good reputation. I say this now, because I’ll have a few criticisms of this work to share. The first is in the title of the paper itself – it was titled, “Density-dependence in the declining population of the monarch butterfly” (here is a link). I feel like this title is not really representative of what the results of the paper were, and it was made to sound very ominous just to garner some attention.

So the gist of the paper, which was published in a very good journal, Scientific Reports, was about trying to determine if the long-term data on the eastern monarch show evidence of “density-dependence.” This is a statistical term that means the population size goes up and down over the long-term, but that the ups and downs influence each other. For the die-hard science nerds in the audience, here is a link to the Wikipedia article on density-dependence. For monarchs, if there is “density-dependence”, that means that when the population is especially high in one year, in the following year the population will tend to be down, or at least lower. And the opposite happens too (low years tend to be followed by higher years). The density in this case is the population size. The idea is that when the monarch numbers increase, so do the parasites, pathogens and predators that feed on them, causing a population crash, and thus, lower numbers the next year. Conversely, if the population is very low one year, then there are few predators, etc., and so the population tends to grow larger the next year. So the lows and highs each influence each other, and thus you have “density-dependence.” I'm not a true statistician, so I may not have given the best description, but I think I got the gist of it.

The authors wanted to know if the long-term data we have on eastern monarchs show a density-dependence pattern. They examined a number of existing long-term datasets to do this. First, they looked at the data on the overwintering colony size in Mexico. We’ve all seen this graph, and it shows a gradual decline over the last 20 years or so. What the authors wanted to know was do the peaks and troughs of this graph (independent of the decline) show evidence of density-dependence. I’ll spare you the statistical mumbo jumbo and just skip to the end – they found that yes, it does. That means when the overwintering population is up one year, it tends to be followed (but not always) by a lower number the next year. Incidentally, this change from one year to the next is called, in statistical lingo, the “population growth rate.” And this growth rate, can be both positive or negative.

Importantly, the authors found something else with the winter data. They showed that over the 20 year period, the growth rate has been steadily declining (not to be confused with the decline in colony size). This means that the year-to-year changes in the wintering population are getting smaller – smaller rises, and smaller dips. In the paper, they put forth a few possible explanations for why this might be occurring, though I’m not sure if they really know why (or would anyone else). From my read, they suggest this is bad because it means the overwintering population is not able to bounce back after especially low years. They spend the majority of the discussion talking about this one result, and only briefly mention another key result in the study, which I’ll explain next.

In addition to the analyses of the overwintering data, the authors also tried to look for density-dependence in the size of the summer and fall monarch population. Kudos to them for doing this, I say. These days, it seems that everyone wants to just focus on the overwintering data, because this is where the most dramatic stuff is happening. I've always said that to get a true picture of the monarch population, we need to be looking at all stages, not just the overwintering one. Anyway, the authors looked at a number of citizen science datasets on summer counts, including the long-term egg density data from MLMP, the counts of adult monarchs in the summer, from the North American Butterfly Association (NABA), and counts of migratory monarchs from the Cape May, NJ, project, and from the Peninsula Point, MI, project. I believe each of these datasets spans about 20 years. Importantly, none of these datasets shows evidence of long-term declines. I've blogged about these patterns before. However, recall the goal of this study was not to look for population declines in these data, but evidence of density-dependence.

So again, sparring the gritty details of the analyses, I’ll jump to the result – in the end the authors again found evidence for density-dependence in the summer and fall data. This means that here too, the monarch population appears to fluctuate in a semi-predictable manner, with high years tending to be (but not always) followed by lower years, and vice-versa. Now, here’s the important part (and that was downplayed in the paper): the authors found no evidence of a decline in population growth rate in these summer and fall datasets. This means that the summer and fall population is fluctuating now to the same degree as it was 20 years ago. And this is despite the loss of milkweed in the agricultural fields in the Midwest over the last 2 decades. So this is the good news from this paper. Somehow, the summer and fall monarch populations are continuing to cycle up and down at the same rate, which means they are not undergoing major crashes that cannot be overcome.

I mentioned earlier that density-dependence is caused by predators, and parasites building up in the population as it grows. Interestingly, we know from studies of density-dependence in other animals, that one other big factor that causes density dependence in animal populations is crowding, and/or not enough resources to go around for the number of animals during those peak years. Imagine a population of lizards living on an island. The island can only hold so many lizards at one time, because the resources (food, hiding places, etc.) are finite. So when the lizard population increases, the animals start running low on resources, plus the level of aggression between them increases, leading to stress, and then higher susceptibility to infections and parasites. This then leads to a population crash, followed by years of population growth (because the resources are now freed up), and the cycle continues. So if the summer monarch population is currently cycling in a density-dependent manner, it may suggest that there is an upper limit to the summer population size that cannot be surpassed.

I should also mention here that this finding - of density dependence in adult monarchs in the summer - is similar to some work that has found density-dependence in larval monarchs in the summer as well. There have actually been many studies showing this. There was a recent paper by Kelly Nail and colleagues in the 2015 collection of monarch studies in the Annals of the Entomological Society (I blogged about this collection). Here is a link to that collection, if you're interested. Nail and colleagues used MLMP data and found that larval survival tended to go down as the larval density in milkweed patches goes up (density-dependence). Tyler Flockhart had a paper a few years ago showing this experimentally (can't recall the paper though). And I think there have been other papers showing this too. So it seems that monarchs show evidence of density-dependence at all life stages!

Finally, since this paper was published I can tell you that it has sparked a fair amount of email discussion among the monarch scientists, because it utilized data from the summer and fall monarch counts. In a recent publication this year, a number of scientists, including Zalucki, made a long-winded argument for why the counts of adult monarchs from the NABA program are misleading, because the counting locations are not within agricultural fields, where milkweed has declined. Now, Zalucki has just utilized these data in the current paper, and this is why there was some polite, but heated, discussion. In this email discussion, he pointed out that these summer data can be used to measure growth rates, but not population size. He may be right, or may not be. Either way, this discussion is typical of the long-running, larger, debate that is going on about these long-term datasets, and which ones are most appropriate for assessing monarch populations. As I mentioned earlier, I've always thought we should use all of them, not just the Mexico colony size. Others disagree.

OK, I think this about covers the new paper - very interesting stuff! And thanks for reading this blog!


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The science of monarch butterflies

A blog about monarchs, written by a monarch scientist, for people who love monarchs

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