BEACON Researchers at Work: Solar and geomagnetic activity forecasting using evolved Markov networks: Darwin vs. space weather hazards

This week’s BEACON Researchers at Work blog post is by MSU graduate student Masoud Mirmomeni

“Space Weather” hazards have achieved a great international scientific and public importance in recent years due to their catastrophic effects on modern technologies such as satellites and other distributed facilities. Today, space weather is a branch of science that will give new insights into the complex influences and effects of our violent Sun and other cosmic sources on interplanetary space, the Earth’s magnetosphere, ionosphere, and thermosphere that can influence the performance and reliability of space-borne and ground-based technological systems, and beyond that, on their endangering affects to life and health (Bothmer & Daglis, 2007; Moldwin, 2008). The Sun–Earth system is a complicated time varying system, ranging from magnetic field reconnection and accelerated solar wind as hot plasma to impact of charged particles on manmade electronic devices and biological systems.

Known space weather hazards on manmade technologies (Lanzerotti, Thomson, & Maclennan, 1997).

Known space weather hazards on manmade technologies (Lanzerotti, Thomson, & Maclennan, 1997).

The effects of our violent sun, as the main source of space weather disturbances, on our space environment ranging from producing faults in spacecraft operations to disruptions of distributed electrical power systems to the manufacturing of precision equipment have been well documented for more than 35 years (Kane, 2006). Space weather hazards on average cause annual losses of the order of more than $100 million (Maynard, 1990). The figure at right shows the known space weather effects on manmade technologies. 

Considering the catastrophic effects of space weather on human technology, accurate predictions of space weather indexes seems to be an urge for modern society. During the past two decades, scientists have been working on this problem and have introduced different approaches to predict solar and geomagnetic activity indexes (Feynman and Gabriel, 2000; Vassiliadis, 2000).

In this research, we evolve Markov networks (MNs) (shown in figure below), which are probabilistic finite state machines (Edlund et al., 2011; Marstaller, Hintze, and Adami, 2013), to predict one of the famous “space weather” indexes in long-term: Sunspot number (SSN) (shown in graph below and are caused by intense magnetic activity, which inhibits convection by an effect comparable to the eddy current brake, forming areas of reduced surface temperature). These networks do not have the mentioned limiting assumptions on model structure and inputs. These networks choose the most informative inputs and the optimal structure through the course of evolution for a given problem; therefore, evolution helps us to solve input selection and structure system identification problem simultaneously. 

A Markov network with 12 nodes and two Probabilistic Logic Gates (PLGs). Once the nodes at time t pass binary information into the PLGs, the PLGs activate and update the states of the nodes at time t+1.

A Markov network with 12 nodes and two Probabilistic Logic Gates (PLGs). Once the nodes at time t pass binary information into the PLGs, the PLGs activate and update the states of the nodes at time t+1.

Sunspot number time series from 1600, showing the 11-year cycles of solar activity. Before 1750, the record is yearly and sporadic, after that we have monthly and daily data.

Sunspot number time series from 1600, showing the 11-year cycles of solar activity. Before 1750, the record is yearly and sporadic, after that we have monthly and daily data.

By using evolutionary algorithms, we are able to discover Markov networks that are able to predict SSN index accurately close to its theoretic prediction limit imposed by the chaotic nature of the signal. We evolved Markov networks and predict daily SSN one-step ahead for different years and states of solar activity to compare its performance with other well-established methods. We found that on average Markov network had the best performance (shown below). 

One step ahead prediction of daily sunspot number: (a) blue: actual sunspot number, red: one step ahead prediction. (b) one step ahead prediction vs. actual SSN time series.

One step ahead prediction of daily sunspot number: (a) blue: actual sunspot number, red: one step ahead prediction. (b) one step ahead prediction vs. actual SSN time series.

Our ultimate goal in this project is to apply evolutionary algorithms to evolve Markov networks that are able to predict the solar and geomagnetic activity indexes near to their theoretic prediction limit imposed by the chaotic nature of space weather. By having an accurate prediction of these indexes, we can have an alarm system to avoid hazards of forthcoming geomagnetic storms on modern technologies. Moreover, we hope that by analyzing the structure of evolved networks, we are able to find time dependencies between lags of these indexes, which are difficult to capture with existing physical models.

References:

  1. M. Moldwin, An Introduction to Space Weather. Cambridge University Press, 2008.
  2. V. Bothmer and I. Daglis, Space Weather: Physics and Effects. Springer Praxis Books /  Environmental Sciences, Praxis Publishing Limited, Chichester, 2007.
  3. I. A. Daglis, Space storms and space weather hazards, vol. 38. Springer, 2001.
  4. R. Kane, “The idea of space weather–a historical perspective,” Advances in Space Research, vol. 37, no. 6, pp. 1261–1264, 2006
  5. L. J. Lanzerotti, D. J. Thomson, and C. G. Maclennan, “Wireless at high altitudes environmental effects on space-based assets,” Bell Labs technical journal, vol. 2, no. 3, pp. 5–19, 1997.
  6. P.-N. Mayaud, Derivation, meaning, and use of geomagnetic indices, vol. 22. American Geophysical Union, 1980.
  7. J. Feynman and S. B. Gabriel, “On space weather consequences and predictions,” Journal of Geophysical Research: Space Physics, vol. 105, no. A5, pp. 10543–10564, 2000.
  8. D. Vassiliadis, “System identification, modeling, and prediction for space weather environments,” Plasma Science, IEEE Transactions on, vol. 28, pp. 1944–1955, Dec 2000.
  9. J. A. Edlund, N. Chaumont, A. Hintze, C. Koch, G. Tononi, and C. Adami, “Integrated informa- tion increases with fitness in the evolution of animats,” PLoS computational biology, vol. 7, no. 10, p. e1002236, 2011.
  10. L. Marstaller, A. Hintze, and C. Adami, “The evolution of representation in simple cognitive net- works,” Neural computation, vol. 25, no. 8, pp. 2079–2107, 2013. 

For more information about Masoud’s work, you can contact him at mirmomen at msu dot edu.

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Using fitness landscapes to visualize evolution in action

BEACONites Bjørn Østman and Randy Olson created a video to visualize evolution in action using fitness landscapes. Read about it below!

Fitness landscapes were invented by Sewall Wright in 1932. They map fitness, or reproductive success, of individual organisms as a function of genotype or phenotype. Organisms with higher fitness have a higher chance of reproducing, and populations therefore tend to evolve towards higher ground in the fitness landscape. Even though only two traits can be visualized this way, we can actually observe evolution in action. Here we explore three phenomena in evolutionary dynamics that can be difficult to comprehend.

First we show dynamic landscapes with two fluctuating peaks in which the population track the peaks as they appear at difference locations in phenotype space. We also demonstrate negative density-dependent selection, which causes the population to split into distinct subpopulations located on separate peaks, illustrating how speciation can occur in sympatry. Lastly, we show the survival of the flattest where the population prefers a tall narrow peak at low mutation rate, but moves to the lower but wider plateau at high mutation rate. These examples highlight how visualizing evolution on fitness landscapes fosters an intuitive understanding of how populations evolve.

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BEACON Researchers at Work: Holey Fitness Landscapes

This week’s BEACON Researchers at Work post is by MSU postdoc Bjørn Østman, and is also posted on his research website.

What do real fitness landscapes look like? Do they look more like the image on the left, a nearly-neutral holey fitness landscape, or the one on the right, a rugged fitness landscape with many distinct peaks?

Those are only in two dimensions, so the question is also if depicting anything in two dimensions conveys intuitions that are at all correct.

Holey fitness landscapes (Gavrilets and Gravner, 1997, Gavrilets 1997) are approximations of real fitness landscapes where all genotypes are assigned a fitness value of either zero or one. After normalizing fitnesses to be between zero and one, those that lower than one are assigned a fitness of zero1. Because real fitness landscapes are of extremely high dimensionality2, and assuming that genotypes have fitnesses that are randomly distributed3, it follows that there exist a nearly-neutral network on genotypes connected by single mutations that has fitness (effectively) equal to one.

The proposition is then that this holey landscape model is a good approximation of real fitness landscapes. It hypothesizes that the evolutionary dynamics on real fitness landscapes is similar to that on holey landscapes, and that distinct peaks like in the image on the right do not really exist. And this is a testable prediction.

Take a look at these videos. They depict populations evolving in two-dimensional fitness landscapes at a very high mutation rate. (You can also download the videos from my research website.)



In all three cases the population size is 2304 (that’s (3*16)2, in case you’re wondering), mutation rate is 0.5, the grid is 200×200 pixels (i.e. genotypes), and mutations cause organisms to move to a neighboring pixel. Ten percent of the population is killed every computational update (which gives an approximate generation time of 10 updates), and those dead individuals are replaced by offspring from the survivors selected with a probability proportional to fitness (asexual reproduction). Top: neutral landscape where all genotypes have the same fitness. Middle: Half-holey landscape with square holes of 10% lower fitness (size of holes is 14×14 pixels). Bottom: Holey landscape where the genotypes in the holes have fitness zero.

The proposition is that the dynamics of the populations should be the same no matter how deep the holes are. The populations in the half-holey and in the holey landscapes should evolve in comparable ways if the holey landscape is a good approximation.

So what do you think?

What I think is that the evolving population in the top (neutral) and middle (half-holey) landscapes resemble each other, whereas they look nothing like the bottom (holey) landscape. In the half-holey landscape the population takes advantage of the holes all the time, meaning that many individuals who are in them reproduce, even though they have a clear fitness disadvantage. The lesson is that being disadvantaged is just okay, and populations can easily cross quite deep valleys in the fitness landscape. But obviously not when the valleys consist of genotype with zero fitness; evolution in holey landscapes are much impeded compared to rugged landscapes, which is why I think they are not a good approximation.

Caveats: These populations are evolving at a very high mutation rate. When I redid it with a much lower mutation rate (0.05), the neutral and half-holey landscapes stop resembling each other, and the half-holey and holey landscapes look more alike. However, evolution happens so slowly in this case that it is difficult to distinguish the dynamics, so the matter is unresolved so far (however, I have other evidence that lower and more realistic mutation rates do not change this conclusion – some preliminary data in √òstman and Adami (2013)). A second caveat is that the whole holey landscape idea relies on the fitness landscape being multidimensional, and so how can I even allow myself to compare evolution of populations in half-holey and holey landscapes in just two dimensions? That is valid question: the intuitions we get from these animations may lead us to think we know something about evolution in multi-dimensional landscapes, while the original premise of Gavrilets’ idea was that we exactly cannot. Unfortunately, while this is an empirical question – meaning that it could be tested – the holey landscape model posits that the neutral network appears at very high dimensionality. What this dimensionality is is unclear, so even if I were to evolve populations in 2,000 dimensions (which is not computationally feasible – the limit is a little over 30 binary loci), one could always claim that not even that many are enough. Sighs.

1 Genotypes with fitness greater than 1 divided by the population size, N, are effectively the same, because selection cannot “see” differences smaller than 1/N.

2 High dimensionality means a large number of genes (loci) or number of nucleotides.

3 We already know that this is not a very good assumption, as there are indications that fitness landscapes are non-randomly structured with high fitness genotypes clustered with other fit genotypes (Østman et al, 2010), but we don’t know if it is enough to render the holey landscape model useless.

References

Gavrilets S, and Gravner J (1997). Percolation on the fitness hypercube and the evolution of reproductive isolation. Journal of theoretical biology, 184 (1), 51-64 PMID: 9039400

Gavrilets S (1997). Evolution and speciation on holey adaptive landscapes. Trends in ecology & evolution, 12 (8), 307-12 PMID: 21238086

Østman B and Adami C (2013). Predicting evolution and visualizing high-dimensional fitness landscapes, in Recent Advances in the Theory and Application of Fitness Landscapes” (A. Engelbrecht and H. Richter, eds.). Springer Series in Emergence, Complexity, and Computation DOI: 10.1007/978-3-642-41888-4_18

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BEACON Researchers at Work: Measuring natural selection in flowers

This weeks BEACON Researchers at Work post is by MSU graduate student Raffica La Rosa. 

Raffica’s face next to an iris flower.Novel traits differ qualitatively from the characters from which they arise, and are generally thought to be adaptive. I study adaptive novel traits by combining studies of present-day natural selection to identify which traits are likely adaptive, and phylogenetic comparative analyses to understand the past evolution of those traits. My study system is the milkweed genus Asclepias. Milkweeds have amazing flowers that are distinct from all other other flowers on Earth. They have unique floral traits that likely influence how they interact with their insect pollinators, but little is known about how the floral traits might be adaptive.

 Milkweed flowers have a number of unusual floral structures. Typically, an angiosperm flower is made up of four whorls. The sepals are the outermost whorl, are often green, and typically form the bud before the flower opens. The next whorl in is made up of petals, which we usually think of as the colorful, attractive part of the flower. The innermost whorls consist of the reproductive organs—the stamen produce pollen (male) and the carpels contain ovules (female). Milkweeds in the genus Asclepias have sepals and petals, but their male and female whorls have fused together and are almost unrecognizable. 

The unique floral structures of milkweed flowers.In the center of the flower is the gynostegium, which forms a chamber containing two carpels. Rather than having loose pollen that might stick to pollinators, the pollen has been clustered together into five pairs of waxy pollen sacks called pollinia. The pollinia reside in the walls of the gynostegium between nectar-holding hoods that often have horn-like protuberances. The exposed dark gland (corpusculum) that attaches adjacent pollen sacks has a tapered slit, like the back of a hammer, that catches onto the hairs, claws, or mouthparts of pollinators, and allows the pollinia to be slipped out and transferred between flowers.

Milkweed seeds dispersing from pod.For pollination to occur, a single pollinium must be deposited into one of five slits around the outside of the gynostegium that lead to the central chamber. Once there, each pollen grain can grow a pollen tube to fertilize an ovule. The pollinium contains enough pollen grains to fertilize all of the ovules within a carpel, so the milkweed fruit (pod) that develops often contains 40-200 seeds that all share the same father. This can be very convenient for researchers, such as myself, who want to study natural selection through female fitness and male fitness, which is rarely done in plants. Measuring male fitness in plants is often very difficult because loose pollen from many individuals is easily jumbled, resulting in a fruit containing seeds sired by many different fathers; in milkweeds however, I can collect a pod, sprout just one seed, run genetic tests to figure out paternity, and then know the paternity of all of the seeds in that pod. This gives me the ability to find the paternity of up to 100% of the seeds in a population by only sampling about 3% of them!

With this handy feature of milkweed flowers, I can measure selection on floral traits through female fitness and male fitness separately to see if the unusual floral traits of milkweeds function more to help the plants produce more seeds (female fitness), or sire more seeds (male fitness). To do so, I just need just three things to run a selection gradient analysis: trait measurements, female fitness measurements, and male fitness measurements.

Honeybee with pollinia on its legs on A. incarnata (swamp milkweed) flowers.To collect trait measurements, I first determine which floral traits might be influencing the attraction, reward, and efficiency of pollinators, since Asclepias species depend on insect pollinators to transfer their pollen. After observing the flowers and their interactions with pollinators in nature, I choose floral traits that I think might be influencing pollinators, and ultimately affecting fitness. For instance, the size of the hoods and gynostegium most certainly affect the visibility of the flowers, the dimensions of the hood could affect the volume of the nectar reward, and the horns and spacing between hoods could influence how easily pollinators remove and deposit pollinia. To measure the traits, I collect several flowers per plant in the population, digitally photographed them, and later measure them from the photographs.

To measure fitness, I collect all of the pods in the population and record how many each plant produces. Later, I count the number of seeds in each pod. From these data alone, I can quantify female fitness, because I can say how many seeds each plant has produced. Measuring male fitness is a much longer process that starts by sprouting one seed from each of the pods. Once the seedlings are large enough, I collect them and extract their DNA. During the summer, I also collect leaf tissue from every possible parental plant in the population and extract DNA, so that I can match the offspring to their parents. I already know who the mothers are, but I can use genetic paternity tests to identify the fathers.  

Selection gradient image

Regression of relative fitness onto a trait; the slope of the fitted line is the selection gradient. Each point represents an individual within the population.

I measure natural selection on each of the traits by using a multiple regression to regress relative fitness onto all six of the traits at once to account for any correlations between traits. The resulting coefficients are the selection gradients. Positive selection gradients mean that individuals with larger trait values will have higher fitness, and negative selection gradients mean that plants with smaller values of that trait have higher fitness. The larger the absolute value of the selection gradient is, the stronger selection is. Finding selection on a trait is a large first step toward knowing if a trait is adaptive. 

Raffica hand pollinating A. incarnata flowers.For more information about Raffica’s work, you can contact her at larosara at msu dot edu.

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BEACON Researchers at Work: Mock Interviews are Nothing to Mock

This week’s BEACON Researchers at Work blog post is by MSU graduate student Emily Weigel. 

Emily WeigelAs a result of my work as a former Future Academic Scholars in Teaching (FAST) Fellow at Michigan State University, I was invited to participate in the CIRTL (Center for the Integration of Research, Teaching, and Learning) Network Exchange program. This program funds students to conduct campus visits, arranged like mock interviews, at one of the 22 CIRTL institutions across the US. For my exchange, I traveled down to the University of Georgia to give presentations on both my Teaching-As-Research (TAR) project and dissertation research.

Preparing for the mock-interview visit took more work than I’d anticipated. I’d thought that planning the visit during Spring Break was a good idea, however, the weeks leading up to my visit were packed full of pre-break exam grading and a conference—both of which delayed my preparations. I now know that I’m not going to be able to do everything full-speed when I go to interview for jobs, and that if I intend to still accomplish many things prior to a visit, I will need to spread my schedule out and leave about twice as much time as I’d allotted. This is necessary not just in constructing the talks, but in leaving adequate time to practice and revise them based on feedback.

Traveling in right after a conference was tough, but my hosts made me feel more than welcome. I was glad that, although my visit was 3 days long, it began at 11am on the first day with lunch with my TAR host. We had a great conversation about the state of evolution education and what her experiences have been as a new professor, and she was also nice enough to share a few details about the venue where I’d be presenting my TAR research. This helped put me at ease and allowed me to focus on the moment, rather than the stress of the talks.

After a few individual meetings with professors and the opportunity to observe some of the classes taught by biology education faculty, it was finally time to present. My TAR talk was modified from presentations I’d given previously at MSU, with a few additions which described my future directions and changes based on feedback from my lab members and the FAST group.  The talk was centered on a model for how we currently teach the genetic basis of evolution and how we might be able to modify it for greater student gains.

I was pleased to be slotted into the normal meeting time for the Biology Education group, which meant I had plenty of people to give quality feedback. Furthermore, a few guests showed up to the group that week, so I was excited to receive feedback from them directly, in addition to the feedback I later got in follow-up, one-on-one meetings and over dinner with faculty and postdocs.

I was somewhat elated that day two involved class observations and meeting with lab groups. I was glad to relax after day one, yet still be able to observe and talk to many people from which I learned a lot. There are many kinds of reforms and research taking place in biology education at UGA, and I hope to bring back some of these to the courses I teach at MSU as early as this semester.

I also had the pleasure of meeting with the graduate students and postdocs in many of the biology labs. They were very hospitable and open with me about their departments, their research, and living in the area. It was nice to be able to compare notes across labs and institutions on the graduate student and postdoc experience.

Finally, I reached day three with just a few meetings and two talks to round out my visit. It was challenging to treat the entire experience like an interview, mostly because I didn’t want to believe interviewing would be this exhausting (Note: snack bars are your *best* friend to keep up!). Nonetheless, on day three, I met with a few faculty and gave two talks: one on my disciplinary research of how stickleback males change how they court with age, and one to the CIRTL leaders meeting at UGA on why these types of exchanges are valuable. I was glad once these talks were over to be able to chat, get feedback, and finally head home from UGA in the late evening.

The CIRTL exchange was a wonderful experience and the preparation required and lessons learned will be invaluable for future job interviews. It was a great exercise in planning, practicing, presenting (both my work and myself) well, and pursuing an academic career. After the effort I spent to prepare my talks and familiarize myself with the work of the people with whom I was meeting, I have a glimpse at what it’s going to be like on the job market, and I’m sure I’ve learned far more than I can even reflect on now.

Thanks so much to everyone who helped to organize, facilitate, and participate in my network exchange, and know I hope to make you proud when job interviews become a reality!

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