利用数学建模预测的人口更替策略的有效性

You can't do Experiments on the ecological scale because that isn't an experiment. It's the actual release. What if something goes wrong?

Remember these mosquitoes transmit a number of very serious diseases. What if they become super bugs and they start transmitting even more effectively? Maybe they'll start transmitting other diseases that they had not been able to transmit in the past.

We really have to formulate our policies based on computer models, just like having computer models for all contingencies in landing someone on the moon. So too, we have to have simulations of all contingencies for what happens after we release gene ape modified mosquitoes. My name's Charles Taylor.

I'm a the univers of California Los Angeles in the Department of Ecology and Evolutionary Biology with my students and postdocs. I've been working on mathematical aspects of the attempt to use genetically modified mosquitoes to control malaria. We've taken several different approaches to doing this for different parts of the the problem.

And today I'll show you a little bit of our work that we've done the last few years and I'll introduce you to one of my students, John Marshall. The modeling we've been doing is that several different sorts. First of all, there are just basic features of the biology that need to be understood that require modeling.

For example, what's the population size, the survival, and the movement, and you'll see some examples of those. Then the next thing is to understand if we're going to release a transposable element, we know that there are at least 2050 variables that are likely to be important. The importance is sometimes hard to judge just by verbal arguments, and we'd like to have good mathematical models to be really precise and to make statements like, if this is going to work, then the fitness of the trans of the transposed mosquito has to be thus and so, or the movement of the mosquito has to be thus.

And so, and you'll see that we've been doing some analytical work in that regard. The next sort of problem is to not just derive expectations, but rather to evaluate what happens after the initial release. If we do a test then and get some results, then what does that mean?

Does it mean we've been successful or we've been a failure? And so more complicated simulations are required for that. Parenthetically, that's what we were first brought into the model, this group four.

And then we have the more serious problems, especially serious problems of, of ethical considerations. What might go wrong? How serious are things that might go wrong?

If we have a a good stop rule, then we have to be very clear about it and know what we're gonna do to clean up the mess if Something goes wrong. Let's say we make a super mosquito. The first sort of studies That we did were to just identify the core parameters and their values in the, for the populations.

What's the population sizes? How much gene flow is there? What's the daily survival of the mosquitoes in this area?

We used a very well established traditional method called Mark Release recapture. To do those, the way that mark release recapture works is we first capture a large number of mosquitoes, let's say a thousand. We go out to the villages, aspirate them from the walls, put them into a vial, and, and then we put a little bit of of dust on that fluoresces under uv, much as is used in making the paints for in stores or for psychedelic paraphernalia.

And then having marked them, we release them again and then we capture from the walls on subsequent nights and based on how many are recaptured and where we can make inferences using mathematical models about how large the population size is, how far they move, and how well they, they they survive. And this first video, you'll see the main results of our first experiments summarized. Well, there are several ways that modeling can assist the, the program for genetically modified mosquitoes.

One of these is simply to help understand the basic biology of the mosquitoes. And this is some of our very first work in the area, trying to estimate what, how much dispersal is going on, what's the population size, what's the survival of the mosquitoes? And looking at this, which is a summary of our research results, there are some basic feature parts of the biology that might be of interest to the viewers.

First of all, we see a village, the village of bottom body where we've done so much of our work in Mali. It consists of approximately 70 different compounds that may have several sleeping homes in, and these are shown here. They're basically made of mud and the mosquitoes can move in and out at will.

The daily biology is reflected by the, the colors out here. This is night. Suppose the twilight, the yellow is the daytime and the pattern of the mosquitoes is different for each.

For example, during the the daytime, they'll remain where they are when it becomes twilight, then they'll start to move around and they'll go out and search of places to feed or to lay their eggs. And then when it's becomes evening, then they'll in, in the middle of the night, they'll come back and you see that the areas around each home is shown in a different color that that shows the gradient of CO2 and body odor that the mosquitoes use to hone in on. One of the most important results that we had during the first year and that this was used for was to understand that within a pop within a village, no matter where we release it a day or two or three, the mosquitoes are distributed homogeneously over several kilometers.

So from the standpoint of subsequent modeling, we could say that a a a A village is, A village is a village. There's no distinction within the village. And it issue then is how much movement occurs between villages and between the different subspecies of the mosquito.

And the next illustration will show you as a our current understanding about the different chromosomal forms and about the movement amongst villages. Okay, Video we've just seen, we see that there's a lots of movement within a village within one or two days. It's basically homogeneous, but there's a lot more complication in real life than shown here.

First of all, there are not just one species of mosquito that transmit malaria. In fact, there are several in this village and Bonham and Mali, there's only a single species, anno Gambia. But that single species has several different subspecies, so to speak, called chromosomal forms that are present in the same location.

And if we in insert the gene into the population, a transposable element into one form, it's gonna have to move through all of them. And what may be very complicated manners, the only way to really understand that is to use computer simulations to understand it further. The population size varies through the year.

And the movement from village to village, which we haven't thought of before, has to be incorporated. So here, let me show you a frame from one of the movies that my students made that illustrate the problem. Here is one chromosomal form.

Here's another, here's another. These are called Mopti Savannah iCal forms. The size of the yellow disc refers to the size of the population.

The, the intensity of the black line shows how much gene flow there is occurring place to place in this location. There is the Niger Nigel River flowing and the disc to scale is probably 10, 15, 30 kilometers from here to here. So let's first look at what happens through the year.

This is a very dry area. It's just below the Sahara Timbuktu is not very far away so that it's pretty close to the edge of the desert. During the dry season, which is most of the year, there's very few mosquitoes cause there's no place to breed.

But once the rainy season starts in June, July, August and extends up until September, October, then we can achieve huge numbers of mosquitoes. One area I work, they get over 500 bytes per person per night. But in this area it's not quite so high.

Nonetheless, the seasonal variation is enormous and it helps to see a movie to understand really what's going on with the population sizes in conjunction with the different chromosomal forms and with the gene flow, all of these are going to be important for what eventually is is done. If we're gonna do a release. Here is one annual cycle.

We start out, the population sizes are fairly small, can see here too. And then by the September, october, you see we have quite large population sizes in each of the different villages and we have lots of gene flow amongst the different villages. As the year continues back into the dry period, the population sizes diminish again and the gene flow gradually diminishes as well.

So you can see that there's lots going on here. And when we introduce the genetics, the situation's even worse. Consequently, we have to view some of these things one by one, not all together in order to get a real understanding, make predictions, and most especially set conditions that simply must be met if we're going to be successful for that, it's really helpful to have it all together, different type of model than, than we've been looking at.Now.

For that, it's helpful to have analytic models as one of my students John Marshall has been working on for the last year or two. Okay, I'm John Marshall. I'm a graduate student in the table lab and I've been working on some of the more genetically focused models modeling efforts, focusing on the parameters of a transposable element as it spreads through a population, a transposable element spread because they replicate and as they replicate then they're inherited more frequently.

So they have the ability to be driven with a drive and effect the gene into a population. So we're interested in, for example, the transposition rate, the way at which it jumps the increase in fitness cost, which is often a consequence of the trans transposition. And also as the transposable element increases its copy number, then it'll transpose less frequently.

So there are those counteracting dynamics and mathematical models can be used to capture that. So here we'll look at the more complicated models this time following it through two years, not just one. And we're going to have the additional feature that the frequency of the transposable element is illustrated by the color of the population.

So remember, population size is the size of the disc and that the color of the disc is the frequency of the transposable element. We start out here with very low frequencies in all the populations. And as the the year progresses slowly we see that the, as we get into the rainy season, we see that the population size is getting larger and initially only the side of the release ban is red.

And here it's for all practical purposes, a hundred percent. The others are still have received insufficient gene flow so that they're still not all transformed, but in spite of low rates of, of gene flow, we see that by the second year almost everything is going to have the transposable element. So at the end of this simulation with these values, the frequency of transposable element is between 99 and a hundred percent in all of the areas that, in all the villages That are being explored.

You'll recall that John Marshall's Studies with the analytic models show that the transposition rate is a critical feature in how the transposable element moves through the population. Similarly, which chromosomal form you release and also makes a big difference. And this alternate scenario, just one of many we've studied, we see that when we release it into the Abaco form, not the mopti form, and that we use a transposition rate that's smaller than the one that I originally shown you.

This one's perhaps more reasonable, more easily achieved, that the outcome is very different after two years. Here is a a two year cycle, and I'll pause it partway through so that you can see the, the remarkable difference. Again, the population increases, but how this time we've released it up in the baco form, not down in the MTI form.

And when the, in the second year, when the population size has increased during the middle of the rainy season, see here it's, it's not red everywhere as it was before. And furthermore, all the transposition seems to be located here. That's because the, there's much less gene flow between the, the iCal form and the MTI form than between the savanna and the, and the mti.

So here, as we follow through to the rest of the year, instead of being a hundred percent, we have rather that the a iCal form area wide is now only 20%The savanna is only 8%And the mopti, for practical purposes, hasn't received any of the transposable elements from the standpoint of designing the experiment or evaluating it. You see, it's critical that we have these simulations and that not only to guide our expectations, But also to evaluate them. Finally, There's a, an aspect of this that has not received nearly the attention it deserves.

And that's the ethical consideration. Most of the work to now has been on the genetic engineering trying to make something that will work. But in fact, even if we have it, that works.

What will happen if it gets released? What if something goes wrong? Remember these mosquitoes transmit a number of very serious diseases.

What if they become super bugs and they start transmitting even more effectively? Or if they have, they become, they have antibiotics and they spread that to other species. Or alternatively, maybe they'll start transmitting other diseases that they have not been able to transmit in the past.

Those are only three of a very large number of horrible things that might happen. And because we're lacking any experimental basis to study, we really have to formulate our policies based on computer models. There are several ways this might be done.

John's looking at just one aspect of things that go wrong, but there are obviously many more. And one thing we will have to do and haven't done yet is to make models that say the problems are bad enough, we have to stop and here's how we remedy what's gone wrong in the past. Hopefully we'll never have to act on that information, but just like having computer models for all contingencies and landing someone on the moon, so too, we have to have simulations of all contingencies for what happens after we release genetically modified mosquitoes.

So these modeling efforts and the other modeling efforts which have been talked about in this segment are important for assessing whether or not the project can work. You can't do experiments on the ecological scale because that isn't an experiment, it's the actual release. So it's important to have some measurements of parameters and then some concept of the how things are working the model, and then give some idea of whether it's not gonna, whether it's gonna work or not.

Additionally, it's important for modeling efforts to make recommendations to molecular biologists on which parameters should be measured, which parameters are important to measure, and when they are measuring them, what sort of values are important For the success of the project.