9 Mile Prairie and the species area curve

Drew Tyre Author

06/29/2018 Added

308 Plays

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A brief introduction to the science of the species area curve, and our visit to 9 Mile Prairie to measure it.

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[00:00:04.800]So welcome.
[00:00:06.100]This is the introduction to the NRES 222 Ecology Lab,
[00:00:10.090]field trip to Nine Mile Prairie.
[00:00:12.390]What I'd like to do is just talk briefly a little
[00:00:14.600]about the science behind what we're going to do
[00:00:17.490]while we're out in the field,
[00:00:18.860]and then very briefly talk about the actual exercise
[00:00:23.400]that we'll do while you're out there.
[00:00:26.030]The TAs will go through more of the exercise
[00:00:29.070]once we are in the preparation week for the trip.
[00:00:39.060]MacArthur and E.O. Wilson,
[00:00:41.730]Robert MacArthur and Wilson,
[00:00:43.560]noticed when they were down in the Caribbean
[00:00:48.550]that as they looked at different islands,
[00:00:51.330]they found, there we go.
[00:00:54.090]They found small islands had few species,
[00:00:57.730]and larger islands
[00:00:59.810]like Cuba and Hispaniola had more species.
[00:01:03.060]And this was looking at amphibians and reptiles.
[00:01:07.870]And in fact, if you plot that same curve on log-log axes,
[00:01:11.770]it turns into a straight line.
[00:01:15.110]And we call this the species-area curve.
[00:01:21.205]This is actually one of the oldest patterns in ecology.
[00:01:25.410]This was actually published in the 19th century.
[00:01:28.060]These are plant species now,
[00:01:29.530]so starting with a little bit of Surrey
[00:01:33.510]and then going up to different,
[00:01:36.130]he called them bits and part pieces,
[00:01:37.980]and then all of Surrey County,
[00:01:40.560]South Thames, Thames, Southern England,
[00:01:43.170]and then the number of plant species in Great Britain.
[00:01:45.850]This is plotted on log axes,
[00:01:47.740]so as you get larger and larger here,
[00:01:51.120]up to the area of Great Britain,
[00:01:52.930]you get more and more species found
[00:01:57.270]in each of those particular areas.
[00:01:59.670]These are nested areas, obviously,
[00:02:01.240]so the bit of Surrey is inside the part piece of Surrey.
[00:02:06.630]Now, this is really quite remarkable
[00:02:08.090]because it turns out that no matter what kind
[00:02:11.160]of species you look at and where you look on the planet,
[00:02:15.600]this slope of this line is almost always the same value.
[00:02:22.120]So this is why we use log-log plots.
[00:02:25.533]The relationship, well, now let's see.
[00:02:26.960]Let's point that way, there we go.
[00:02:31.056]The curve is a power law.
[00:02:32.980]So the number of species is equal to a constant c,
[00:02:36.360]times the area, raised to the power z.
[00:02:39.340]And it's this value z that's constant across,
[00:02:43.640]or not exactly the same,
[00:02:45.100]but appears to be very consistent
[00:02:46.870]across many different groups of species
[00:02:49.760]in many different places.
[00:02:51.930]If we take logarithms of both sides,
[00:02:54.930]so now we have the log of S,
[00:02:57.640]there they are right there, okay,
[00:02:59.670]is equal to the log of c,
[00:03:02.530]plus z times the log of A.
[00:03:09.838]It's a bit hard to see,
[00:03:10.700]but this is actually the equation of a line.
[00:03:12.980]So this is gonna be our intercept.
[00:03:14.890]This value, log of C, is the intercept.
[00:03:17.440]And then we have z is the slope,
[00:03:19.400]and the x-axis variable is the logarithm of the area.
[00:03:23.500]So by doing this logarithmic transformation
[00:03:26.160]on this equation, on this power law,
[00:03:28.330]we end up with the equation of a straight line.
[00:03:30.290]And that makes it very easy for us to estimate
[00:03:32.950]this particular value here, z,
[00:03:35.570]which is the one that has the consistent value.
[00:03:39.460]So here just to demonstrate the point,
[00:03:41.220]here's some more graphs for reptiles, fishes, and mammals
[00:03:46.520]across some much larger,
[00:03:48.890]I keep wanting to point that direction,
[00:03:50.770]much larger areas here.
[00:03:52.890]10,000, up to 10,000 square kilometers.
[00:03:56.630]And sort of, again,
[00:03:58.440]the slope of those lines is very consistent.
[00:04:00.980]It's about .28 averaged across many, many different studies.
[00:04:05.720]Sometimes as low as .2,
[00:04:07.570]in other studies as high as .4,
[00:04:10.170]but generally around that average value of .28.
[00:04:15.710]Now, it does change a little bit
[00:04:17.240]depending on the scale at which you look.
[00:04:22.480]One of the reasons why we
[00:04:25.430]see more species as we go up is that we're moving into areas
[00:04:29.810]with different types of habitats.
[00:04:32.240]So if we look in this case for this particular study,
[00:04:35.110]they were talking about provinces.
[00:04:39.520]These are ecological provinces, not Canadian provinces.
[00:04:42.190]But within a particular province,
[00:04:44.130]so within a particular kind of homogenous habitat,
[00:04:48.520]you get a fairly flat slope.
[00:04:50.010]So it's still increasing.
[00:04:51.450]The larger the province that you look at,
[00:04:53.840]the more species you get.
[00:04:55.710]But the slope is a little bit lower.
[00:04:57.640]If you start working among provinces now,
[00:05:01.210]so now you're working at this top end.
[00:05:03.340]So now the areas are all quite large
[00:05:05.070]because now as we add provinces together, right,
[00:05:09.780]we're working on quite big areas.
[00:05:11.610]There, now we're working between extremely different types
[00:05:14.660]of provinces or perhaps even biomes
[00:05:18.600]as we're working across these different areas.
[00:05:21.820]We add new species quite rapidly.
[00:05:27.580]And there's sort of an intermediate slope here
[00:05:30.490]where we're working between different islands.
[00:05:35.870]What appears to be happening is that
[00:05:37.800]if you are working within a homogenous ecological area,
[00:05:42.230]you get a lower slope.
[00:05:43.500]If you work across different ecological areas,
[00:05:46.080]you get a much steeper slope.
[00:05:50.580]So we visualize that sort of a different way.
[00:05:53.320]I keep wanting to point at myself in some way.
[00:05:55.960]We start off in local areas.
[00:05:57.560]So, say, within Nine Mile Prairie,
[00:05:59.780]we're gonna be working down here in this kind of scale.
[00:06:02.120]So we only get one slope there.
[00:06:04.040]As we move from Nine Mile Prairie
[00:06:06.100]if we were to keep our sampling regime
[00:06:07.840]and expanding outwards from Nine Mile Prairie, say across
[00:06:12.070]the larger Tallgrass Prairie ecoregion,
[00:06:16.450]right, that includes all of the Great Plains,
[00:06:20.130]we might start to see we're really sampling the same kinds
[00:06:23.790]of biomes, but now over there,
[00:06:25.220]so the scale might flatten out.
[00:06:26.830]And then as we get up into start moving
[00:06:28.940]out of the Tallgrass Prairie ecoregion
[00:06:31.500]and into other ecoregions
[00:06:34.070]like the Eastern Deciduous Forest to the east of us
[00:06:36.660]or Rocky Mountain Alpine habitats to the west of us,
[00:06:40.010]the rate of species accumulation is gonna pick up again.
[00:06:48.121]It's a bit tricky trying to figure out exactly.
[00:06:51.090]Well, it's not difficult figuring out where you are.
[00:06:52.970]I mean, within a particular scale area, right,
[00:06:57.970]we're going to be seeing a fairly consistent slope.
[00:07:00.460]So we're not gonna be able to work our way
[00:07:02.520]across this sort of region, this sort of problem here.
[00:07:10.000]So you might wonder, why would we care
[00:07:11.640]about species-area curves?
[00:07:14.020]What's the point of measuring species-area curves?
[00:07:16.790]Okay, so it's a very consistent pattern in ecology.
[00:07:18.960]Who cares?
[00:07:20.160]Well, it turns out that in conservation biology,
[00:07:23.800]one of things we're interested in is
[00:07:26.560]how a given amount of management is,
[00:07:28.960]how many species is a given amount
[00:07:30.640]of management going to affect?
[00:07:32.730]This is some work that was done in Australia
[00:07:35.460]comparing three different sorts of management options:
[00:07:39.410]invasive predator control...
[00:07:44.180]What's the middle one here?
[00:07:45.013]This is the phytophthora management.
[00:07:46.217]Phytophthora is a fungal disease that affects plants,
[00:07:50.680]invasive fungal disease.
[00:07:52.350]And then revegetation up here.
[00:07:57.150]Each of these, the curves sort of represents
[00:08:00.460]a different number of at-risk species
[00:08:02.890]that are going to be affected
[00:08:04.710]by that particular kind of management.
[00:08:08.600]Plants aren't particularly affected by invasive predators.
[00:08:11.890]There we go.
[00:08:15.600]So there's not very many species that are helped there.
[00:08:18.190]More species are helped by phytophthora management,
[00:08:20.840]and even more species are helped by revegetation.
[00:08:26.140]Now, they also carry different sorts of costs, though.
[00:08:30.409]One of the things that we're looking at is
[00:08:33.200]how much have we already done?
[00:08:35.700]That's where these squares are, right?
[00:08:37.730]So there's quite a bit of revegetation
[00:08:39.170]that's already been done.
[00:08:44.430]There. (laughs)
[00:08:45.890]There's no square on the phytophthora curve
[00:08:47.710]because we haven't done any phytophthora management.
[00:08:50.070]And we've done a little bit of invasive predator control,
[00:08:52.770]but not very much.
[00:08:55.020]What we can see is that there's,
[00:08:57.590]if I look at this figure over here.
[00:09:00.270]If we were to increase our investment
[00:09:02.110]in phytophthora management from zero,
[00:09:04.440]which is where we're at now, up to,
[00:09:07.520]I think this is in terms of kilometers squared, right?
[00:09:12.020]We could add 108 species that we're protecting
[00:09:15.590]based on this estimated species-area curve.
[00:09:18.330]In contrast, our invasive predator control,
[00:09:21.070]so making a similar kind of area investment,
[00:09:24.850]is only gonna take us from 86 species to 89 species
[00:09:28.440]because we're already doing
[00:09:29.520]about as much invasive predator control
[00:09:31.420]as we expect to help.
[00:09:32.820]And the same is true for revegetation.
[00:09:35.020]We're only going to protect an additional four species
[00:09:38.170]by adding 200
[00:09:41.640]square kilometers to our revegetation efforts.
[00:09:47.140]So this can help us allocate our resources appropriately
[00:09:50.670]and find out where we're at.
[00:09:52.810]This is a very simple model.
[00:09:54.320]Doesn't take a lot of data in order to estimate it,
[00:09:57.510]and yet we can actually use it
[00:09:59.230]in applied ecological decision-making,
[00:10:02.290]trying to figure out how we ought to allocate our resources.
[00:10:05.610]These bottom curves are the same,
[00:10:07.900]except that now the x-axis is actually
[00:10:10.440]in terms of the amount of money that we could invest,
[00:10:14.800]how much it's gonna cost, right?
[00:10:16.010]Because phytophthora management costs
[00:10:18.440]different amounts than revegetation.
[00:10:20.570]Revegetation is quite expensive.
[00:10:23.010]So we can use these simple models
[00:10:25.810]in an applied decision-making context
[00:10:28.170]in order to get better conservation outcomes.
[00:10:34.380]So what are we gonna do next week?
[00:10:35.580]So next week what we're gonna do,
[00:10:37.630]you can see these students right here are,
[00:10:41.520]the red flags in the prairie
[00:10:43.550]are marking out their nested quadrats.
[00:10:46.610]And what they're doing is they're searching
[00:10:48.870]progressively larger and larger areas
[00:10:53.100]for new plant species.
[00:10:55.340]Here's some of the sorts
[00:10:56.260]of plant species you're going to find out.
[00:10:57.920]Don't ask me what these are.
[00:10:58.960]These ones down here are rose hips.
[00:11:00.790]I think this is a bad picture of a round-headed bush clover.
[00:11:05.360]So you're gonna see lots and lots of flowering plants,
[00:11:07.590]and that makes 'em easy to identify.
[00:11:09.600]Unfortunately, there's also a lot of grass,
[00:11:11.700]which is much harder to identify.
[00:11:13.460]We're not asking you to identify things to species.
[00:11:15.740]We just need to know,
[00:11:16.780]is this different from things that you've already seen?
[00:11:21.720]What we'll do is you'll collect species' identifications
[00:11:25.970]at larger and larger areas,
[00:11:27.840]and then we'll be able to,
[00:11:29.040]in the following week we'll be able
[00:11:30.420]to take that information, estimate those curves,
[00:11:33.180]and we'll be able to see,
[00:11:34.580]does our data from Nine Mile Prairie
[00:11:38.090]match our theoretical expectations
[00:11:40.250]from all the other work that we're doing?
[00:11:41.970]And we can also do a little bit of
[00:11:43.800]what we would call a mensurative or an observation
[00:11:46.370]or a found experiment,
[00:11:48.980]in that we have fields that have different times since fire.
[00:11:52.660]So fire is an important part of the prairie ecosystem,
[00:11:57.110]and we have some fields that were burned this year,
[00:12:00.400]some that were burned previous years.
[00:12:04.429]Each lab section will work in a different field
[00:12:07.030]and will get estimates of these slopes
[00:12:11.540]and see whether they vary with time since fire.
[00:12:17.680]So some of the learning objectives
[00:12:19.100]for this particular exercise.
[00:12:21.240]We're gonna be practicing species identification.
[00:12:24.370]You'll be estimating parameters of a non-linear function.
[00:12:27.090]Well, actually fitting a linear function,
[00:12:28.760]but it gives you the parameters for the non-linear one.
[00:12:31.550]You'll be comparing those estimates with expected values
[00:12:34.660]using confidence limits.
[00:12:36.200]And finally, you'll be evaluating a theoretical claim
[00:12:39.520]with empirical data.
[00:12:42.350]So those are the sorts of things
[00:12:43.440]that we were hoping that you, well, not hoping,
[00:12:45.490]that we expect you will get
[00:12:46.710]out of participating in this exercise.

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9 Mile Prairie and the species area curve

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