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[Music]

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hi there I'm Alex Plum my talk is on

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auto catalytic chemical ecosystems in

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spatial settings uh

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so I wanted to start with this quote

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from the French naturalist George cuvier

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I don't think it's a good definition of

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life but I think it captures one feature

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of life that's very important uh

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specifically this feature of

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autocatalysis which I think is the

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central Motif for self-propagation that

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we see kind of all across life and it

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may have been relevant in life's

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earliest stages so we say that a process

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is auto catalytic if the products of

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that process catalyze the process itself

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here I'm going to be talking about Auto

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catalytic Cycles where you have a

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sequence of reactions that form a cycle

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such that with every turn of the cycle

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you get a stoichiometric increase in the

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number of some set of chemicals that

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we'll call member chemicals you can take

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all of the chemicals involved in an auto

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catalytic cycle and partition them into

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food chemicals into member chemicals and

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into waste chemicals based on which

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sides of the reactions they show up in

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and so here's a simple example where you

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just have two reversible reactions you

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have two member chemicals M1 and M2 you

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have one food that's being used for both

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reactions and waste chemical and in

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principle these can be be irreversible

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here I've drawn them as reversible and

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because they're reversible you can drive

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them in either direction if you have an

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abundance of food they can be driven in

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the productive direction that provides

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the stoichiometric increase in the

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member chemicals allowing them to

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self-propagate but if instead you have

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an accumulation of waste it can kind of

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wind down in the other direction and you

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can get a stoichiometric decrease in the

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number of member chemicals as well

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so we've analogized these Auto catalytic

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Cycles to biological species in part

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because they're consuming food they're

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producing waste and self-propagating

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themselves and we've demonstrated that

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they can exhibit logistic growth

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if you put them in a closed reactor some

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amount of food available some seed

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member species

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they can start growing and they can

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reach equilibrium concentrations but

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this isn't of great interest in an

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origins of Life context because life

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isn't out of equilibrium process so in

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practice we typically simulate these

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cycles and chemostats when you have an

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inflow of food from a source that drives

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them in the productive or autocatalytic

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Direction and where everything is

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diluted out of the system and this has

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two implications one it helps to offload

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the waste to kind of keep it from being

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driven in the other direction and it

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also provides a selective pressure so

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that now if the cycle doesn't replicate

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or propagate its member species quickly

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enough they'll just be diluted out of

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the reactor so it's not trivial that

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these Cycles are going to persist

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anymore persistence becomes a problem

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something that they have to kind of

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achieve

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so when you simulate these you can get

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time series that looks like this plot

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over here

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where you have a depletion of food

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through time you have logistic growth in

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the concentrations of member chemicals

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here in blue and you also have a buildup

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of waste

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you can choose to simulate them using

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ordinary differential equations if

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you're in a well-mixed reactor

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and that assumes that you have large

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enough quantities that you can treat

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continuous concentrations of chemicals

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the other approach is to simulate things

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stochastically and in kind of the large

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and limit this looks very similar to The

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Continuous case but as you go to smaller

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and smaller numbers of chemicals things

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look a lot noisier and you can start to

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have more contingency in the Dynamics

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where you can have the stochastic loss

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of a single chemical or the stochastic

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dispersal of a single chemical in a new

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location changing the dynamic somewhere

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else and so in everything I show here

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I'll be taking this to catch a

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stochastic approach

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so that's all the Dynamics for a single

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cycle we're ultimately interested in

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combining different cycles and seeing

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how they interact ecologically so here I

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show the the member chemical

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concentrations over time or counts over

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time for the different Auto catalytic

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Cycles shown on the left here they can

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exhibit competitive exclusion

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competitive coexistence when they share

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a common food source they can also

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exhibit mutualisms wherein the food or

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the waste of one chemical serves as food

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for another Auto catalytic cycle

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they can also exhibit predation where in

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the member chemicals of one cycle serve

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as the food for another cycle and the

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Dynamics resemble those that you get in

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the lack of Altera equations in ecology

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where you can get both stable and damped

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oscillations predator or prey dominance

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or coexistence of the the predator and

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prey and you can also get priority

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effects wherein two cycles might

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mutually inhibit one another so that it

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matters if one cycle gets seated in a

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location first versus the other since

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they'll suppress the growth of the other

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cycle

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so why is this relevant to the origin of

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life we think that these Auto catalytic

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Cycles provide one of the simplest ways

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in the absence of needing compartments

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or polymer genetics to get this sort of

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self-propagation that you see in

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metabolism

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and we think that they can provide an

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Avenue for the accumulation of

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complexity to ultimately serve as

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precursors or scaffolds for later stages

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in the origin of life so as an Avenue

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for kind of increasing the chemical

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diversity that you might need to achieve

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later stages and we think that you can

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do that by taking individual Cycles

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composing them through various

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ecological interactions and then using

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the sorts of avenues that we see in

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ecology for the accumulation of

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complexity

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ecology one way is through ecological

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succession wherein you have some species

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that lay the groundwork for others to

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later succeed them you can imagine this

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in a Chemical Context where the waste or

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member chemicals enable the activation

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of new Cycles they couldn't have been

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activated into those first Cycles were

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activated you also have ideas on ecology

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about how to maximize biodiversity for

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example through the intermediate

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disturbance hypothesis and finally you

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have ideas about how spatial structure

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can be relevant to the accumulation of

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complexity in ecosystems where you have

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meta ecosystems and diversity among them

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and migration between them that allows

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for recombination in the formation of

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new ecological States

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so in an origins of Life context we

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often think about these chemical

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ecosystems as persisting and spatially

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structured environment like adsorbitive

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mineral surfaces uh moving across those

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surfaces where they're effectively

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concentrated where their diffusion is

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effectively lowered and those different

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ecosystems might interact

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when they interact they might annihilate

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they might continue to coexist they

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might fuse and modify one another and so

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we wanted to understand how uh these

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chemical ecosystems behave in space so

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the earlier kind of ecological time

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series that I showed you were all in

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well-mixed reactors now we're going to

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consider these systems in space so

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here's an example where a cycle is

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seated in the center and diffuses

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outwards kind of spreading to new

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sources of food and of course we know

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that spatial Dynamics are important for

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auto catalytic chemical systems we have

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classic examples like the belazov's

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abatinsky reaction it's out of

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equilibrium process we know that they

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can form stable patterns

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so I want to consider cases where Cycles

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mutually inhibit one another because

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getting more complex ecosystems is easy

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when there are mutualisms between the

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Cycles it's hard when you have

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inhibition between them and there are

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various ways that Cycles can inhibit one

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another for example you can have the

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waste of one cycle interfere with the

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food of another cycle or you can have

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their member species annihilate a much

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simpler example that I show in the

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bottom this is the one that I'm going to

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be working with in the subsequent slides

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so you can put these in space here I

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have a hexagonal lattice with chemicals

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reacting within each site and diffusing

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between sites

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and I'm coloring them according to the

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fraction of member species that belong

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to one of these two mutually inhibiting

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Cycles red for cycle a B for are blue

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for cycle B and with slow diffusion they

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stop interacting and just form these

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stable patches with much higher

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diffusion you can see one cycle starts

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to crowd the other out globally and we

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can look at this more systematically

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varying the diffusion of all the

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chemicals involved kind of gradually

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increasing in the low case low diffusion

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case you end up with pretty randomly

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distributed ecological outcomes and the

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very high case you end up with one

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Global winner one cycle Drive in the

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other extinct and you can look at the

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heterogeneity of chemicals across this

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hexagonal lattice and what we find is

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that an intermediate diffusion regimes

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this heterogeneity is maximized

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and insofar as these Cycles are

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inhibiting one another through these

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reactions that might produce other

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chemicals that could help to provide

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support for the activation of future

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Cycles

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you don't have that sort of interaction

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in the very very low diffusion case and

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you also lose it in the height of each

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in case when one cycle is driven extinct

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and so this suggests that some

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intermediate diffusion regimes are the

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most favorable to uh kind of this

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biodiversity so to speak of these

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chemical ecosystems

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that's all with keeping these Cycles on

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an equal playing field where they have

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the same reaction kinetics and the same

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diffusion properties what I want to show

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next is when you vary the properties of

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these two cycles asymmetrically so I'm

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showing time series here on the right of

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both Cycles being seated in some Central

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site in a three by three array and they

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can diffuse outwards I make cycle a in

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Red fiercer so that it consumes

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food more quickly than cycle B and

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because of that it starts to drive cycle

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B extinct initially

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but cycle B is made faster than cycle a

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meaning that it can diffuse outward more

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quickly and access new sources of food

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and so despite initially being driven

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down it manages to dominate in these

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outer sites and eventually reinvade so

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that in the long term it ends up driving

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cycle a extinct

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and you can kind of vary these

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properties systematically and construct

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a phase diagram here I vary the relative

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fierceness and relative fastness of the

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two cycles and you find regimes in which

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either of the Cycles can be favored

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suggesting that spatial environments can

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select for new types of traits such as

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the diffusivity of these member

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chemicals once you put them in a spatial

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environment a well-mixed reactor would

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be blind to these sorts of traits

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notably you can also look at other types

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of inhibition that don't involve

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explicit chemistry you can look at

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competition for absorption sites on

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Mineral surfaces and there we find very

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similar Dynamics and I think that this

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is suggestive that something like the

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Intermediate disturbance hypothesis

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might hold even for these chemical

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ecosystems and of course in an origins

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of Life context there are lots of

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different types of disturbances that you

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could have the noise of the spatially

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structured environment that you have

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different impacts

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and so with that I'd like to acknowledge

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David Baum my undergraduate advisor at

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the University of Wisconsin-Madison and

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Chris campus my mentor and collaborator

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at the Santa Fe Institute some excellent

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grad students and postdocs including

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profile who just defended this thesis

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last week and some excellent undergrads

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that I've had the opportunity to work

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with including Gage actually you should

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be on here

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all right with that I'll take any

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questions

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[Music]

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just wants to give you know their name

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and affiliation and ask a question

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that'd be great

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hi my name is George schaible I'm from

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Montana State University and I should

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preface I am a microbiologist so um but

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that was a great talk I thought you did

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a good job breaking down for us uh I'm

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just curious when diffusion happens

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that's I think of it in like a

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three-dimensional space so you were

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showing a lot of two-dimensional graphs

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so what does that look like in three

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dimensions

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yeah so I didn't do simulations in

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three-dimensional space in part because

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I think the most like origins of Life

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relevant spatial structures are going to

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be these two-dimensional environments I

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think the two-dimensional environments

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can help to constrain kind of the

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effective diffusion that you would have

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they can concentrate chemistry lots of

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origins of Life theories that look at

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adsorbed Mineral surfaces already so we

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were kind of committed to that sort of

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scenario and here the idea of

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intermediate diffusion being favorable

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for chemical diversity I think that

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that's further support that that's the

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type of scenario that might be important

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I think there's a quote from Gunter

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washer who kind of pioneered some of

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these ideas that we don't build planes

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in the sky we build them on the ground

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and that's for a reason

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um I just to follow up with that what

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what kind of mineral surface would would

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you like consider this yeah so that kind

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of the experimental side of my group in

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undergrad we um we were using pyrite

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surfaces

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um but here we're chemically agnostic

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and we're also agnostic to the exact

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hi I'm Ellie I'm from CU Boulder and I

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was wondering so I'm mainly a lab

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chemist and I was curious if you had any

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any like personal thoughts of how you

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would want a chemist to do some of this

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work or what kind of questions you would

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want a lab chemist to do to help ground

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truth some of the modeling that you do

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because I work a lot of like mineral

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absorption and mineral facilitated

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chemistry and of course when we do a lot

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of this stuff it is an equilibrium

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reaction because you're kind of waiting

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for it to resolve to equilibrium we're

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basing our reactions on that so like how

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would you kind of design something like

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this or like theorize or like hope for

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something right so a lot of what I

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showed that in the well-mixed cases we

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were working with chemostats and

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certainly chemostats are an

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experimentally kind of realizable

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approach

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um there's another side to our group uh

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that looked for kind of real Auto

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catalytic cycles and known chemical

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reaction networks both biotic and

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abiotic and so I think one promising

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approach is to look at how these

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chemical ecosystems might explore that

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space where you seed with one chemical

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that activates maybe a single cycle or a

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small set of cycles and then through the

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addition of subsequent seeds you might

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activate kind of new cycles and so I

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think there are kind of experimental

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approaches that can be done there and I

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think people in our group are continuing

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okay hello we have a question from

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online actually so this comes from user

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Alex he's asking can you simulate

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tipping points hysteresis spatially with

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this method tipping points uh it's hard

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to ask for a clarification via Zoom okay

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Alex if you can hear this um please

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clarify our question and we'll come back

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hi I'm Jake from UCSD um can you clarify

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why you used a stochastic process to

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like just solving differential equations

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analytically yeah so you can have cases

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in these chemical ecosystems where

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there's kind of some unstable fixed

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point and those unstable fixed points

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you need some degree of stochasticity to

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break out of them so that's one reason

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if I just use deterministic simulations

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you could get stuck in those uh it's

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also the case that in ecology we're

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interested in lots of contingency and

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stochasticity and then doing lots of

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replicates allows you to explore all

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those contingent outcomes that's largely

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00:14:42,839 --> 00:14:54,530
okay we return for one more question

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hi I'm Donna from Indiana University I'm

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an ecologist by training and it was

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really interesting to see all of those

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theories that I've been trained for in

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00:15:09,790 --> 00:15:06,540
this context

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00:15:12,710 --> 00:15:09,800
um as ecologist we abandoned

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intermediate disturbance hypothesis

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00:15:19,069 --> 00:15:15,720
because we haven't observed in nature

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00:15:23,210 --> 00:15:19,079
yeah for doing years I was wondering if

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there are ways to test experimentally

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um

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what do you think about that and also

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[Music]

443
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looking for tipping points I think

444
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the online person mentioned you can

445
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probably see the signals before

446
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transitions like time or talk increasing

447
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Time auto correlation

448
00:15:46,310 --> 00:15:44,660
um or coefficient of variation

449
00:15:47,870 --> 00:15:46,320
absolutely thank you for the question

450
00:15:49,730 --> 00:15:47,880
yeah so I think an ecology that

451
00:15:51,170 --> 00:15:49,740
intermediate disturbance hypothesis is

452
00:15:53,689 --> 00:15:51,180
controversial and many people have

453
00:15:55,550 --> 00:15:53,699
abandoned it I think in this kind of

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modeling context it's very easy to kind

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00:16:01,189 --> 00:15:57,660
of look for it just because we're doing

456
00:16:02,870 --> 00:16:01,199
experiments in silico and

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I think that

458
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if it does hold in the biological case

459
00:16:08,509 --> 00:16:06,480
certainly it holds in the chemical case

460
00:16:09,949 --> 00:16:08,519
there's a possibility that it holds in

461
00:16:11,090 --> 00:16:09,959
the chemical case and not the biological

462
00:16:12,889 --> 00:16:11,100
case

463
00:16:14,030 --> 00:16:12,899
um I think the weak version of this is

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that there are certain types of

465
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disturbance regimes that can be

466
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beneficial for chemical diversity even

467
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if the intermediate disturbance

468
00:16:23,629 --> 00:16:21,360
hypothesis doesn't hold her at large to

469
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the Tipping points question I think you

470
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do see sort of kind of signs in the

471
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diffusion cases I kind of vary it you

472
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end up seeing sort of power loss scaling

473
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in the patch size

474
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um sort of like you would see in an

475
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icing model in physics and so the sort

476
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of theory that looks at tippling points

477
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there would also apply here