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we know a lot about the biological tree

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of life

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and can trace life's evolutionary

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history all the way back to a last

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universal common ancestor

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but for all that we understand about the

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tree of life there's still a great deal

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that we don't understand about its root

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system

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research on the origin of life can focus

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on any of a number of stages in life's

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emergence

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some origins of life research takes a

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top-down approach

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looking at the proximate ancestors to

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the last universal common ancestor

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with all of the historical contingencies

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they may have picked up along the way in

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alternatively one can take more of a

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bottom-up approach investigating the

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earliest stages of life's emergence

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when it only has the first intimations

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of lifelike behavior

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and when few significant historical

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auto catalytic cycles may have been an

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important part of life's chemical roots

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providing a means by which chemicals can

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collectively

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self-propagate the chemicals involved in

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auto-catalytic cycles

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can be split into three categories food

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species which only show up as reactants

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waste species that only show up as

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products and member species which show

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up as both products and reactants

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and whose abundance grow with each turn

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of the cycle

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here we have a simple toy model for an

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auto catalytic cycle consisting of two

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reversible reactions

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the first of which produces an

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intermediary member species and the

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second of which produces two of the

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original member species

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this provides a stoichiometric asymmetry

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that allows the cycle to grow and spread

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we simulate auto catalytic cycles in

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flow reactor environments where food

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flows in from a source to drive the

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system out of equilibrium

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and where all chemicals flow out of the

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reactor such that if a cycle doesn't

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propagate itself fast enough it will go

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extinct

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these simulations can be performed using

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mass action kinetics in which case

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chemical concentrations are continuous

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and the simulations are deterministic

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we're using the gillespie algorithm in

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which case chemical counts are discrete

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and the simulations are stochastic we

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use the gillespie algorithm in this

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presentation

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an example is on the right you can see

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the logistic growth of member species

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and waste species as food is depleted

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in 2020 we published a paper

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investigating the different types of

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ecological interactions that auto

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catalytic cycles might exhibit

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extending the analogy of auto catalytic

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cycles as species in an ecosystem

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we showed that auto catalytic cycles can

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compete for food sources

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exhibit facultative and obligate

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mutualisms with the waste of one

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serving as the food for another that the

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one cycle can prey on the member species

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of another cycle and that cycles can

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mutually inhibit one another

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the idea is that different ecological

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interactions can be composed to form

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stable ecosystems of increasing

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complexity

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to provide the scaffolding for later

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stages in the emergence of

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this previous work limited its analysis

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to auto catalytic cycles in well-mixed

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environments

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but the ecological possibilities for

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chemical ecosystems might be expanded if

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we consider different types of spatially

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structured environments instead

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for example reaction diffusion systems

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where cycles can spread

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to occupy new locations and thereby gain

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access to new food

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these will be the primary focus of this

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presentation

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there are several reasons the spatial

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structure might be important to the

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dynamics of chemical ecosystems

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first it might help to sustain more

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complex chemical ecosystems by

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permitting the coexistence of cycles

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that couldn't coexist in a well-mixed

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environment

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might select for spatial properties of

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auto catalytic cycles

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such as the permeability or diffusivity

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of their constituent chemicals

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and third spatial structure might create

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new levels of selection

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either favoring traits that couldn't be

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favored in the well-mixed

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environment analogous to group structure

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favoring different traits and biological

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populations

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or creating new units of selection

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altogether

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first i'm going to present a simple

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example where a spatially structured

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environment permits a more complex

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chemical ecosystem to be maintained

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then could otherwise be maintained in

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the well-mixed case this is going to be

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similar in spirit to the bz reaction

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which has auto catalytic mechanisms

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and which while oscillating between two

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states in the wellmix case

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exhibits stable and dynamic patterns and

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as a reaction diffusion system

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this example is going to consist of two

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mutually inhibiting auto catalytic

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cycles

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a and b which are colored red and blue

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respectively

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each cycle is supplied with an

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independent food source so that they're

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not directly competing for food

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each consists of two reversible

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reactions identical to the toy model i

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initially showed

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additionally we include two reversible

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inhibition reactions

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which react the waste of one cycle with

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the food of the other cycle to produce

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another species

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x or y that neither cycle can directly

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use

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the effect of this is that if one cycle

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increases its abundance more quickly

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the waste that it produces can inhibit

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the growth of the other cycle

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ultimately driving it extinct and once

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again all chemicals will be constantly

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diluted

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creating a selective pressure for cycles

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that can propagate more quickly

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instead of simulating this chemical

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reaction network

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in a singular flow reactor will simulate

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it in a reaction diffusion system

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where each pixel has inflow from a

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source and outflow into a sink

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but also exchanges its chemical contents

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with neighboring pixels via diffusion

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more specifically we'll use a 5x5

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reaction diffusion system with periodic

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boundaries

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now if we were to seed every pixel in

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this system

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uniformly with equal amounts of cycles a

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and b

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but with no diffusion it would be

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possible to have an outcome like this

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in which cycles a and b dominate

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in adjacent pixels and stably coexist

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because there is no interaction between

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those pixels if we were to add diffusion

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in

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this sort of outcome would be unstable

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for example with any slight imbalance

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like blue coming to dominate in the

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center

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accumulated member species by cycle b in

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the center could diffuse outwards

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and strengthen the invasion of pixels

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and with high enough diffusion rates we

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would expect the whole system to reach

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one global outcome

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here we have stochastic simulations of

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the reaction diffusion system

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under three different conditions where

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we're varying

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the rate constant for the diffusion of

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all chemicals in the system

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we have a slow diffusion case a moderate

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diffusion case and a fast diffusion case

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here we have time series plots for the

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total number of member species belonging

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to each cycle

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and each pixel of the reaction diffusion

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system for each of the three cases

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on the left in the slow diffusion case

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we can see that each pixel

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quickly has one cycle dominate and that

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a low amount of material is exchanged

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between reactors

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such that each cycle struggles to invade

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adjacent pixels

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on the right we see the opposite extreme

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a large amount of chemicals are

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exchanged between adjacent pixels

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so that the plots tend to resemble one

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another and a global outcome is quickly

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reached

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approximating a well-mixed reactor in

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the moderate diffusion regime each pixel

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alternates between being dominated by

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cycle a

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and cycle b neither cycle wins globally

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and each shifts around its advantage

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forming patterns reminiscent

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of the spatial patterns of the bc

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reaction in a petri dish

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next i'll continue using the example of

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mutually inhibiting cycles in a reaction

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diffusion system

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to show a case where the spatial

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properties of auto catalytic cycles can

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be selected for

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we'll take the same two mutually

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inhibiting cycles that we had before

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but instead of making them identical to

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one another in their rate constants

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and the diffusion constants associated

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with their chemicals

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we're going to make them differ in two

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ways

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the red cycle is going to be fiercer in

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the sense that it's going to have

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reactions with higher rate constants

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but the blue cycle is going to be faster

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meaning that its member species are

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we are going to do this in a 3x3

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reaction diffusion system with periodic

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boundaries

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where both cycles are only seated in the

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center pixel

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the expectation is that cycle a in red

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being fiercer will tend to dominate in

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the central pixel

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whereas cycle b in blue being faster

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will tend to spread

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more quickly to adjacent pixels and

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thereby access new food more quickly

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as cycle b continues to expand it might

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be able to build up

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enough of an advantage in the

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surrounding pixels to re-invade the

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central pixel

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and overcome cycle a here we have an

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animation of the unfolding of time

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series of the total number of member

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species for each cycle in each pixel of

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in the central pixel cycle a being

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fiercer

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drives cycle b to the brink of

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extinction but cycle b being faster

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is able to diffuse into adjacent sites

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and build up an advantage in those

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pixels more quickly

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so that it can suppress the growth of

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cycle a

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eventually cycle b is able to re-invade

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the central pixel

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to such an extent that it begins to

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drive cycle a towards extinction

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the outcome of this type of simulation

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largely depends on the relative fastness

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and fierceness of cycles a and b

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here we have a heat map in which we

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sweep over those parameters

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on the left we sweep over the diffusion

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constants for the chemicals of cycle b

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where as we go down cycle b gets

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increasingly fast

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on the bottom we sweep over the reaction

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rate constants

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for cycle b's reactions whereas we move

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from right to left

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cycle b gets increasingly less fierce

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the colors in the heat map encode the

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final frequency

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of member species for cycles a and b

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aggregated

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over the reaction diffusion system we

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find parameter combinations where

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fastness overcomes fierceness and where

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fierceness overcomes fastness

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meaning that either could be selected

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for

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additionally while it is always better

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to be fiercer it is not always better to

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be faster

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in the bottom left we see a region where

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cycle b

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being faster gives it a disadvantage to

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cycle a

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likely because its members diffuse so

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quickly that they can't stably

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accumulate

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in addition to simple reaction diffusion

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systems there are various other

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spatially structured environments that

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may be relevant to the origin of life

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and to the dynamics of auto catalytic

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chemical ecosystems

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for example mineral surfaces where

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chemicals can adsorb and desorb from a

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surface

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and also provide a new basis for

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competition between auto catalytic

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cycles as they compete for adsorption

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sites

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compartments are another important class

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of spatial structures that might affect

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the dynamic

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chemical ecosystems they might be

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semi-permeable or closed

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they might grow and or divide some

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examples of these in the origins of life

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literature

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are vesicles and coagulate some forms of

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spatial structure

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especially compartments provide the

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possibility of new levels of selection

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especially when the dynamics of the

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spatial structure become coupled to the

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chemistry itself

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i'd like to gratefully acknowledge my pi

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00:11:41,670 --> 00:11:40,399
david baum who i've been working with

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through the hildale undergraduate

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faculty research fellowship at the

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wisconsin institute for discovery

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and chris kemp is my mentor at the santa

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fe institute for the undergraduate

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complexity research program

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also the graduate students and

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post-doctoral students that i've been

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working with at the wisconsin institute

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for discovery

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and the other undergraduates in the bomb

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lab as well

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for additional reading you can check out

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our paper from last year in ecological

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framework for the analysis of prebiotic

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chemical reaction networks