Figures and data
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Schematic for artificial selection on collectives.
Each selection cycle begins with a total of g Newborn collectives (black open circles), each with N0 total cells of slow-growing type (S, red-colored dots) and fast-growing type (F, blue-colored dots). During maturation (over time τ), S and F cells divide at rates r and r + ω (ω > 0), respectively. S mutates to F at rate μ. In the selection stage, the Adult collective with F frequency f closest to the target composition
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Initial and target compositions determine the success of artificial selection on collectives.
(a-c) Mutant frequency of the selected Adult collective (f ∗) over cycles. The target frequency
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Intra-collective selection and inter-collective selection jointly set the boundaries for selection success.
a The change in F frequency over one cycle. When
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Expanding the success region for artificial collective selection.
a Reducing the population size in Newborn N0 expands the region of success. In gold area, the probability that
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In higher dimensions, the success of artificial selection requires the entire evolutionary trajectory remaining in the accessible region.
a During collective maturation, a slow-growing type (S) (with growth rate r; dark red) can mutate to a fast-growing type (F) (with growth rate r + ω; blue), which can mutate further into a faster-growing type (FF) (with growth rate r + 2ω; purple). Here, the rates of both mutational steps are μ, and ω > 0. b Evolutionary trajectories from various initial compositions (open circles) to various targets. Intra-collective evolution favors FF over F (vertical blue arrow) over S (horizontal blue arrow). The accessible regions are marked gold (see Sec. 1 in Supplementary Information). We obtain final compositions starting from several initial compositions while aiming for different target compositions in i, ii, and iii. The evolutionary trajectories are shown in dots with color gradients from the initial to final time. (i) A target composition with a high FF frequency is always achievable. (ii) A target composition with intermediate FF frequency is never achievable. (iii) A target composition with low FF frequency is achievable only if starting from an appropriate initial composition such that the entire trajectory never meanders away from the accessible region. The figures are drawn using mpltern package (35).
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Comparison between the calculated Gaussian distribution (“Gauss”, with the mean and variances computed from Eq. [7,8,15,19]) and simulations using tau-leaping (“tau”) and sampling (“samp”) methods. The simulations run 500 times. The initial number of cells are S0 = 200 and F0 = 800. The parameters are r = 0.5, ω = 0.03, μ = 0.0001, and τ = 4.8.
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Comparison between consecutive sampling and independent binomial sampling. A parent collective is divided into 10 collectives. The histogram labeled with ‘MHG’ is the probability mass function of F of the fifth collective sampled via multivariate hypergeometric distribution. The independent binomial sampling is labeled with ‘BN’. The initial numbers of cells are S = 8000 and F = 2000 for the left panel, and S = 20 and F = 5 for the right panel. 10000 samples are drawn for each distribution.
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Color map of the absolute error
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a Trajectories of F frequency for 10 collectives (g = 10) over time. The collective whose frequency is closest to the target value is selected in every cycle (black lines). The gray lines denote the other collectives. For parameters, we used S growth rate r = 0.5, F growth advantage ω = 0.03, mutation rate μ = 0.0001, maturation time τ ≈ 4.8, and N0 = 1000. b Comparison between frequency trajectories with (black) and without (blue) selection clearly shows the effect of artificial selection. The black line indicates F frequency of the selected collective
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The probability density functions of the selected collective’s frequency
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Scaling relation of F frequency variance (Eq. [27]) with Newborn collective size N0. The initial F frequency is 0.3. The parameters are r = 0.5, ω = 0.03, μ = 0.0001, and τ ≈ 4.8.
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Color map of the absolute error
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Comparison of selecting Top-tier 5 with Top 1. We breed 100 collectives and choose 5 collectives with the closest to the target value.
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Artificial selection also works for deleterious mutation. a Conditional Probability density functions of
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a The schematic procedure to determine accessible regions by collective selection. From the given parent composition (blue dot), the probability distribution of offspring Adults (Eq. [68]) is computed (marked in the orange-colored area). From Adult compositions, the probability distribution of the selected collective (Eq.[79]) is computed (marked in the green area). If the signs of the changes in both F frequency and FF frequency after the selection (from blue dot to green dot) are opposite to that of maturation (from blue dot to orange dot), the given composition is accessible. Otherwise, the composition is not accessible and will change after cycles. b The accessible regions are marked by the gray area. The vector field is the flow of compositions during maturation. The length and color of the arrows indicate the speed of composition changes. The figures are drawn using mpltern package (7).