Abstract
Understanding populations is important as they are a fundamental level of biological organization. Individual traits such as aging and lifespan interact in complex ways to determine birth and death, and thereby influence population dynamics; however, we lack a deep understanding of the relationships between individual traits and population dynamics. To address this challenge, we established a laboratory population using the model organism Caenorhabditis elegans and an individual-based computational simulation informed by measurements of real worms. The simulation realistically models individual worms and the behavior of the laboratory population. To elucidate the role of aging in population dynamics, we analyzed old age as a cause of death and showed, using computer simulations, that it was influenced by maximum lifespan, rate of adult culling and progeny number/food stability. Notably, populations displayed a tipping point for aging as the primary cause of adult death. Our work establishes a conceptual framework that could be used for better understanding why certain animals die of old age in the wild.
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Code availability
The code for modeling population dynamics/wormPOP is available at https://github.com/mitteldorf/C-elegans_pop_dynamics41. Data for Figs. 1–6 was analyzed and plotted with the corresponding source data using Excel with the exception of Figs. 2m,n,p and 4f, which are analyzed using R. Additional information including data analysis with R (v.3.6.1. and v.4.1.1.)/RStudio (v.1.4.1717) at https://github.com/Kerry-Kornfeld-Lab/wormPOP1.0 (ref. 42).
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Acknowledgements
We are grateful to J. Losos for evolutionary insight and eagle viewing; L. Taber for agent-based model insight; C. Huang, S. Hughes, K. Evason, J. Collins and C. Pickett for establishing experimental foundations; W. Tao, L. Chen, A. Sigala and A. Earnest for preliminary studies; and S. Kirchner for scientific advice, discussion and editing. We thank the Caenorhabditis Genetics Center (funded by NIH Office of Research Infrastructure Programs (P40 OD010440)) for providing strains. This work was supported by the NIH grant R01 AG02656106A1 to K.K. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.
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A.S. and K.K. conceived and designed the experiments. A.S., B.A., D.S., F.S., B.B., N.R. and G.D. performed experiments, A.S., H.J. and K.K. analyzed data, A.S., Z.K., C.T., A.W. and K.K. provided scientific input, and A.S., J.M. and K.K. contributed reagents/materials/analysis tools. A.S., J.M., and K.K. wrote the paper.
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Extended data
Extended Data Fig. 1 Diagram of wormPOP, an individual-based computational simulation model.
Worms exist in one of five nodes that are displayed as ovals and labeled egg, larva, adult, parlad and dauer. Diamond-shaped boxes indicate yes/no decisions. “culled?” indicates a stochastic decision whether an animal dies from culling or not.”Die of old age?” indicates a stochastic decision whether an adult animal dies from old age or not. “too long a dauer” indicates a stochastic decision whether a dauer stage animal dies from starvation or not. Other decisions are deterministic and depend on the number of time steps an animal has been in a stage, the mass of the animal in ng, or the amount of bacterial food ingested in a time step. Rectangular boxes indicate (1) bacterial ingestion, which depends on the size of the animal, the concentration of bacteria, and the appetite of other worms. Bacterial ingestion is somewhat stochastic, since it is influenced by other worms, and (2) growth and egg production.
Extended Data Fig. 2 Population dynamics in the laboratory population and computational simulation in four conditions.
(A-D) Data from worms in the laboratory population (black) and corresponding simulations (red) graphed as in the laboratory population; culling and feeding schedules show the parameter that was varied in blue. The laboratory population data in panel B (10% culling all stages and 10 mg feeding every 24 hours) was used as the training set to determine the value of the following parameters: 1) cost of living and 2) metabolic efficiency (see Supplementary Section 4). (E-G) Comparisons of population summary statistics from the laboratory population (black) and corresponding simulations (red): Average and maximum worm number in initialization and maintenance phase; average, maximum, and minimum worm number in the maintenance phase (see Fig. 1B). Culling and feeding schedules show the parameter that was varied in blue. The red simulated data show similar patterns as the black laboratory data with changing culling and feeding conditions. Values are mean + /- standard deviation of three biological replicates conducted in parallel of wild-type worm populations in the laboratory and three computational simulations.
Extended Data Fig. 3 Comparisons of laboratory and simulated populations in four conditions.
(A-F) Data from worms in representative laboratory populations and corresponding simulations; culling and feeding schedules show the parameter that was varied in color, with data in the corresponding color. (A,C,D,F) Red curves show the laboratory population or simulation with 10% culling of all stages every 24 h and 10 mg feeding every 24 h. (A,B,D,E) Purple curves show the laboratory population or simulation with 10% culling of all stages every 24 h and 5 mg feeding every 24 h. (B,E) Blue curves show the laboratory population or simulation with 5% culling of all stages every 24 h and 5 mg feeding every 24 h. (C,F) Green curves show the laboratory population or simulation with 10% culling of all stages every 48 h and 10 mg feeding every 48 h. (A) Comparison of laboratory populations with 5 mg (purple) and 10 mg (red) feeding. (B) Comparison of laboratory populations with 5% (blue) and 10% (purple) culling. (C) Comparison of laboratory populations with 24 h (red) and 48 h (green) feeding and culling. (D) Comparison of simulations with 5 mg (purple) and 10 mg (red) feeding. (E) Comparison of simulations with 5% (blue) and 10% (purple) culling. (F) Comparison of simulations with 24 (red) and 48 h (green) feeding and culling. The same data are shown in Extended Data Fig. 2.
Extended Data Fig. 4 Flow diagrams of the life cycle in the computational simulation in four conditions.
(A-D) Flow diagrams of simulated populations with indicated feeding and culling schedules. Panel B is the same as Fig. 3H. The node size represents the average number of worms in the population. The arrows represent the average number of worms that transit per 3-hour period from one worm stage to another worm stage. Green, birth transition; blue, developmental transitions; black, cull; brown, starve. The key shows the relationship between node size and average number of worms in that node during the 100-day simulation. Similarly, the key shows the relationship between arrow size and the average number of worms making the transition during a 3-hour time period. Numbers indicate precise arrow values.
Extended Data Fig. 5 Larva & dauer culling influences the size and dynamics of the worm nodes.
Representative simulated populations with 10 mg feeding and 10% (A), 75% (C), 80% (E), and 85% (G) stage-specific culling of larva and dauers (from 4, 6, 7, and 3 simulated populations, respectively). (B,D,F,H) Enlargements show days 50–75, corresponding to the yellow boxes. The number of worms in each node (egg, larva, dauer, adult, and parlad) is shown separately, and the black line shows the sum of all nodes. Note that the adults starve and transition to parlads one or more times in panels B and D, whereas this is not observed in panels F and H. The same simulated populations are shown in Figs. 4,5, Extended data Fig. 6, Supplementary Fig. 11–17
Extended Data Fig. 6 Larva & dauer culling influences the transitions of the bacteria node.
(A-L) Representative simulated populations with 10 mg feeding and 10% (A-C), 75% (D-F), 80% (G-I), and 85% (J-L) stage-specific culling of larva and dauer. The bacteria node is associated with four transitions: (1) bacteria input, bt(i > b), is user programmable and was set to 10 mg/24 h, (2,3) bacteria ingestion by larvae bt(b > l) and adults bt(b > a), (4) bacteria culling, bt(b > c). Because bacteria culling is set to zero as an input parameter in this computational simulation, bt(b > c) is not shown. The transitions of the bacteria node are displayed as mg bacteria/3 hours. (B,E,H,K) Enlargements show days 50–60, corresponding to the yellow boxes. (C,F,I,L) Flow diagrams of the bacteria node. Values represent average mg bacteria/3 hours. The same simulated populations are shown in Figs. 4,5, Extended Data Fig. 5, Supplementary Fig. 11–17
Extended Data Fig. 7 Framework explaining why diverse animals (elephant, C. elegans and mayfly) in populations die of old age.
In life cycle diagrams (left side), lower arrows indicate progeny production, labelled with typical ranges; arrow thickness indicates extent of progeny culling. Arrows on the right show cause of adult death, with thickness indicating fraction: old age (straight purple labelled with maximum lifespan), starve (curve gold), and cull (curve black). Combinations of intrinsic traits (maximum lifespan and progeny number) and environmental conditions (progeny and adult culling) result in elephant, C. elegans in state 2, and mayfly dying of old age in a population.
Supplementary information
Supplementary Data 1
Output file of a single simulated worm.
Source data
Source Data Fig. 1
Laboratory population worm counts and OD’s of bacteria—statistical source data.
Source Data Fig. 2
Individual worm measurements (laboratory and simulation).
Source Data Fig. 3
Laboratory population worm counts and simulated population worm counts.
Source Data Fig. 4
Simulated population counts.
Source Data Fig. 5
Simulated population counts (worm numbers and rates).
Source Data Fig. 6
Simulated population counts.
Source Data Extended Data Fig. 2
Laboratory population worm counts and simulated population worm counts.
Source Data Extended Data Fig. 3
Laboratory population worm counts and simulated population worm counts.
Source Data Extended Data Fig. 5
Simulated population counts (worm numbers and rates).
Source Data Extended Data Fig. 6
Simulated population counts (worm numbers and rates).
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Scharf, A., Mitteldorf, J., Armstead, B. et al. A laboratory and simulation platform to integrate individual life history traits and population dynamics. Nat Comput Sci 2, 90–101 (2022). https://doi.org/10.1038/s43588-022-00190-8
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DOI: https://doi.org/10.1038/s43588-022-00190-8
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