Abstract
Understanding populations is important because 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 C. 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.
Introduction
Animals maintained in laboratories or captivity, where conditions are gentle and consistent, display age-related degenerative changes and progressive frailty; eventually this frailty becomes so severe it results in death, referred to as dying of old age. It is possible to determine the maximum adult lifespan of animals in such a population, which depends on genotype and environment. Maximum adult lifespan varies widely between animals, ranging from ~1 day in mayflies, ~40 days in C. elegans, ~80 years in Asian elephants, and ~120 years in humans. However, animals evolved in the wild, where conditions are neither gentle nor consistent, leading to an important question: do animals in wild populations also display age-related degenerative changes that result in frailty and lead to death? Alternatively, extrinsic causes of mortality such as disease, predation, accident, or starvation may kill wild animals before the onset of age-related frailty. In a foundational paper, Medawar suggested the answer is important for understanding the evolutionary biology of aging1. Based on contemporary studies by field scientists, Medawar thought few senescent-related deaths would occur in wild populations because individuals typically succumbed to extrinsic mortality, an understanding deeply imbedded in the theory he proposed. However, starting in the 1990s, extensive field studies have documented senescence in wild animals from insects to birds and mammals 2–4. For many species, wild animals display age-related degenerative changes that are likely to contribute to mortality, although the extreme frailty displayed by animals aged in captivity are not observed 5,6.
To gain deeper insights into how individual traits such as lifespan impact population dynamics, we used C. elegans, a nematode worm that is a major model system to investigate the molecular and cellular control of aging. Individual C. elegans cultured in the laboratory display age-related degenerative changes that ultimately result in frailty and death, similar to other animals in captivity. However, in nature worms live in populations and environmental conditions fluctuate. To understand the role of aging in these conditions, we established a laboratory system in which a population of C. elegans with an E. coli food source can be propagated indefinitely. By measuring the number of worms and the amount of bacteria, we can monitor the population as it fluctuates over time. C. elegans is well suited for this purpose because of their brief, well-defined lifecycle of ~3 days, brief mean lifespan of ~15 days, and ability to build clonal populations due to its hermaphroditism. Worms can be cultured in liquid medium and counted using an automated system, enabling frequent monitoring of large populations. Laboratory populations, also referred to as experimental microcosms, have a long history in ecology. Ecosystems developed for Didinium nasutum and its prey Colpidium campylum, as well as Daphnia and its prey phytoplankton, have revealed important aspects of population dynamics and predator-prey interactions 7–9.
Individual-based models (also called agent-based) have been used in a variety of applications from economics to ecology. In this modeling approach, the system consists of individuals that operate in an environment. At each time step, the model updates the environment and computes individual behaviors as specified by a series of rules. These models are powerful because the behavior of individuals considered in aggregate results in emergent properties of the population, which are not directly specified. We designed the laboratory population to be well suited for simulation modelling, and the coordinated development of the laboratory population and the individual-based model is a distinctive feature of this study10. Here we describe the development of an individual-based model called wormPOP that is informed by measurements of individual worms in multiple food environments. The model specifies how worms ingest bacteria, grow, transition between stages, lay eggs, and die from old age, starvation or culling. The model is based on conceptualizing the C. elegans life cycle as a flux system, and the outputs include intuitive graphical representations of life cycle dynamics. Thus, the model links the growth and development of individual worms to the emergent properties of the population. The behavior of individual worms in the model closely resembles individuals cultured in the laboratory, and population dynamics in the model closely resemble population dynamics in the laboratory system. We used the simulation to determine how environmental conditions and intrinsic traits of worms influence whether animals in a population die of old age. Large numbers of progeny destabilize food availability, resulting in adult death from starvation. Controlling progeny number by culling stabilizes the bacterial food supply and permits adults to die of old age. The transition between these states displayed tipping point behavior. These results define conditions that make it possible for animals in a population to die of old age, and suggest that populations may alternate between periods when conditions permit animals to die of old age and conditions where this is a rare event.
Results
Experimental design of laboratory populations of C. elegans
To initiate a laboratory population, we introduced 250 wild-type larvae into 5 mL of liquid S-Medium in a 50 mL culture bottle and cultured at 20°C (Figure 1A). To analyze the population, we removed 500 µL (10% volume) samples at regular intervals. We refer to removing volume as culling, since it is a form of extrinsic mortality that mimics predation, disease, or accidents. Culling is randomly distributed over the population, whereas extrinsic mortality in the wild may be influenced by properties of individuals. To maintain a constant volume and provide a source of food, we added 10 mg live E. coli in 500 µL S-Medium immediately after culling, which we refer to as feeding. Culling and feeding were performed every 24 hours for 100 days. Following this procedure, populations can be maintained indefinitely (Supplementary section 1).
Figure 1. A laboratory population of C. elegans and E. coli.
(A) Schematic of the laboratory population: one-time initialization followed by periodic culling, analyzing and feeding. (B,C) Data from wild-type worms in representative laboratory populations. Culling values indicate percent culled (10%), culling interval (24h), and stage of worms culled (all stages). Feeding values indicate amount of bacteria (10mg) and feeding interval (24h). (B) Analysis of summary statistics: time spans (black double arrows) and worm numbers (red double arrows) (C) Bacteria (black squares) and worms (gray circle) were analyzed daily. Yellow box indicates region enlarged in D. (D) Bacteria were analyzed hourly on day 9; bacteria were added between 0 and 1 hour (indicated by red arrow). (E) Three worm populations were initiated on the same day with larvae from the same group of synchronized worms and bacteria from the same concentrated solution (replicate 1a-1c). For the next 100 days, these laboratory populations were maintained separately and never mixed. We designate 1a-1c as biological replicates conducted in parallel. Replicate 1a is shown in panel B. (F) Replicate 2a was initiated on a different day with larvae from a different group of synchronized worms and bacteria from a different concentrated solution. We designate replicate 2a and replicate 1a/1b as biological replicates conducted at different times. Replicate 2a is shown in Figure 3A. (G) Lifecycle of C. elegans in the laboratory population. Adult, egg, larva, dauer and parlad are the five life stages. Birth transition arrows are green: adult to egg, and parlad to dauer. Developmental transition arrows are blue. Death transition arrows are orange (starve), black (cull), and purple (old age). (H) The lifecycle forms the foundation of the computational simulation. The five life stages are the worm nodes. Each node has three to six arrows that depict the worm transitions (wt). The bacteria node has four arrows that depict bacteria transitions (bt). abbreviations: a, adults; b, bacteria; c, cull; d, dauer; e, egg; i, input; l, larva; o, old age; p, parlad; s, starve.
Samples were analyzed using (1) a COPAS Biosort to count the number of worms, and (2) a spectrophotometer to measure OD600, which was converted to bacterial concentration (mg/mL) (Supplementary Figure 1). Populations consistently displayed two phases: (1) the initialization phase extends from beginning the culture until the population peaks and returns to the average size, and (2) the maintenance phase extends from the end of the initialization phase until the end of the experiment (Figure 1B). The initialization phase displayed an increase to a maximum of ~127,000 worms on day 29, and then declined to ~74,000 worms on day 40 (Supplementary Table 1). This pattern reflects the concentration of bacteria, which accumulated during days 1–5, since bacteria are added daily and there are few worms at the beginning (Figure 1C). As the number of worms increases, they consume the excess bacteria and settle into a pattern in which the daily feeding is largely consumed in ~5 hours (Figure 1D). During the maintenance phase (day 41 to 100), the number of worms oscillated with a maximum of ~112,000, minimum of ~58,000 and average of ~81,000. To address reproducibility, we analyzed biological replicates of laboratory populations conducted in parallel or years apart. While every culture displayed a unique pattern of fluctuations of worm number, the overall features are consistent (Figure 1E,F, Supplementary Table 1). However, we have not developed analytic techniques to distinguish between chaotic fluctuations and regular oscillations or measure amplitude and periodicity of the oscillations.
Development of wormPOP using individual worm measurements
Conceptualizing the C. elegans life cycle as a flux system:
The tools to analyze laboratory populations have limitations and do not reveal details such as the developmental stages of individuals, longitudinal information about individual life histories, or cause of death. To complement the laboratory population and address these issues, we created an individual-based computational model where the agents are C. elegans 11–13. The environment of the simulation consists of bacteria in a 5 mL volume. We conceptualized the C. elegans lifecycle as a flux system that accounts for individuals and mass flow (Figure 1G,H). Five nodes correspond to developmental stages of worms: egg, larva, dauer, adult, and parlad (parent/larva/dauer). Dauer is an alternative L3 larval form that is stress resistant. Parlad, also called “bag of worms”, is the result of matricidal hatching, which occurs when hermaphrodites stop laying eggs and self-fertilized eggs hatch into larvae and mature into dauers inside the hermaphrodite 14,15. Starvation can trigger matricidal hatching in fertile hermaphrodites which promotes survival of the fertilized eggs and is most likely adaptive16. Each node is characterized by two values: the number of worms and the total mass of those worms. Nodes are connected by arrows labeled worm transition (wt) that represent rates in units worms/time or mass/time. An egg transitions to a larva when it hatches. A larva eats bacteria and grows; it transitions to an adult when food is plentiful and to a dauer when food is limiting. A dauer transitions to a larva when food is plentiful. An adult eats bacteria, grows, and generates eggs when food is plentiful, thereby transferring germline parental biomass to progeny. An adult transitions to a parlad when food is limiting. A parlad generates dauers, thereby transferring somatic parental biomass to larval progeny. A worm transitions out of the system when it dies from one of three possible causes: all stages can die from culling, larvae and adults can die of starvation, and adults can die of old age. Worm transition rates are not directly specified as parameters of the model but rather are emergent properties of the system.
The system contains one bacteria node that has a value equal to the mass of bacteria in the system. The bacteria node is connected by arrows labeled bacterial transition (bt) that represent rates in units mass/time (Figure 1H). Bacterial mass enters the node by periodic feeding and can exit the system by culling. Bacterial mass transitions to C. elegans larval and adult mass by ingestion. The system is grounded by conservation of mass–worms must consume bacterial mass to grow and produce progeny. The model uses discrete time steps of 3 hours. At each time step, the environment and every virtual worm is evaluated and updated based on a defined set of decision trees (Extended Data Figure 1). The Methods describes the basic decision trees, Supplementary section 2 is an Overview, Design concepts, and Details (ODD) protocol17,18 description of the model, and Supplementary section 3 provides detailed descriptions of decision trees and a comparison to the laboratory population. The frequency and amount of bacteria input, and the frequency and percent culling rate are user-programmable parameters specified for each run. The model compiles the complete trajectory of each individual, including rates of growth, time of transitions, production of progeny, and cause and time of death (Supplementary Table 2 and Supplementary Data 1). Individual data can be combined to yield properties of the population.
Laboratory measurements of worms to inform the simulation:
To create a realistic model, we measured the properties of individuals cultured in conditions similar to the laboratory population: growth of larvae and adults, egg-laying by adults, transition of dauer to reproductive growth, and adult lifespan. The concentration of bacteria was varied to evaluate this key environmental factor. Growth, egg-laying, and dauer transition to reproductive growth were highly sensitive to the concentration of bacteria, whereas adult lifespan was relatively insensitive (Figure 2). Measured data were coded into the decision trees so that virtual worms mimic the behavior of real worms. Simulated individual worms and worms measured in the laboratory displayed similar behavior, providing a first level of validation (Figure 2, Supplementary Figure 2–7, Supplementary Table 3–6). There is variability between biological replicates in the laboratory and between runs of the simulation model. Supplementary Tables 3–6 indicate that variability in the laboratory tends to be greater than variability in the simulation, but not in all cases.
Figure 2. A realistic computational simulation based on measurements of individual animals.
(A-P) Wild-type, self-fertile hermaphrodites were cultured in S-Medium with the indicated concentrations of E. coli bacteria in the laboratory (gray-black lines). Worms were computationally simulated in bacteria concentrations that correspond to the laboratory conditions (red lines). (A, B) Average daily progeny production of individual adults in the laboratory and simulation. The single red curve in A corresponds well with the grey laboratory data with the same concentration of E. coli. (C) Summary statistics: time spans are black arrows (1–3); peak egg number is a red arrow (4); total egg number is the grey area under curve (5). (D) Comparison of peak egg number and total egg number from laboratory and simulations. Values for maximum size are mean +/−s.d. of minimum three independent experiments and for sexual maturity size the mean of two independent experiments for maturation size. (E,F) Average daily mass of individuals in the laboratory and simulation. The single red curve in E corresponds well with the grey laboratory data with the same concentration of E. coli. (G) Summary statistics: time spans are black arrows (1–2); mass values are red arrows (3–4). (H) Comparison of size at sexual maturity and maximum size from laboratory and simulations. Values for maximum size are mean +/−s.d. of minimum three independent experiments and for sexual maturity size the mean of two independent experiments for maturation size. (I,J) A population of dauers were cultured with bacteria starting at t = 0 (data show average percent of larvae in the population). Laboratory animals were in the dauer stage for as long as ten days. Average percentage larva in the laboratory (i) and simulation (i,j). The single red curve in I corresponds well with the grey laboratory data with the same concentration of E. coli. (K) Summary statistics: time span is a black arrow (1); percent larvae is a blue arrow (2). (L) Comparison of percent of dauers that transition after 120 hours from laboratory and computation. Values are mean +/− standard deviation of minimum three independent experiments. (M,N) Survival curves for populations of individuals cultured with the bacterial concentration beginning at the L1 stage in the laboratory (m) and the simulation (m,n) Lower concentrations of bacteria did not cause a substantial extension of adult lifespan, as might have been expected based on studies of caloric restriction. Notably, we initiated exposure to the bacterial concentration at the L1 and L4/young adult (Supplementary Figure 8) stage and continued this same concentration throughout the adult life, whereas caloric restriction experiments often involve specific protocols for exposure to the restricted food environment. (O) Summary statistics: time spans are black arrows (1–2) (P) Comparison of mean adult lifespan from laboratory conditions and computational simulations.
Comparing population dynamics in laboratory and simulation
To compare simulated and laboratory population dynamics, we performed three biological replicates of the laboratory population and three runs of the simulation using 10% culling and 10 mg bacterial feeding every 24 hours for 100 days (Figure 3A,B, Extended Data Figure 2–4, Supplementary Figure 9, Supplementary Table 7). The simulation initialization phase increased to a maximum of ~122,000 worms on day 10, and then declined to ~60,000 on day 18. This pattern reflects the concentration of bacteria, which accumulated for 6 days before declining into a daily oscillation (Figure 3C,F,G). The laboratory population initialization phase increased to a maximum of ~120,000 worms on day 26, and then declined to ~35,000 on day 39. During the maintenance phase, the simulated population oscillated with an average of ~62,000, a maximum of ~104,000, and a minimum of ~21,000; the laboratory population oscillated with an average of ~32,000, a maximum of ~71,000, and a minimum of ~3,000. Although the simulated population displayed larger average, minimum, and maximum numbers of worms, the overall patterns of initialization and maintenance phases were similar.
Figure 3. Population dynamics in the computational simulation.
(A) Data from three biological replicates conducted in parallel of wild-type worms in the laboratory population with culling and feeding schedules shown. These data were used as the training set for the computational simulation (Supplementary Section 4). (B) Data from three computational simulations corresponding to the laboratory population shown in panel A; 1 value/24 h is graphed. (C-G) Stages are shown separately and combined; enlargements show days 40–49. The lines represent 8 values/24 hours (every three hours) (C) Gray line displays the total number of worms (all stages combined), and the black line displays the concentration of bacteria. The lines represent 8 values/24 hours (every three hours). The yellow box indicates the interval enlarged in panels E-G. (D) Stages are shown separately and combined. (E-G) Enlargements show days 40–49, corresponding to the yellow boxes in panels C and D. The number of worms in each node (egg, larva, dauer, adult, and parlad) is shown separately and combined in panel E; panel F only shows stages separately and bacteria. Panel G shows only bacteria, adults and parlads. The worm scale was adjusted to visualize the dynamics of adults in panels E-G. Note that the bacteria level drops to zero on day 43 and day 44 (red arrow), triggering adults to starve and transition to parlads. (H) Flow diagram shows average number of worms in a node by the size of the circle and average number of worms transitioning per 3-hour time step by the size of the arrow; numbers specify arrow values more precisely. See Extended Data Figure 4 for scale bars.
The simulation data includes longitudinal measurements of every individual, allowing a detailed understanding of population dynamics. Figure 3D–G displays the number of animals in each node over time; the population reached a minimum size of ~17,000 animals on day 41, including ~3,000 adults. With food available, these adults produced a burst of eggs that peaked on day 43 with ~60,000 eggs. Eggs hatched into larvae that peaked at ~85,000 on day 45. This large population depleted the bacterial food, triggering starvation as adults transitioned to parlads on day 44 and larvae transitioned to dauers that peak on day 46. As the population declines and bacterial food increases, adults begin to appear on day 47 and a new cycle begins. The average behavior of the system can be displayed graphically, which reveals that most worms are eggs, larvae, and dauer, with few adults and parlads. Adults primarily generate progeny by forming eggs, and primarily die of starvation and culling; very few die of old age. Most larvae starve or form dauer; relatively few transition to adults (Figure 3H).
In constant food environments, individual traits of simulated worms correspond closely to individual traits of worms measured in the laboratory, validating the simulation model in this specific environment. However, in variable food environments the longitudinal experiences of individual simulated worms were not validated by measuring worms in the laboratory. Thus, the model might diverge from reality in these cases, and similarities between population dynamics in the simulation and laboratory population do not formally validate the longitudinal experience of worms in the simulation.
The influence of feeding and culling on population dynamics
Common-sense predicts that decreasing bacterial feeding will decrease the average worm number in the population. To quantitatively investigate this relationship and evaluate the correspondence between laboratory and simulation, we reduced bacterial feeding from 10 mg/24h to 5 mg/24h in both (Extended Data Figure 2B,C,F, 3B,E, 4B,C, Supplementary Table 7). In the laboratory, the average number of worms decreased from 35 ×103 to 15 ×103 (~58%); in the simulation, the average number of worms decreased from 59 ×103 to 33 ×103 (~44%). Thus, laboratory and simulation displayed the same trend, confirming the common-sense prediction. The quantitative change is similar (about 50%), although the absolute number of worms in the simulation is higher than the laboratory.
Common-sense predicts that decreasing culling percent would increase average worm number. Using 5 mg/24h feeding, we reduced culling from 10%/24h to 5%/24h in both laboratory and simulation (Extended Data Figure 2C,D,E, 3B,E, 4C,D, Supplementary Table 7). In the laboratory, the average number of worms increased from 15 ×103 to 29 ×103 (~93%); in the simulation, the average number of worms increased from 33 ×103 to 37 ×103 (~11%). While the quantitative change was larger in the laboratory, the simulation and laboratory displayed the same trend, confirming the common-sense prediction.
We changed both culling and feeding simultaneously by comparing 10 mg bacteria and 10% culling every 24 hours to every 48 hours in both laboratory and simulation (Extended Data Figure 2A,B,G, 3C,F, 4A,B, Supplementary Table 7). Because these changes to culling and feeding have opposite effects, the outcome is not a common-sense prediction. In the laboratory, the average number of worms decreased from 36 ×103 to 26 ×103 (~28%); in the simulation, the average number of worms decreased from 59 ×103 to 24 ×103 (~59%). Thus, the decrease in food is the dominant factor compared to the decrease in culling. The trend is the same in the laboratory and simulation, and the percent decrease was greater in the simulation. In the feeding and culling every 48-hour regime, the number of worms in the laboratory population (26 ×103) and simulation (24 ×103) were very similar. Importantly, simulation parameters were fixed according to the training set (Extended Data Figure 2B) and never changed afterwards to fit laboratory data (see Supplementary section 4).
Old age as a cause of death in the simulation
Progeny number and death from old age:
The simulation indicates adults typically die of starvation and culling, but rarely of old age. To identify conditions where adults frequently die of old age, we reasoned that culling only dauer and larva stages in the simulation would (1) decrease competition for food, thereby reducing starvation as a cause of adult death and (2) by definition eliminate culling as a cause of adult death. When dauer and larva culling in the simulation was varied from 0–85%/24h, the average number of worms decreased from ~66,000 to ~13,000 (Figure 4A). The fraction of eggs and adults increased progressively, whereas the fraction of larva and dauer decreased progressively (Figure 4B,C, Supplementary Table 8). The amount of bacteria displayed an upward inflection around 80%, indicating overall consumption decreases dramatically at this level of dauer and larva culling (Figure 4D). Aging as a cause of adult death displayed tipping point behavior (Figure 4E). With 75%/24h dauer and larva culling, periodic episodes of food deprivation caused ~99% of adults to die of starvation, whereas only ~1% died of old age (Figure 5A–C). Slightly increasing dauer and larva culling to 80%/24h reduced food deprivation to just 3 episodes at the transition to the maintenance phase, and ~52% of adults died of starvation whereas ~48% died of old age (Figure 5D–F). Slightly increasing dauer and larva culling to 85%/24h eliminated episodes of food deprivation, and 100% of adults died of old age (Figure 5G–I). The simulation makes it possible to examine the behavior of each node in these different environments (Extended Figure 5–6, Supplementary Figure 10–17). The egg laying behavior of individual adults in the simulation revealed that dauer and larva culling of 10%/24h results in a low average total progeny number of 25, because adults frequently die of starvation. By contrast, dauer and larva culling of 85%/24h results in an average total progeny number of 106, since adults have adequate bacterial food their entire lives (Figure 4F).
Figure 4. Analysis of the impact of progeny culling on simulated populations.
(A-F) Summary statistics for simulated populations with a variable percentage of dauer & larva culling (values are averages of minimum three independent simulations ): (A) Average number of all worms. (B) Average percent of eggs, larva, and dauer among all worms. The black arrows show the tipping point for 50% and 100% old age as a cause of adult death. (C) Average percent of adults and parlad among all worms. (D) Average amount of bacteria in the bacterial node. (E) Cause of death for adults; with no adult culling, adults only die of starvation or old age. At each point on the horizontal axis, the values sum to 100%. (F) Total progeny number of individual adults in populations with 10, 75, 80, and 85% dauer & larva culling; values are the average +/− SD of three independent simulations with n=153, 258, 83 and 56 total worms, respectively. One-way ANOVA with F=197.3, Df=3, and p < 0.001 followed by a Tukey’s post-hoc HSD, 10–75: P=0.0012, 10–80 P=0.0000003, 10–85 P=0.0000001, 75–80 P=0.000008, 75–85 P=0.000002, 80–85 P=0.17). (G-H) Summary statistics for simulated populations with a variable percentage of egg culling (values are averages of 10 independent experiments): (G) Cause of death for adults; with no adult culling, adults only die of starvation or old age. (H) Average percent of eggs, larva, adults, dauer, and parlad among all worms. (I-J) Summary statistics for simulated populations of mutant worms that do not accumulate as dauers with a variable percentage of dauer & larva culling (values are averages of 10 independent experiments): (I) Cause of death for adults; with no adult culling, adults only die of starvation or old age. (J) Average percent of eggs, larva, adults, dauer, and parlad among all worms.
Figure 5. A tipping point for old age as a cause of death between 75–85% dauer and larva culling.
(A, D, G) The death transitions of the adult node, starve (wt(a>p)) and old age (wt(a>o)), are displayed as number of worms/3 hours. One representative simulated population is depicted for dauer & larva culling of 75% (A), 80% (D), and 85% (G). (B, E, H) Pie charts display the cause of adult death for 75, 80, and 85% dauer & larva culling. (C, F, I) Flow diagrams of the adult node displaying all worm transition rates for 75, 80, and 85% dauer & larva culling. Values in B-I are based on representative simulations. Average values are documented in Supplementary Table 10.
The tipping point is associated with a reservoir of dauers:
To investigate the tipping point phenomenon, we analyzed the effect of culling only eggs in the simulation. When egg culling was varied from 0–90%/6h, the fraction of eggs and adults increased progressively and then displayed an upward inflection around 84% (Figure 4H, Supplementary Table 9). The fraction of larva decreased progressively, and the fraction of larvae, dauer, and parlad displayed a downward inflection around 84%. Aging as a cause of adult death displayed tipping point behavior, with a sharp inflection around 84% (Figure 4G, Supplementary Table 9). These results indicate the tipping point is caused by reducing progeny number, which can be accomplished at the stage of eggs or dauer and larvae. To explore the role of dauers in the tipping point phenomenon, we analyzed simulated mutant worms that cannot effectively transition from larvae to dauer or adult to parlad, and rapidly die of starvation in the dauer stage. This greatly reduced but did not entirely eliminate dauers from the system. When dauer and larva culling in the simulation was varied from 0–85%/24h, the fraction of eggs and adults increased progressively, whereas the fraction of larva decreased progressively (Figure 4J, Supplementary Table 10). Aging as a cause of adult death did not display tipping point behavior, but rather displayed a fairly linear increase in the percentage of animals that die of old age starting at 20% culling (Figure 4J, Supplementary Table 10). Thus, the tipping point phenomenon is associated with a reservoir of dauers and is not intrinsic to the design of the computational simulation.
Maximum lifespan and death from old age:
Having established conditions in the simulation where all adults die of old age, we investigated the effects of intrinsic adult lifespan. Maximum adult lifespan is a user-programmable parameter that was initially set to 40 days based on laboratory measurements 19. To explore this life history trait, we analyzed virtual mutant worms with maximum lifespans of 25 or 60 days. Both mutants displayed a tipping point in the simulation, but the percent dauer and larva culling necessary to cause 50% of adults to die of old age shifts from 77% to 80% to 85% as maximum adult lifespan increased from 25 to 40 to 60 days, respectively (Figure 6A–C, Supplementary Table 8,11–12). Thus, if maximum adult lifespan is longer, then progeny culling must be more stringent to allow adults to die of old age.
Figure 6. Analysis of adult death in simulated populations with different maximum lifespans and adult culling.
(A, B) Average percent of adults that die of old age for simulated populations with a variable percentage of dauer & larva culling. Maximum lifespan was 25, 40, or 60 days. Yellow box indicates enlargement in panel B. (B) Gray lines and numbers depict the lowest percent of dauer & larva culling that causes 50% of adults to die of old age: 25 days (1), 40 days (2), 60 days (3). (C) Bars depict the lowest percent of dauer & larva culling that causes 50% of adults to die of old age based on the data in panel B. (D-F) Summary statistics for simulated populations with a variable percentage of adult culling: average percent of adults that die of starvation, old age or culling. At each point on the horizontal axis, the values sum to 100%. We used the dauer & larval culling value that causes 50% of adults to die of old age with 0% adult culling: 77% for the 25-day maximum lifespan (D), 80% for the 40-day maximum lifespan (E), and 85% for the 60-day maximum lifespan (F). (G) Bars depict the lowest percent of adult culling that causes 0% of adults to die of old age based on the data in panels D-F. (H) Summary of the relationship between maximum lifespan, food security (progeny survival), and extrinsic adult death (culling). Triangles indicate conditions in which more than 50% of adults die of old age. (I) Multiple factors influence the number of adults in the population that die of old age. Values are averages of minimum three independent experiments.
Adult culling and death from old age:
Starting with conditions in the simulation that cause 50% of adults to die of old age and 50% to die of starvation, we analyzed the effect of adult culling. When adult culling was varied from 0–40%/24h, aging and starvation as causes of adult death decreased rapidly, replaced by culling (Figure 6D–F, Supplementary Table 13–15). Long-lived worms were the most sensitive to adult culling, with no animals dying of old age at an adult cull rate of ~20%/24h. By contrast, short-lived worms maintained some adults dying of old age until 40%/24h adult culling (Figure 6G). These results confirm a common-sense prediction, which validates the simulation model, and also establish quantitative relationships between adult culling and the ability of adults to die of old age.
Thus, these observations in the simulation identify three factors that influence aging as a cause of adult death: (1) Large numbers of juveniles create food instability, increasing starvation as a cause of adult death and thereby decreasing old age as a cause of adult death. (2) Adult culling, or extrinsic adult death, decreases old age as a cause of adult death. (3) Intrinsic adult lifespan plays an important role, with short life increasing old age as a cause of adult death and long life doing the opposite (Figure 6H–I).
Discussion
Biological systems are characterized by levels of organization that proceed from microscopically small to immense; understanding the emergent properties that appear at each level is a challenging and important research goal that is inherently interdisciplinary. These levels include atoms, simple molecules, complex macromolecules, organelles, cells, organs, and organisms, encompassing the fields of biochemistry, cell biology, physiology, and developmental biology. In the next level, organisms assemble to form populations, which display the emergent property of population dynamics. We reasoned that life history traits of individual organisms ultimately determine population dynamic behavior, and new tools were needed to elucidate rules that govern the interface between the level of individual organisms and population dynamics. To bridge this gap, we developed a laboratory population with just two species: C. elegans and its food source E. coli. A complementary computational model that simulates C. elegans population dynamics as a flux system based on measured individual traits adds data depth and predictive power.
Controlled laboratory ecosystems have been previously established, mainly with plankton-algae in large water tanks 20, and used to investigate topics such as prey evolution 21, steady state biomass levels 8, or toxicity heavy metals 20. Although the zooplankton species Daphnia magna is used as a model organism 22, it is rarely used in aging studies. By contrast, C. elegans is a premier model organism for studies of development and aging 23. The experimental system described here is distinct in several respects. (1) The C. elegans laboratory population was designed to facilitate a complementary individual-based simulation, so it is well suited for this purpose. (2) The simulation outputs include intuitive graphical representations of the C. elegans life cycle, conceptualized as a flux system, integrating the development and physiology of individuals with the properties of the population. (3) The simulation was designed to facilitate the analysis of mutant worms, creating a platform that complements the large collections of C. elegans mutants that can be analyzed in the laboratory.
C. elegans is difficult to analyze in nature because of its small size and subterranean lifestyle. Wild C. elegans populations are hypothesized to undergo boom-bust cycles 24. A cycle begins when a dauer enters a new food patch, such as a rotten apple. The dauer transitions into a larva, matures, and reproduces to initiate a new population. This population proliferates until the food source is exhausted, leading to the generation of many dauers. These dauers must disperse to find a new food patch to restart the cycle 25. Galimov and Gems (2020) developed an individual-based simulation to test the hypothesis that programmed death is an adaptive strategy for C. elegans to secure food for clonal progeny 26. They modeled a single food patch on a grid that allowed worms to disperse; the endpoint was the number of dauers formed when food is exhausted, interpreted as a measure of colony fitness. Dispersal rates, progeny production, and adult lifespan influenced the number of dauers produced in a single boom-bust cycle. While there are similarities, the approach described here is different in several ways. We measured individual worms in the laboratory as a function of food concentration to establish parameters for the model. wormPOP models an accessible, real-world situation - the laboratory population - and we measured the behavior of the laboratory population to compare with the simulation results. wormPOP has strict mass accounting, which constrains growth and progeny production to the amount of bacterial food ingested by an individual.
In the laboratory population that was analyzed, simulation modeling indicates adults typically die of starvation and culling rather than old age. The simulation was used to identify conditions where adults frequently die of old age. One key factor is progeny number, which was manipulated by stage specific culling. Interestingly, old age as a cause of adult death displays tipping point behavior–it rarely occurs with high levels of progeny but can become frequent when progeny levels are reduced to a critical level. The tipping point did not occur when simulated mutant worms cannot accumulate in the dauer stage, indicating that the tipping point is not an inevitable outcome of the model design. The results suggest that a reservoir of dauers promotes adult death from starvation, because whenever food becomes abundant dauers reenter reproductive development, and consume the excess food. The tipping point suggests the population can exist in two states. State 1 is characterized by frequent episodes of starvation and an abundance of dauers; state 2 is characterized by a stable food supply and an absence of dauers. This result may be related to observations in the wild - abrupt shifts of ecosystems from one state to another state have been observed and described 27,28. We have not confirmed that the tipping point occurs in the laboratory population; thus, it is possible the model deviates from reality in this respect. Future experiments to validate the tipping point in the laboratory require development of new methods to perform stage-specific culling, which may be possible using size exclusion nets, and to determine the cause of adult death, which may be possible by detailed visual inspection and individual culture of worms from the laboratory population.
A second key factor is adult culling. As expected, when adult culling increases, fewer adults die of old age. The third key factor was maximum adult lifespan, with shorter maximum lifespan increasing death from old age compared to longer maximum adult lifespan. However, maximum lifespan only matters in specific conditions; when no animals die of old age or all animals die of old age, maximum adult lifespan was not relevant. Thus, conditions that promote adults dying of old age include, (1) reproductive restraint, which leads to food stability and minimizes death from starvation, (2) infrequent adult culling, and (3) a short maximum adult lifespan.
The factors defined here provide a framework that can explain diverse animals that die of old age in the wild (Extended Data Figure 7). For example, elephants are intrinsically long-lived animals that have been observed to have aging as a cause of adult death in nature. Our model predicts that elephants must have a low level of adult culling and a small number of juvenile animals. Indeed, elephants make very few progeny, and their large size makes them essentially immune to predation29–31. Mayflies have a very short intrinsic lifespan and have been observed to have aging as a cause of adult death in nature. These adults do not ingest food, so they are immune to starvation, and even though they are subject to high levels of adult culling, the lifespan is so short they can still frequently die of old age 32,33.
Our future goal is to combine this experimental platform with the advanced tools of C. elegans genetics to bridge the gap between individual traits and the behavior of populations and expand our understanding of “eco-devo” 34. The current laboratory experiments only involved wild type worms. One future direction is to measure the population dynamics of mutants that have different growth rates, egg laying behavior, adult lifespan, or altered dauer entry and exit behaviors. In the current version of wormPOP, all worms have the identical genotype. The simulation model can be modified to have two or more different genotypes in the same environment, and the laboratory population can also be modified to perform competitions between two or more different genotypes of worms. These advances would allow this platform to integrate population dynamics with population genetics to understand how specific alleles flow through a dynamic population over time. The laboratory population is based on regular addition of E. coli bacteria that do not reproduce because they lack a carbon source. The system could be modified to include a carbon source for bacteria, resulting in two reproducing species and greater ecological relevance. The system has the potential for a deeper investigation of aging. Hughes et al. (2007) proposed that reproductive aging is an adaptive trait that promotes an optimal number of progeny and stabilizes population dynamics35. The experimental system described here establishes the foundation to test this intriguing hypothesis.
Methods
General experimental methods
All experiments were conducted at 20°C with E. coli OP50 and the C. elegans wild-type strain N2. Eggs were isolated by bleach treating gravid adults (2 mL NaOH, 4 mL NaClO, 4 mL H2O) and incubated in M9 for 15–18 hours on a shaker to allow L1 larvae to hatch and arrest development.
Measurements of individual worms
Egg-laying:
Hatched larvae were cultured in 1 mg/mL E. coli/S-Medium for 72 hours until the L4 larval stage, washed 3x with S-medium, and single animals were placed into 96 well plates. The final volume was 150 µL per well with E. coli concentrations of 4, 0.5, 0.25, 0.125, or 0.06 mg/mL. Worms were transferred to new wells every 24 hours, and hatched progeny were counted.
Growth:
Hatched larvae were cultured in 30 mL S-Medium with 16, 12, 4, 2, or 0.4 mg/mL E. coli. Worms were imaged every 24 hours (cross sectional) with a Leica M80 microscope equipped with a camera, and images were analyzed with Image J and the worm sizer plugin 36. Worms were scored as adults when they displayed eggs, and measurements were continued until the first progeny matured to adults. Worm mass was calculated using the measured volume and reported mass densities 37.
Lifespan:
For exposure to different bacteria concentrations from the L1 larval stage, hatched larvae were cultured in 96 well plates with approximately 5–10 larvae per well. Each well contained 100 µl S-Medium and 4, 2, 1, or 0.5 mg/mL E. coli. For exposure to different bacteria concentrations from the L4 larval stage, hatched larvae were first cultured in 2 mg/mL E. coli for 2 days. L4 larvae were then washed and cultured in 96 well plates with approximately 5–10 larvae per well. Each well contained 100 µl S-Medium and 2, 1, 0.5, 0.25, 0.125, or 0.06 mg/mL E. coli. After 48 hours, 0.15 mM 5-fluorodeoxyuridine (FUDR) was added to prevent progeny development. Adults were scored as alive or dead based on movement and body tension. This method was adapted from Petrascheck and Buck (2007)38.
Dauer transition to larva:
To obtain dauer larvae, we cultured a population in liquid medium, starved the animals for 10 days or 1 month, and isolated dauers by treatment with 1% SDS for 30 min 39. 5–10 dauers were placed in 96 well plates with 2, 1, 0.5, 0.25, 0.125, 0.06, 0.03, or 0 mg/mL E. coli. The transition to larvae was scored after 12 hours and every 24 hours thereafter by visual inspection. After 120 hours, we added 4 mg/mL E. coli to the control with no E. coli and measured transition to larvae.
Laboratory population
The population in the laboratory was initialized with 250 larvae and 5 or 10 mg live E. coli in 5 mL of liquid S-Medium 38 in 50 mL cell culture bottle. To analyze the worm number and/or E. coli concentration, we removed 5–10% of the volume every 24 or 48 hours. To maintain a constant volume and provide a source of food, we immediately added 5 or 10 mg live E. coli in 250 or 500 µL S-Medium. Samples were analyzed using (1) a COPAS Biosort to count the number of worms in a 10–50 µL sample, which was used to calculate the total number of worms in the population, and (2) a spectrophotometer to measure OD600, which was converted to bacterial concentration (mg/mL) using a standard curve (Supplementary Figure 1).
Statistics & Reproducibility
Data was organized and plotted in Excel Office 2016 or R (version 3.6.1.,4.1.1.)/RStudio (Version 1.4.1717). Statistical analysis of egg-laying behavior of simulated worms in populations with different dauer & adult culling was done with R (version 3.6.1.,4.1.1.)/RStudio (Version 1.4.1717), using a one-way ANOVA with F=197.3, Df=3, and p > 0.001 followed by a Tukey Post-hoc test (see Figure 4F). All error bars show standard deviations. In lifespan assays, wells with worms were excluded if FUDR treatment failed and P0 could not be distinct from F1 or bacteria concentration was too dense to clearly to observe worms. Worms were censored if wells could not be measured during a lifespan experiment due to worms sticking to plastic walls or cloudiness. In population dynamic experiments data points were excluded if the COPAS biosort failed. No statistical method was used to predetermine sample size. Sample size were chosen based on standard C. elegans procedures, and usually involve 20–100 individual animals which in the experience of C. elegans genetic experiments is thorough35,40. Worms were randomly assigned through pipetting to different food concentrations to measure individual characteristics. The investigators were not blinded to allocation during experiments and outcome assessment.
Design of the individual-based computational simulation model wormPOP
wormPOP is an individual-based model, implemented in Delphi Pascal vx 7. It is programmed in console mode, text only, with input in the form of a single text file and output in the form of CSV files. Source code is available at https://github.com/mitteldorf/C-elegans_pop_dynamics. The only environmental variable is the amount of food in the 5 mL of medium in the vial. Periodically, a portion of the medium is removed and replaced with new food, at times scheduled according to the program input file. When (for example) 1 mL of the medium is removed to be replaced with food, the pre-existing food is reduced by 20%, and every worm at every stage of life is exposed to a probability 0.2 of disappearing from the model. The total volume in the vial is always 5 mL. The amount of food in the vial is decreased with every worm’s consumption, in every time step.
Besides the food in the medium, there are only worms. Individual worms are characterized by the following variables
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Stage of life, with 6 possible values: egg, larva, dauer, adult, parlad, dead (all dead worms are removed from the model at the end of each time step and no longer tracked).
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Birthday: the timestep in which an egg was laid or a parlad burst to release dauers.
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Time of last transition (from egg to larva, or from larva to adult, etc. ).
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Body mass.
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Egg mass (stored by adults, not yet laid).
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Food available in last time step. (Note: Starvation transitions depend on averaging available food over two time steps. Each worm sees a different amount of food in each time step, because worms eat sequentially. More details below.)
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Time of entry into dauer (if applicable), or a notation that this worm has never entered into dauer (if not). This is important because the dauer option is only available to a larva once during its lifetime.
Worm behaviors in each time step are dependent on the amount of food in the environment, on the internal state and, in some cases, on chance. In each time step, the worms are taken in a (different) random order, and the possibilities appropriate to its stage of life are programmed (Extended Data Figure 1). Time is tracked as a floating point variable, and each time step is divided into a number of increments equal to the number of worms alive in that time step. Thus the time of each event is tracked not as an integer count of time steps, but as the real time when that event occurred.
At the beginning of each time step, a number called “appetite” is computed for each worm. How much food would it eat if the current food concentration were available, without competition from other worms? These numbers are summed and each worm is allotted a pro rata “portion” of the available food. Food consumption for each worm is then computed as worms are taken in a random order, and the formula for food consumption for each worm is such as not to exceed that worm’s portion. This helps to mitigate the arbitrary effect of random ordering.
Only larvae and adults eat food. Since lab measurements of food consumption are impractical, appetites are inferred from energy requirements. For larvae, appetite is the sum of (energy required for metabolism + biomass needed for growth) divided by an efficiency constant. Growth is a function of current mass which is derived from an empirical curve that has been fitted to a hyperbolic tangent. For adults, appetite is the sum of these same terms + (biomass needed for reproduction) divided by the same efficiency constant. Exact algorithms for appetite are in Supplementary Table 17.
Eggs:
Eggs are uniform in size, each of mass=65ng. All eggs hatch after (at least) 15 hours = 5 time steps, after which time they have become larvae of 65ng. If an egg is laid late in one time step, and its random order comes up early in the ordering 5 time steps later, it could take almost 6 time steps before the hatching event.
Larvae:
Larvae consume food according to a semi-empirical schedule, depending on their size, the concentration of food in the medium, and the other worms competing for that same food. Food consumption may be limited either by the size of the larva, or by competition for available food. The amount of food consumed in a 3-hour time step is computed according to a formula that takes the two limits into account, and is always less than the smallest of the two. The exact algorithm is in Supplementary Table 17. Biomass consumed by a larva in a given time step is divided among (1) growth, (2) inefficiencies in conversion of food biomass to growth, and (3) energy consumed by metabolism. If food is below a threshold averaged over two consecutive time steps and if the larva is within a range (0.6 x canonical dauer mass < m < 2 x canonical dauer mass) then the larva becomes a dauer. If the larva is smaller or larger than the specified mass range, then it starves to death. If the larva does not dauer or starve, it continues to grow at a rate determined by ingested food. Between time steps 20–28, if its mass exceeds a threshold value=800 ng, it becomes an adult. If it does not achieve this mass by 28 time steps, then it dies of starvation.
Dauer:
Dauers consume no food and lie dormant. They will turn back to larvae and resume growth if they detect sufficient food. The probability per time step for a dauer resuming life as a larva is proportional to the square root of the food concentration times a constant, fixed by experiment at 3.24*10−5, independent of how long it has been a dauer. If a dauer resumes life as a larva, it picks up exactly where it left off, with the same mass and the same (constructive) age. Larvae that have once been dauers cannot take this path a second time. In practice, this means that if food availability again becomes low, they probably will not grow sufficiently to graduate to adulthood, so they will starve.
Adults:
Adults ingest food according to a formula governed by the same two limits described for larvae above. Adults continue to grow. The food they eat is partitioned between metabolism, growth, and egg production, in accordance with measured curves for both growth and fertility. Food consumption slows with age because egg production declines with age. As determined by experiment, egg production rises rapidly to a peak and then declines. The model fertility curve is matched to the experimental curves for five different food levels, and our model of food consumption is inferred from growth and fertility (Supplementary Figure 18). Death from old age is controlled by a Gompertz curve which is calibrated to lab results (independent of food and fertility). Formulas for food consumption and egg production are in Supplementary Table 17. Eggs are rounded down to an integer before appearing as a reproductive event. The fraction is stored as “egg mass” and carried over to the next time step. Logistic growth continues with an asymptotic maximum size. When total food falls below a threshold of 2,500 ng for two successive time steps, an adult transitions to a parlad.
Parlad:
The parlad is dead and does not ingest bacteria, but is presumed to be consumed by the growing larvae within. Worms hatched from a parlad start life as dauers with canonical dauer mass, fixed as 228 ng, which is the geometric mean between egg mass and minimum adult mass. After 10 time steps=30 hours (independent of external conditions), the parlad bursts and releases a number of dauers into the population. The number is determined by reducing the parlad’s biomass by an efficiency factor =2/3, then dividing by mass of one dauer.
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 Figure 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 24h and 10 mg feeding every 24h. (A,B,D,E) Purple curves show the laboratory population or simulation with 10% culling of all stages every 24h and 5 mg feeding every 24h. (B,E) Blue curves show the laboratory population or simulation with 5% culling of all stages every 24 h and 5 mg feeding every 24h. (C,F) Green curves show the laboratory population or simulation with 10% culling of all stages every 48h and 10 mg feeding every 48h. (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 24h (red) and 48h (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 48h (green) feeding and culling. The same data are shown in Extended Data Figure 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 Figure 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 Figure 4,5, Extended data Figure 6, Supplementary Figure 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/24h, (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 Figure 4,5, Extended data Figure 5, Supplementary Figure 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 Material
Acknowledgments
We are grateful to Jonathon Losos for evolutionary insight and eagle viewing; Larry Taber for agent-based model insight; Cheng Huang, Stacie Hughes, Kim Evason, Jim Collins, and Chris Pickett for establishing experimental foundations; Wei Tao, Lu Chen, Alex Sigala, and Asa Earnest for preliminary studies; and Scott 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 and R01 AG057748 to K.K. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Footnotes
Code Availability
The code for modeling population dynamics / wormPOP is available at https://github.com/mitteldorf/C-elegans_pop_dynamics 41. Data for Figures 1–6 was analyzed and plotted with the corresponding source data using Excel with the exception of Figures 2M, 2N, 2P and 4F, which are analyzed using R. Additional information including data analysis with R (version 3.6.1.,4.1.1.)/RStudio (Version 1.4.1717) at https://github.com/Kerry-Kornfeld-Lab/wormPOP1.042.
Declaration of Interest
The authors declare no competing interests.
Data Availability
The settings for the simulation experiments are described in the Supplementary Section 4 and in Supplementary Tables 18–20. Details for the experimental laboratory data is described in the Methods section. Source data for Figures 1–6 and Extended Data Figures 2–6 are provided with this paper.
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Supplementary Materials
Data Availability Statement
The settings for the simulation experiments are described in the Supplementary Section 4 and in Supplementary Tables 18–20. Details for the experimental laboratory data is described in the Methods section. Source data for Figures 1–6 and Extended Data Figures 2–6 are provided with this paper.