Ecology

RESEARCH BRIEFINGS
07 September 2022

A diverse range of marine predators — including tunas, billfishes and sharks — in the North Pacific Ocean cluster together in clockwise-rotating eddies, seemingly to hunt deep-ocean prey, which are unusually abundant there. This suggests that there is a relationship between the foraging opportunities of predators and the energetics of this marine biome. More

We used two agent-based simulation models to investigate the concepts of “cooperate for the spread” and “pay for the escape,” both were net logo models created by Dr. Susan Hanisch.Afterward, we modified the first model to represent the concept of sharing the dispersal costs. We used the second model without modifications. Instead, we assigned definite values of some parameters that highlight the pay for the escape strategy.First modelThe original model was entitled “Evolution and patchy resource”18. She first developed it for educational purposes. It illustrates the concepts of cooperator-cheater competition, natural selection, spatial structure mechanisms, multilevel selection, and founder effects.Changeable variables

Distance-resource-areas: the distance between the centers of the resource areas.

Size-resource areas: the size of resource areas as a radius in the number of patches.

Living costs: the costs that each agent has to deduct from energy per iteration for basic survival.

Mutation rate: The probability that offspring agents have different traits than their parents.

Evolution: the ability of agents to produce offspring.

Constant variables

The number of patches is 112 × 112 patches.

Carrying capacity per patch: Resource = 10, Agents = 1

The growth rate of the resource = 0.2

The resources on a patch regrow by a logistic growth function up to the carrying capacity: New resource level = current resource level + (Growth-Rate × current resource level) × (1 – (Current resource level/carrying capacity)).

The cost for producing offspring is ten subtracted units of energy.

The initial level of energy of agents is set at living costs.

Role of randomness

Agents are distributed randomly in resource areas at the beginning of a simulation.

Sustainable behavior is distributed randomly with a probability of percent sustainables among the initial agent population.

The order in which agents move and harvest within one iteration is random.

Agents move to a randomly selected patch if several patches fulfill the objectives.

The order in which agents produce offspring within one iteration is random.

Agents reproduce offspring with a probability of (0.0005 × Energy).

Agents place offspring on a randomly selected unoccupied neighboring patch.

Offspring mutate with a potential mutation rate.

Model processesIn each iteration, each agent moves around in random order. There are three likelihoods:

If there are no unoccupied patches in a two-patch radius, they stay on the current patch.

If there are unoccupied patches with resources amounting to more than living costs, the agents move to them.

If the resource amount is less than the living costs, the agents move randomly to other unoccupied patches.

The agents harvest the resources from separated patches to gain energy for metabolism and proliferation. If the energy level of any agent falls to zero, it dies. The cooperator type harvests half of the resource, while the greedy type consumes 99%.The living costs are deducted from the energy amount of the agent constantly everywhere all the time. This process occurs whether an agent moves within the patch, between the patches, or even not. Therefore, the model does not consider dispersal cost explicitly.If there is an unoccupied neighbor patch, the agent can reproduce with a probability of 0.0005 of his energy, place the offspring on the unoccupied neighbor patch, and then transfer ten units of the energy to his offspring.Resources regrow only on resource patches. When the resource amount is more than or equal to 0.1, then it regrows. When the resource is less than 0.1, its value is set to 0.1.Output diagrams and monitors

The average energy of agents: average energy levels of sustainable and greedy agents, resulting from resource harvest minus living costs and reproduction.

Trait frequencies: the relative frequencies of sustainable and greedy agents in the total population, resulting from mutations, different reproduction rates, and death.

Agent population: the absolute number of the total population size resulting from reproduction and death.

ModificationsIn the first modification, we added a different type of cost that agents only incur when they disperse from one patch to another (in-between the patches). It is the slider entitled “dispersal costs”.In the second modification, we added another sharing dispersal costs tool to reduce them by dividing their value by the number of included agents (flock-mates) in the identified range from the same type. It is the slider entitled “group-dispersal-range.” which is the flock mate’s areas as a radius in the number of patches. Therefore, changing the value of the group dispersal range will change the area around every agent. Accordingly, the number of its flock mates who share the dispersal costs also adjusts.The group dispersal range is not confined to greedy agents but applies to all agents. Therefore, it represents the case of the wild-type cooperators who can also cooperate for the spread. The group dispersal range also does not only target the agents in between patches. However, it counts the agents inside and outside the patches. For example, once an agent starts its dispersion with a determined range containing ten agents, four from another type, three non-dispersal agents from the same type that existed inside a patch, and three dispersal agents from the same type outside the patches. The dispersal costs for this agent will be divided by 6.Our assumption that non-dispersal agents at the pre-departure stage share dispersion costs with dispersal agents; seems justified because they reap mutual benefits by reducing kin competition inside patches if they promote the migrators. However, can agents remotely pay the dispersion costs? Yes. For instance, some bacterial species can trigger the migration of other species if located in their vicinity, even if the two bacterial colonies are separated by a barrier19,20 or if they are non-motile21. On the other hand, dispersion is an extended process with many factors, including escape from predators, suppression of host defense mechanisms, and production of biosurfactants to reduce surface tension to facilitate motility. Therefore, the agent’s contribution (inside/outside the patches) to support such factors is considered a shared dispersal cost.Finally, cheaters can arise within cooperator patches by mutation or immigration. Therefore, to investigate the efficacy of migration, the mutation rate value should be 0 to cancel its effect in the meta-population dynamics.Second modelThe model is entitled “Evolution, resources, monitoring, and punishment.”22 is a simulation of a population with four types of agents competing for the same resource. It demonstrates many concepts, such as kin selection, cooperation, selfishness, public good, monitoring, punishment, sharing the costs, positive/negative frequency-dependent selection, and multilevel selection. The four agent colors and types: (1) Red: greedy, non-punishing. (2) Orange: greedy, punishing. (3) Turquoise: sustainable, non-punishing. (4) Green: sustainable, punishing.Punishing agents can perceive other agents in their environment to some degree (perception accuracy) and react to their behavior. There are three kinds of punishment: Punishers can kill agents with greedy harvesting behavior, stop them from harvesting in the next iteration, or have them pay a penalty fee to their neighbors.Agents have a cost (energy) to pay for, both detection and punishment, so this behavior is altruistic. Punisher agents of one type share punishment costs equally.Changeable variables

Death rate: the probability that agents die independent of their energy level.

Carrying capacity: the maximum amount of resource units on a patch from 1 to 100.

Growth rate: the rate at which resources on patches regrow. The maximum sustainable yield is calculated based on the carrying capacity and growth rate.

Harvest-sustainable: the number of resource units harvested by sustainable agents.

Harvest-greedy: the number of resource units harvested by sustainable agents.

Perception accuracy: the probability with which punishing agents notice greedy agents.

Costs-perception: the costs in units of energy, punishing agents have to pay for perceiving other agents.

Costs-punishment: the costs as units of energy that punishing agents have to pay in each iteration to punish other agents. All punishing agents of an agent divide the costs of punishment.

Punishment: the kinds of punishing behavior that punishing agents perform.

Fine: if the kind of punishment is “pay fine”, the fine in energy units that punished agents have to pay (shared between all their neighbors).

Living costs and mutation rate: see the first model.

Constant variables

The number of patches: There are 60 × 60 patches in the world.

The initial energy level of agents is set at living costs + 1.

The initial number of resource units on a patch is set to the carrying capacity.

The resources on a patch regrow: see the first model.

Role of randomness* In addition to items in the first model.

Agents take on their traits (harvest preference and ability to notice and punish) randomly based on the probability of percent-sustainable and percent-punishers.

The order in which punishing agents notice greedy agents within one iteration is random.

Greedy agents are noticed by punishing agents with a probability of perception accuracy.

The order in which detected greedy agents are punished within one iteration is random.

Agents produce offspring with a probability of (0.001 × Energy).

Agents die with a probability of (death-rate).

Model processesIn each iteration, each agent attempts to harvest resources from the patches it is on and the eight neighboring patches until the harvest preference level is reached, except for the punished agent with the sanction (suspend harvest once), its harvest amount = 0 in the current iteration. If the amount of resources available is lower than the amount that the unpunished agent attempts to harvest. Then, the agent moves to a neighboring unoccupied patch with the most resources after losing one energy unit as a move cost.Punishers pay the costs of perceiving the greedy agents. The greedy neighbors have been noticed with the probability of perception accuracy. The agent lost an amount of energy as living costs. The agent dies with the likelihood of death rate or if the energy level falls to zero.If there is an unoccupied neighbor patch, the agent can reproduce with a probability of 0.001 of its energy, place the offspring on the unoccupied neighbor patch, and then transfer half of its energy to its offspring that mutate according to the probability of the mutation rate.Resources regrow on all patches. When the resource amount is more than or equal to 0.1, then it regrows. When the resource is less than 0.1, its value is set to 0.1.Output diagrams and monitors

Populations (% of carrying capacity): the state of the resource and the agent population in the world as a percentage of total carrying capacity resulting from resource harvesting behavior and resource regrowth, agent reproduction, and death.

Average harvest per iteration: the average harvested amounts of agents per iteration by trait, resulting from harvested resource units, minus costs for monitoring and punishing (for punishing agents), minus fines (for punished agents in case of punishment “Pay fine”)

The average energy of agents and trait frequencies: see the first model.

How does the model represent a conditional defector strategy?The model aims to highlight the role of kin selection and punishment mechanisms in supporting cooperation evolution against cheats. We did not need to modify the model but just thought about what the conditional defector should do to upside down the game. The answer was to pay for the escape.For instance, if the standard Harvest-greedy of a cheater (greedy, non-punishing) was 13 and the Perception-accuracy of its actual punishers was 75%. Now suppose this cheater faces troubles, and it cannot dominate. However, if it gives up some of its profit to become 12, to escape punishment, and to reduce the perception accuracy to 60%, it could dominate and take over the population.The conditional cheater can pay something and reduce its profit to escape punishment by reducing perception accuracy if there is a positive correlation between these two variables. Therefore, this model is appropriate if it can support/deny such a correlation. More

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Effects of Se and K-humate on nitrogen concentrationsThe N concentration in the soil varied in availability and total content in oat straw and seeds after the foliar application of Se and K-humate. Se alone increased the availability of N in the soil in the following order: Se3  > Se2  > Se1  > control. Thus, Se was found to increase the available N-soil in an application-rate-dependent manner (Table 2). The availability of N-soil after Se application was improved via the simultaneous application of K-humate with the same rate-dependence as observed with Se alone. Comparable results were found using the sum of means for analysis. The insignificant difference found between the sum of means for control and treatment at an Se concentration of 12 × 10−3 mM Se may reflect the relatively low concentration of Se used.Table 2 Effect of selenium and K-humate on nitrogen content.Full size tableThe total N-straw content increased as a result of an increased content of N-plant (Table 2). Differences were found to be insignificant between Se concentrations of 12 × 10−3 mM, 63 × 10−3 mM, and controls. Likewise, the simultaneous application of K-humate showed insignificant differences between Se concentrations of 63 × 10−3 mM and 88 × 10−3 mM. Insignificant differences were noted between the control and Se concentration of 12 × 10−3 mM and the Se concentration of 63 × 10−3 and 88 × 10−3 mM using the sum of means. The total N-seeds content increased for application rates of 12 × 10−3–88 × 10−3 mM, and the simultaneous application of K-humate augmented this increase. The application rate dependency of the effects of Se and K-humate application was identical to that observed in N-soil and N-straw. No significant differences among Se and K-humate applications were observed. An insignificant difference was observed among the sum of means for Se and K-humate applications at concentrations of 63 × 10−3 and 88 × 10−3 mM.The application of Se caused proportional increases in N-soil, N-straw, and N-seeds, and the simultaneous application of K-humate improved this effect. Previously, the application of Se resulted in an increase in the accumulation of NPK which altered N and K distribution. However, the distribution of P was not affected19. Furthermore, the application of Se ultimately resulted in an increase in the accumulation of N, calcium (Ca), K, and Mn20. A significant increase in concentrations of N and S in the rice grain plants grown under N-limiting conditions was also observed while the Ca that have been treated with Se regardless of N supply21. Thus, a synergistic interaction between Se and N in total grain proteins was reported21.Effects of Se and K-humate on PThe effect of applications of different Se concentrations without K-humate on the available P-soil showed a reduction in the following order: Se3  > Se2  > Se1  > control (Table 3). Thus, the foliar application rate of Se caused a rate-dependent increase in the available P-soil. Simultaneous application of K-humate further increased P-soil availability. A rate dependency similar to Se alone was also observed with simultaneous Se and K-humate application. A similar result was observed using the sum of means for data analysis. Significant differences were observed among all treatments.Table 3 Effect of selenium and K-humate on phosphorous content.Full size tableFoliar application of Se increased total P-straw. An insignificant difference was found between the control and Se concentrations of 12 × 10−3 and 63 × 10−3 mM, which was similar to findings observed after the application of K-humate. Moreover, insignificant differences were observed between the applications of Se and Se + K-humate. An insignificant effect was found between control and Se concentrations of (12 × 10−3 and 63 × 10−3 mM), and K-humate application using the sum of means.The application of Se having concentrations ranging from 12 × 10−3 to 88 × 10−3 mM resulted in increased P-seeds and the addition of K-humate augmented this effect (Table 3). The effect of Se and K-humate applications showed a decrease in the following order: Se3  > Se2  > Se1  > control. Insignificant differences between values were observed when Se was applied without K-humate at concentrations of 12 × 10−3 and 63 × 10−3 mM, and for the sum of means for Se and K-humate applications at concentrations of 12 × 10−3 and 63 × 10−3 mM. Thus, the application rate of Se caused a proportional increase in P-soil, P-straw, and P-seeds. Furthermore, the simultaneous application of K-humate augmented this effect.Consistently, concentrations of P and Ca increased in response to the application of selenite-Se (Na2SeO3⋅5H2O) to maize seedlings22, and the application of Se led to an increase in the accumulation of NPK, with alteration of N and K distribution. However, the distribution of P was not influenced19.Effects of the foliar application of Se and K-humate on KDifferent application rates of Se without humate increased K-soil and this effect showed a decrease in the following order: Se3  > Se2  > Se1 = control (Table 4). Again, the foliar application rate of Se causes a proportional increase, in this case, in K-soil. The application of K-humate with Se augmented this effect. A similar rate dependency was also observed with simultaneous application and when the sum of means was used. An insignificant difference was observed between the sum of means for controls and Se concentrations of 12 × 10−3 mM.Table 4 Effect of selenium and K-humate on potassium content.Full size tableThe foliar application of Se led to a slight increase in the total K-straw content (Table 4). An insignificant change was observed for Se concentrations from 12 × 10−3 to 88 × 10−3 mM, and similar results were found with the additional application of K-humate.The application of Se at concentrations from 12 × 10−3 to 88 × 10−3 mM resulted in a slight increase in K-seeds, and the additional application of K-humate only slightly increased the accumulation of K (Table 4). An insignificant difference was observed between Se alone and with K-humate. Similar findings were noted when the sum of means was used for analysis. Se application rates thus produce a proportional increase in K-soil but not in K-straw or K-seeds. Comparable data were noted after K-humate addition. Concentrations of K previously decreased in response to selenite-Se (Na2SeO3⋅5H2O) application to maize seedlings; however, magnesium (Mg) concentrations did not change22. Moreover, the application of Se led to the accumulation of NPK and altered N and K distribution without affecting the P distribution19. Consistently, the application of Se ultimately resulted in increasing K accumulation20.Effects of Se and K-humate application on oat growthApplication of Se improved the yield, which was assessed as kg × 10−3/feddan (Table 5). Higher concentrations of Se produced a higher yield of oat. The effect of Se showed a reduction in the following order: Se3  > Se2  > Se1  > control. The simultaneous application of K-humate increased the yield only slightly, resulting in insignificant differences. Similar findings were also observed when the sum of means was used. In contrast, seed production was not significantly affected, and plant length (m × 10–2) did not show a significant response. In contrast, Se application to potato plants enhanced tuber yield, plant growth, and quality compared with controls. Moreover, Se application along with different N additions ultimately increased potato productivity compared with Se or N alone23. Similarly, the grain yield increased when Se was applied; this application was significant at low levels24.Table 5 Effect of Se and K-humate application on oat growth.Full size tableEffects of Se and K-humate applications on OMS (%) and non-enzymatic antioxidants and total phenols in oat plantsThe total OMS content increased with increasing Se concentrations, perhaps due to stimulation of root growth or microbial biomass. This effect showed a decrease in the following order: Se3  > Se2  > Se1  > control. The addition of K-humate by foliar application significantly augmented the OMS content (%) (Table 6). Application of Se also increased the non-enzymatic antioxidant content; however, the increases were insignificant at Se concentrations of 12 × 10−3 and 63 × 10−3 mM. The highest values for non-enzymatic antioxidants were observed at Se concentrations of 88 × 10−3 mM. The application of K-humate along with Se did not significantly augment the effects observed after the application of Se alone. Analyses using the sum of means were completely consistent with these findings.Table 6 Effect of selenium and K-humate application on organic matter in soil (OMS), non-enzymatic antioxidant, and total phenols in oats.Full size tableSe positively enhanced the total phenol content with effects decreasing in the following order: Se3  > Se2  > Se1  > control. Furthermore, this effect was significantly amplified with the simultaneous application of K-humate. Analysis using the sum of means gave comparable results. Se enhances the ability of plants to cope with stress by stimulating plant cell antioxidant capacity though the upregulating of antioxidant enzymes, such as CAT, SOD, and GSH-Px. Se also increases the synthesis of PCs, GSH, proline, ascorbate, alkaloids, flavonoids, and carotenoids. Se may also induce the spontaneous dismutation of the superoxide radical into H2O2. Elevated antioxidant capacity can reduce lipid peroxidation by lowering ROS accumulation under metal-induced oxidative stress conditions25. Application of Se using foliar spray also induced an increase in the concentration of rosmarinic acid20.Effects of Se and K-humate applications on Se contentAfter the application of Se, Se-soil concentrations increased. The effects of Se concentrations decreased in the following order: Se3  > Se2  > Se1  > control. The additional application of K-humate significantly amplified these effects (Table 7). The treatment of K-humate that increased Se content in the soil may be owing to experimental errors, however, increasing Se content in either straw or seeds may be owing to the increased stimulating movement from soil to different parts of the plant. Se-straw content increased with increasing the Se foliar application; this effect decreased in the following order: Se3  > Se2  > Se1  > control. The simultaneous application of K-humate augmented the effects observed after the application of Se alone. Total Se concentration also increased Se-seeds like Se-straw for Se alone, Se with K-humate, and using the sum of means for analysis.Table 7 Effects of Se and K-humate applications on Se content.Full size tableEffects of Se and K-humate application on Cr contentThe highest concentrations of Cr were observed in control plants followed by Se2  > Se3  > Se1. In response to Se application, the Cr-straw content decreased (Table 8). The difference between Se2 and Se3 was insignificant. K-humate addition induced a notable increase in Cr-straw in the following order: control  > Se3  > Se2  > Se1. This may be owing to the increased stimulating movement of Cr from soil to different parts of the plant. Results obtained from Se treatments varied depending on the presence of K-humate. Cr-seeds decreased in the following order: Se2  > Se3  > Se2  > control. The addition of K-humate increased the Cr-seed content compared with Se alone; however, the difference between Se2 and Se3 was insignificant. Analysis using the sum of means did not produce significant differences.Table 8 Effects of Se and K-humate application on Cr content.Full size tableEffects of Se and K-humate applications on Fe contentVariable effects were produced using different application rates of Se on Fe-straw, and this effect was observed in the following order: Se3  > Se1  > control  > Se2 (Table 9). Differences were insignificant among control, Se1, and Se2. K-humate caused concentrations of Fe-straw to significantly increase in the following order: control  > Se3  > Se2  > Se1. Differences between control and Se3 as well as Se1 and Se2 were insignificant. Analysis using the sum of means was similar. Neither Se nor Se with K-humate applications produced significant changes in Fe-seeds. Analysis using the sum of means was similar. Low concentration of Se application may enhance plant productivity and encourage phytoremediation by improving plant tolerance to stress and enhancing photosynthesis25. Further, a significant increase was observed in concentrations of Fe and S in rice grain grown in N-limiting conditions while Ca that have been treated with Se regardless of N supply21.Table 9 Effects of Se and K-humate applications on Fe content.Full size tableEffects of Se and K-humate application on Mn contentApplication of Se reduced the Mn-straw content, and this effect was observed in the following order: control  > Se2  > Se1  > Se3. No significant difference was found between control and Se1 (Table 10). In contrast, K-humate addition further reduced Mn-straw concentrations in the following order: control  > Se1  > Se3  > Se2. The control and Se1 were not significantly different when using the sum of means for analysis. Likewise, no significant difference was seen between Se1 and Se3. Accumulation of Mn in seeds varied among treatments in the following order: control  > Se2  > Se3  > Se1. K-humate addition altered this order to be in the following order: control  > Se2  > Se1  > Se3. No significant differences were observed between Se2 and Se3 when the sum of means for analysis was used. Previously, the application of Se increased the concentrations of Mg and molybdenum in grains grown in 16 and 24 mM N compared with N-limited plants21.Table 10 Effects of Se and K-humate application on Mn content.Full size tableEffect of Se and K-humate applications on Zn content in oat plantsApplication of Se2—the middle concentration of Se—resulted in highest accumulation in Zn-straw, and this effect was observed in the following order: Se2  > Se1  > control  > Se3 (Table 11). The application of K-humate with Se resulted in some insignificant variations compared with the application of Se alone. Control, Se1, and Se3 were insignificantly different when the sum of means was used for the analysis. Concentrations of Zn in seeds were reduced after Se application. K-humate with Se foliar application altered the concentration of Zn in seeds with impacts in the following order: control  > Se3  > Se1  > Se2. The difference between Se1 and Se3 was insignificant. Additionally, insignificant differences in Zn concentrations after application of Se1, Se2, and Se3 were found when the sum of means was used for analysis. Low concentrations of Se possibly enhance plant productivity and phytoremediation capacity by improving the ability of plants to tolerate stress and enhancing photosynthesis25.Table 11 Effect of Se and K-humate applications on Zn containing oat plant.Full size tableEffects of Se and K-humate application on Cu contentIncreasing concentrations of Se from 12 × 10−3 to 88 × 10−3 mM increased the concentration of Cu-seed, and this effect was observed in the following order: Se1  > control  > Se2  > Se3 as it shown in Table 12. Application of Se with K-humate showed significant changes in the Cu-straw content in the following order: Se1  > Se2  > control  > Se3. No significant differences were observed using the sum of means for analyses. In contrast, the foliar application of Se resulted in increases in Cu-seed at concentrations of Se1 and Se3; however, at 63 × 10−3 mM (Se2), a reduction in Cu-seed was observed. K-humate with Se simultaneously resulted in increased Cu-seed content with impacts decreasing in the following order: Se3  > Se1  > control  > Se2. The sum of means analysis showed no significant variation between control and Se2. Previously, the application of Se led to a decrease in the concentrations of Cu in grains grown in 16 and 24 mm N compared with N-limited plants21.
Table 12 Effects of Se and K-humate application on Cu content.Full size table More

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