Marginal Value Theorem Research Articles

A reward self-bias leads to more optimal foraging for ourselves than others.

People are self-biased for rewards. We place a higher value on rewards if we receive them than if other people do. However, existing work has ignored one of the most powerful theorems from behavioural ecology of how animals seek resources in everyday life, the Marginal Value Theorem (MVT), which accounts for optimal behaviour for maximising resources intake rate. Does this self-bias help humans maximise rewards when foraging for their own benefit compared to foraging for the benefit of others? Participants had to decide when to leave patches where reward intake was gradually depleting, in environments with different average reward rates. Half of the time participants foraged for themselves, and in the other half they collected rewards for an anonymous stranger. The optimal MVT derived solution states people should leave when the instantaneous reward intake in a patch equals the average rate in an environment. Across two studies, people were more optimal when foraging for self, showing a reduced sensitivity to instantaneous rewards when foraging for other. Autistic traits were linked to reduced sensitivity to reward rates when foraging for self but not for other. These results highlight that the self-bias may be adaptive, helping people maximise reward intake.

Stoichiometric theory in optimal foraging strategy.

Understanding how organisms make choices about what to eat is a fascinating puzzle explored in this study, which employs stoichiometric modeling and optimal foraging principles. The research delves into the intricate balance of nutrient intake with foraging strategies, investigating quality and quantity-based food selection through mathematical models. The stoichiometric models in this study, encompassing producers and a grazer, unveils the dynamics of decision-making processes, introducing fixed and variable energetic foraging costs. Analysis reveals cell quota-dependent predation behaviors, elucidating biological phenomena such as "compensatory foraging behaviors" and the "stoichiometric extinction effect". The Marginal Value Theorem quantifies food selection, highlighting the profitability of prey items and emphasizing its role in optimizing foraging strategies in predator-prey dynamics. The environmental factors like light and nutrient availability prove pivotal in shaping optimal foraging strategies, with numerical results from a multi-species model contributing to a comprehensive understanding of the intricate interplay between organisms and their environment.

No matter what you do, travel is travel in visual foraging

In visual foraging, foragers collect multiple items from a series of visual displays (or “patches”). When the goal is to maximize the total or the rate of collection of target items, foragers must decide when to leave a depleted patch given that “traveling” from one patch to another incurs a temporal cost. In three experiments, we investigated whether the interposition of a secondary task during travel between patches in visual foraging altered patch-leaving behavior. Over the course of 10- or 30-minute experiments, participants foraged in simulated “berry patches” and traveled to the next patch at will. While they traveled, they either actively performed a secondary task or simply observed passing visual stimuli. Travel time was varied across conditions. The addition of a secondary task, regardless of its relevance to visual foraging, to traveling, or to both, did not impact patch-leaving times in the primary visual foraging task. In Experiment 1 and more weakly in Experiment 2, the patch-leaving decision was based on how long the travel took as predicted by the Marginal Value Theorem (MVT). In Experiment 3, however, patch-leaving did not depend on travel time. Participants ‘overharvested’ in a manner that suggests that they may have adopted rules different from those of MVT. Across all three experiments, patch-leaving did not depend on the nature of the travel.

Differential patch-leaving behavior during probabilistic foraging in humans and gerbils

Foraging confronts animals, including humans, with the need to balance exploration and exploitation: exploiting a resource until it depletes and then deciding when to move to a new location for more resources. Research across various species has identified rules for when to leave a depleting patch, influenced by environmental factors like patch quality. Here we compare human and gerbil patch-leaving behavior through two analogous tasks: a visual search for humans and a physical foraging task for gerbils, both involving patches with randomly varying initial rewards that decreased exponentially. Patch-leaving decisions of humans but not gerbils follow an incremental mechanism based on reward encounters that is considered optimal for maximizing reward yields in variable foraging environments. The two species also differ in their giving-up times, and some human subjects tend to overharvest. However, gerbils and individual humans who do not overharvest are equally sensitive to declining collection rates in accordance with the marginal value theorem. Altogether this study introduces a paradigm for a between-species comparison on how to resolve the exploitation-exploration dilemma.

Applying the marginal value theorem when risk affects foraging behavior

Applying the marginal value theorem when risk affects foraging behavior

Gaze-based human intention prediction in the hybrid foraging search task

An agent’s ability to predict a human’s intention can facilitate the effectiveness of a human-agent team. The aim of this study was to explore the feasibility of predicting human intention in the hybrid foraging search task using eye gaze data and machine learning. In the hybrid foraging search paradigm, the human performs searches in patches and decides to stay and exploit a patch or to leave and explore another patch. Researchers have modeled the “patch-leaving problem” on the collective level using the marginal value theorem. However, few have attempted to predict the exact moment when the human will leave. In the current study, 40 participants performed the hybrid foraging search task while eye gaze data were collected with an eye-tracker. The leaving intention was associated with larger pupil size, shorter average fixation duration, larger number of fixations, longer saccade amplitude, and faster saccade velocity compared to the searching intention. A cross-subject machine learning model with an artificial neural network algorithm was able to predict whether a participant would leave the current patch with up to 78% accuracy with a 2-second data analysis window. The length of the data analysis window did not significantly affect prediction accuracy. Furthermore, the earlier the behavior prediction was made, the lower the reliability of the prediction. These results demonstrate that eye gaze features and machine learning algorithms are useful in predicting human intention in visual search tasks.

School of Rocks: a Transmission Time Investment Model for Pleistocene Lithic Technology

We propose a transmission time investment model for integrating the tenets of human behavioral ecology and cultural evolutionary theory to investigate agency and optimality in the social transmission of lithic technologies. While the cultural transmission process is often overlooked in discussions of optimality, we view it as a critical area for the application of adaptive reasoning to further understand the mechanisms responsible for change in lithic technologies. The proposed model modifies a technological intensification model based on the marginal value theorem (Bettinger et al. Journal of Archaeological Science, 33(4), 538–545, 2006; Mohlenhoff and Codding Evolutionary Anthropology, 26(5), 218–227, 2017) to explore how transmissibility may have affected the complexity of socially transmitted lithic production systems during the Pleistocene. This transmission investment model is contrasted with a passive demographic model derived from traditional explanations for changes in lithic technologies. To highlight how optimal considerations of transmissibility may have affected the long-term evolution of lithic technologies, we apply this model to three Pleistocene archaeological case studies investigating increases and decreases in lithic technological complexity. We propose that technological changes in each of these case studies is consistent with the predictions of the model, suggesting that time management strategies may have played a role in the long-term evolution of Pleistocene technologies. It is unlikely that transmission constraints alone were wholly responsible for the observed patterns, and future research should refine the measures of time availability and cost used here, as well as explore the interplay between transmission investment and other optimizing and social constraints.

Drivers of polar bear behavior and the possible effects of prey availability on foraging strategy

BackgroundChange in behavior is one of the earliest responses to variation in habitat suitability. It is therefore important to understand the conditions that promote different behaviors, particularly in areas undergoing environmental change. Animal movement is tightly linked to behavior and remote tracking can be used to study ethology when direct observation is not possible.MethodsWe used movement data from 14 polar bears (Ursus maritimus) in Hudson Bay, Canada, during the foraging season (January–June), when bears inhabit the sea ice. We developed an error-tolerant method to correct for sea ice drift in tracking data. Next, we used hidden Markov models with movement and orientation relative to wind to study three behaviors (stationary, area-restricted search, and olfactory search) and examine effects of 11 covariates on behavior.ResultsPolar bears spent approximately 47% of their time in the stationary drift state, 29% in olfactory search, and 24% in area-restricted search. High energy behaviors occurred later in the day (around 20:00) compared to other populations. Second, olfactory search increased as the season progressed, which may reflect a shift in foraging strategy from still-hunting to active search linked to a shift in seal availability (i.e., increase in haul-outs from winter to the spring pupping and molting seasons). Last, we found spatial patterns of distribution linked to season, ice concentration, and bear age that may be tied to habitat quality and competitive exclusion.ConclusionsOur observations were generally consistent with predictions of the marginal value theorem, and differences between our findings and other populations could be explained by regional or temporal variation in resource availability. Our novel movement analyses and finding can help identify periods, regions, and conditions of critical habitat.

Dispersal and distribution of a generalist predator in habitats with multiple food resources

The ability to locate suitable food resources affects fitness in animals. Therefore, movements are necessary to optimize foraging in habitats where food is distributed in patches of different qualities. The aim of this work was to investigate the dispersal and distribution of females and males of the omnivorous mirid D. hesperus in mesocosms composed by food patches of different values in terms of fitness. In agreement with the Marginal Value Theorem (MVT) and the Ideal Free Distribution (IFD), individuals were expected to aggregate in the highest quality patches. Besides, the proportion of individuals in patches was predicted to be proportional to fitness, and interference among individuals was expected to rise as the density of individuals increased. Emigration rates were predicted to be higher for low- than for high-quality patches, while the opposite was predicted for immigration. Three types of habitats each with different combinations of food resources were tested: (1) habitat including patches of tomato plants with no-prey, and patches infested with either mite or whitefly; (2) with no-prey and whitefly; (3) with no-prey and mites. Each type of habitat was set up in a tomato greenhouse compartment and replicated four times. Individuals were tracked by mark-recapture methods using luminous paintings. The number of females and males in whitefly patches was significantly higher than in mite and no-prey patches, but a significant interaction sex*habitat and sex*patch was found. In habitats with only one type of prey, D. hesperus adults fitted the IFD, while in mixed prey habitats their distribution diverged from IFD. Interference was found to be significant, with female fitness decreasing as their density increased. Emigration rates were significantly lower for whitefly patches with a significant interaction patch*sex; the opposite was found for immigration. This research shows that it is unlikely that D. hesperus forage according to the omniscient principle of IFD and MVT; in contrast, it strongly suggests that it uses some simple rules to make decisions about inter-patch movement, and emigration from habitats and patches.

Quitting rules in hybrid foraging search: From early childhood to early adulthood

In hybrid foraging, observers search for multiple instances of multiple target types. Children regularly perform such tasks (e.g., collecting LEGO pieces or looking for different teammates within a game). Quitting rules (When do you leave the search?) are important in foraging (e.g., I found enough LEGOs or teammates). However, the development of quitting behavior has not yet been experimentally studied, and it could give us significant information about executive function development. We tested 279 observers (4–25 years old) using classic feature and conjunction foraging. The results show that while children’s performance improved with age, all groups made similar "quitting" decisions roughly following optimal choices as defined by Charnov’s Marginal Value Theorem (MVT), with the youngest 4–5 years old children quitting slightly earlier. It seems that mature quitting rules in search operate relatively early in development, suggesting that those rules are quite basic aspects of the human cognition. • We studied the development of quitting rules in foraging under the Charnov's MVT. • We obtained similar results in feature/conjunction and real-world stimuli foraging. • Children as young as 4 years-old show roughly optimal quitting behavior. • Results show MVT-consistent quitting rules seem to operate early in development. • Other results replicate previous works on visual search development.

Estimating the time when the population leaves the patch

The article analyzes a classical result of the optimal foraging theory – E. Charnov’s Marginal Value Theorem (MVT), according to which the population leaves the patch containing a food resource at the time instant when the average rate of energy consumption is maximum. Observations show that the real time spent by the population in the patch often differs significantly from thetime predicted according to MVT. The proposed model takes into account the state of food resources in the patch, permitting to formulate a new approach to estimating the time when the population will leave the patch. In doing so, we use the concept of food attractiveness of the patch introduced previously by one of the authors. It is shown that the time of the population’s departure from the patch lags behind the departure time estimated by MVT, which is consistent with real-life observations

Rat Anterior Cingulate Cortex Continuously Signals Decision Variables in a Patch Foraging Task.

In patch foraging tasks, animals must decide whether to remain with a depleting resource or to leave it in search of a potentially better source of reward. In such tasks, animals consistently follow the general predictions of optimal foraging theory (the marginal value theorem; MVT): to leave a patch when the reward rate in the current patch depletes to the average reward rate across patches. Prior studies implicate an important role for the anterior cingulate cortex (ACC) in foraging decisions based on MVT: within single trials, ACC activity increases immediately preceding foraging decisions, and across trials, these dynamics are modulated as the value of staying in the patch depletes to the average reward rate. Here, we test whether these activity patterns reflect dynamic encoding of decision-variables and whether these signals are directly involved in decision-making. We developed a leaky accumulator model based on the MVT that generates estimates of decision variables within and across trials, and tested model predictions against ACC activity recorded from male rats performing a patch foraging task. Model predicted changes in MVT decision variables closely matched rat ACC activity. Next, we pharmacologically inactivated ACC in male rats to test the contribution of these signals to decision-making. ACC inactivation had a profound effect on rats' foraging decisions and response times (RTs) yet rats still followed the MVT decision rule. These findings indicate that the ACC encodes foraging-related variables for reasons unrelated to patch-leaving decisions.SIGNIFICANCE STATEMENT The ability to make adaptive patch-foraging decisions, to remain with a depleting resource or search for better alternatives, is critical to animal well-being. Previous studies have found that anterior cingulate cortex (ACC) activity is modulated at different points in the foraging decision process, raising questions about whether the ACC guides ongoing decisions or serves a more general purpose of regulating cognitive control. To investigate the function of the ACC in foraging, the present study developed a dynamic model of behavior and neural activity, and tested model predictions using recordings and inactivation of ACC. Findings revealed that ACC continuously signals decision variables but that these signals are more likely used to monitor and regulate ongoing processes than to guide foraging decisions.

The role of food odor in invertebrate foraging.

Foraging for food is an integral part of animal survival. In small insects and invertebrates, multisensory information and optimized locomotion strategies are used to effectively forage in patchy and complex environments. Here, the importance of olfactory cues for effective invertebrate foraging is discussed in detail. We review how odors are used by foragers to move toward a likely food source and the recent models that describe this sensory-driven behavior. We argue that smell serves a second function by priming an organism for the efficient exploitation of food. By appraising food odors, invertebrates can establish preferences and better adapt to their ecological niches, thereby promoting survival. The smell of food pre-prepares the gastrointestinal system and primes feeding motor programs for more effective ingestion as well. Optimizing resource utilization affects longevity and reproduction as a result, leading to drastic changes in survival. We propose that models of foraging behavior should include odor priming, and illustrate this with a simple toy model based on the marginal value theorem. Lastly, we discuss the novel techniques and assays in invertebrate research that could investigate the interactions between odor sensing and food intake. Overall, the sense of smell is indispensable for efficient foraging and influences not only locomotion, but also organismal physiology, which should be reflected in behavioral modeling.

A stone in the hand is worth how many in the bush? Applying the marginal value theorem to understand optimal toolstone transportation, processing, and discard decisions

Obtaining and transporting material for manufacturing flaked stone tools comes at a cost. Numerous studies evaluate how processing may reduce transport costs, often using models of optimal foraging theory such as central place foraging and field processing. However, to date these studies do not adequately address the continued reuse of toolstone through space and time, or the repeated use of toolstone by multiple individuals. To remedy this, we offer a novel theoretical framework for the conveyance of lithic material derived from the logic of the marginal value theorem. This framework explains changes in lithic acquisition, use, and discard in terms of changing environmental context. Specifically, this study examines the effect of distance from a geological source of lithic material on access to anthropogenic sources of lithic material, including previously discarded tools and cores, and quantifies these spatial patterns in terms of optimal processing before discard. We evaluate the strengths and weaknesses of past and current modeling approaches, and test predictions developed using the marginal value theorem through an artifact inventory and analysis of archaeological sites in the lower Dolores River canyon lands in southeastern Utah. The results of this case study support model predictions, showing that the degree of processing and use intensity represented in lithic assemblages increase in response to the decreasing quality and abundance of available lithic material that occurs with increased distance from the geological source. This theoretical framework offers some general insights that can explain variation in the distribution of lithic artifacts across diverse archaeological contexts.

Whither the science in wildlife management?

Whither the science in wildlife management?

A model of naturalistic decision making in preference tests

Decisions as to whether to continue with an ongoing activity or to switch to an alternative are a constant in an animal's natural world, and in particular underlie foraging behavior and performance in food preference tests. Stimuli experienced by the animal both impact the choice and are themselves impacted by the choice, in a dynamic back and forth. Here, we present model neural circuits, based on spiking neurons, in which the choice to switch away from ongoing behavior instantiates this back and forth, arising as a state transition in neural activity. We analyze two classes of circuit, which differ in whether state transitions result from a loss of hedonic input from the stimulus (an "entice to stay" model) or from aversive stimulus-input (a "repel to leave" model). In both classes of model, we find that the mean time spent sampling a stimulus decreases with increasing value of the alternative stimulus, a fact that we linked to the inclusion of depressing synapses in our model. The competitive interaction is much greater in "entice to stay" model networks, which has qualitative features of the marginal value theorem, and thereby provides a framework for optimal foraging behavior. We offer suggestions as to how our models could be discriminatively tested through the analysis of electrophysiological and behavioral data.

Certainty and uncertainty of the future changes planning and sunk costs.

Many foraging experiments have found that subjects are suboptimal in foraging tasks, waiting out delays longer than they should given the reward structure of the environment. Additionally, theories of decision-making suggest that actions arise from interactions between multiple decision-making systems and that these systems should depend on the availability of information about the future. To explore suboptimal behavior on foraging tasks and how varying the amount of future information changed behavior, we ran rats on two matching neuroeconomic foraging tasks, Known Delay (KD) and Randomized Delay (RD), with the only difference between them being the certainty of the cost of future opportunities. Rats' decision-making strategies differed significantly based on the amount of future certainty. Rats on both tasks still showed suboptimality in decision-making through a sensitivity to sunk costs; however, rats on KD showed significantly less sensitivity to sunk costs than rats on RD. Additionally, on neither task did the rats account for travel and postreward lingering times as heavily as prereward foraging times providing evidence problematic for the Marginal Value Theorem model of foraging behavior. This suggests that while future certainty reduced decision-making errors, more complex decision-making processes unaffected by future certainty were involved and likely produced these decision-making errors within subjects on these foraging tasks. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Patch use and departure rules by gull-billed tern Gelochelidon nilotica

Abstract The gull-billed tern Gelochelidon nilotica feeds on the fiddler crab Leptuca uruguayensis, which settles forming patches in south-eastern temperate mudflats of Argentina. Through field observations, we evaluated whether gull-billed terns used patches following the marginal value theorem (MVT). Gull-billed tern residence time in a patch was not related to crab density or travel times. The number of captures was also unrelated to crab density. Most of the times (44.6%) terns captured only one crab from each patch, and 35% of the times they left without a capture. However, crab density was lower when terns left the patches than when they arrived. This suggests that following several capture attempts by terns, crabs hide, producing a temporary decrease in their availability, forcing tern departure from the patches, which are no longer profitable. Thus, when prey availability is affected more by predator activity than by consumption, the MVT may not necessarily apply.

Uncertainty drives deviations in normative foraging decision strategies.

Nearly all animals forage to acquire energy for survival through efficient search and resource harvesting. Patch exploitation is a canonical foraging behaviour, but there is a need for more tractable and understandable mathematical models describing how foragers deal with uncertainty. To provide such a treatment, we develop a normative theory of patch foraging decisions, proposing mechanisms by which foraging behaviours emerge in the face of uncertainty. Our model foragers statistically and sequentially infer patch resource yields using Bayesian updating based on their resource encounter history. A decision to leave a patch is triggered when the certainty of the patch type or the estimated yield of the patch falls below a threshold. The time scale over which uncertainty in resource availability persists strongly impacts behavioural variables like patch residence times and decision rules determining patch departures. When patch depletion is slow, as in habitat selection, departures are characterized by a reduction of uncertainty, suggesting that the forager resides in a low-yielding patch. Uncertainty leads patch-exploiting foragers to overharvest (underharvest) patches with initially low (high) resource yields in comparison with predictions of the marginal value theorem. These results extend optimal foraging theory and motivate a variety of behavioural experiments investigating patch foraging behaviour.

Be different to be better: the effect of personality on optimal foraging with incomplete knowledge

Many animal populations include a diversity of personalities, and these personalities are often linked to foraging strategy. However, it is not always clear why populations should evolve to have this diversity. Indeed, optimal foraging theory typically seeks out a single optimal strategy for individuals in a population. So why do we, in fact, see a variety of strategies existing in a single population? Here, we aim to provide insight into this conundrum by modelling the particular case of foraging seabirds, that forage on patchy prey. These seabirds have only partial knowledge of their environment: they do not know exactly where the next patch will emerge, but they may have some understanding of which locations are more likely to lead to patch emergence than others. Many existing optimal foraging studies assume either complete knowledge (e.g. Marginal Value Theorem) or no knowledge (e.g. Lévy Flight Hypothesis), but here we construct a new modelling approach which incorporates partial knowledge. In our model, different foraging strategies are favoured by different birds along the bold-shy personality continuum, so we can assess the optimality of a personality type. We show that it is optimal to be shy (resp. bold) when living in a population of bold (resp. shy) birds. This observation gives a plausible mechanism behind the emergence of diverse personalities. We also show that environmental degradation is likely to favour shyer birds and cause a decrease in diversity of personality over time.