Food web context modifies predator foraging and weakens trophic interaction strength.

Trophic interaction modifications (TIM) are widespread in natural systems and occur when a third species indirectly alters the strength of a trophic interaction. Past studies have focused on documenting the existence and magnitude of TIMs; however, the underlying processes and long-term consequences remain elusive. To address this gap, we experimentally quantified the density-dependent effect of a third species on a predator's functional response. We conducted short-term experiments with ciliate communities composed of a predator, prey and non-consumable 'modifier' species. In both communities, increasing modifier density weakened the trophic interaction strength, due to a negative effect on the predator's space clearance rate. Simulated long-term dynamics indicate quantitative differences between models that account for TIMs or include only pairwise interactions. Our study demonstrates that TIMs are important to understand and predict community dynamics and highlights the need to move beyond focal species pairs to understand the consequences of species interactions in communities.

Foraging rates from metabarcoding: Predators have reduced functional responses in wild, diverse prey communities.

Functional responses describe foraging rates across prey densities and underlie many fundamental ecological processes. Most functional response knowledge comes from simplified lab experiments, but we do not know whether these experiments accurately represent foraging in nature. In addition, the difficulty of conducting multispecies functional response experiments means that it is unclear whether interaction strengths are weakened in the presence of multiple prey types. We developed a novel method to estimate wild predators' foraging rates from metabarcoding data and use this method to present functional responses for wild wolf spiders foraging on 27 prey families. These field functional responses were considerably reduced compared to lab functional responses. We further find that foraging is sometimes increased in the presence of other prey types, contrary to expectations. Our novel method for estimating field foraging rates will allow researchers to determine functional responses for wild predators and address long-standing questions about foraging in nature.

A taste of space: Remote animal observations and discrete-choice models provide new insights into foraging and density dynamics for a large subarctic herbivore.

Competition for resources and space can drive forage selection of large herbivores from the bite through the landscape scale. Animal behaviour and foraging patterns are also influenced by abiotic and biotic factors. Fine-scale mechanisms of density-dependent foraging at the bite scale are likely consistent with density-dependent behavioural patterns observed at broader scales, but few studies have directly tested this assertion. Here, we tested if space use intensity, a proxy of spatiotemporal density, affects foraging mechanisms at fine spatial scales similarly to density-dependent effects observed at broader scales in caribou. We specifically assessed how behavioural choices are affected by space use intensity and environmental processes using behavioural state and forage selection data from caribou (Rangifer tarandus granti) observed from GPS video-camera collars using a multivariate discrete-choice modelling framework. We found that the probability of eating shrubs increased with increasing caribou space use intensity and cover of Salix spp. shrubs, whereas the probability of eating lichen decreased. Insects also affected fine-scale foraging behaviour by reducing the overall probability of eating. Strong eastward winds mitigated negative effects of insects and resulted in higher probabilities of eating lichen. At last, caribou exhibited foraging functional responses wherein their probability of selecting each food type increased as the availability (% cover) of that food increased. Space use intensity signals of fine-scale foraging were consistent with density-dependent responses observed at larger scales and with recent evidence suggesting declining reproductive rates in the same caribou population. Our results highlight potential risks of overgrazing on sensitive forage species such as lichen. Remote investigation of the functional responses of foraging behaviours provides exciting future applications where spatial models can identify high-quality habitats for conservation.

Effects of whaling and krill fishing on the whale-krill predation dynamics: bifurcations in a harvested predator-prey model with Holling type I functional response.

In the Antarctic, the whale population had been reduced dramatically due to the unregulated whaling. It was expected that Antarctic krill, the main prey of whales, would grow significantly as a consequence and exploratory krill fishing was practiced in some areas. However, it was found that there has been a substantial decline in abundance of krill since the end of whaling, which is the phenomenon of krill paradox. In this paper, to study the krill-whale interaction we revisit a harvested predator-prey model with Holling I functional response. We find that the model admits at most two positive equilibria. When the two positive equilibria are located in the region { ( N , P ) | 0 ≤ N < 2 N c , P ≥ 0 } , the model exhibits degenerate Bogdanov-Takens bifurcation with codimension up to 3 and Hopf bifurcation with codimension up to 2 by rigorous bifurcation analysis. When the two positive equilibria are located in the region { ( N , P ) | N > 2 N c , P ≥ 0 } , the model has no complex bifurcation phenomenon. When there is one positive equilibrium on each side of N = 2 N c , the model undergoes Hopf bifurcation with codimension up to 2. Moreover, numerical simulation reveals that the model not only can exhibit the krill paradox phenomenon but also has three limit cycles, with the outmost one crosses the line N = 2 N c under some specific parameter conditions.

The inappropriate application of imidacloprid destroys the ability of predatory natural enemies to control pests in the food chain: A case study of the feeding behavior of Orius similis on Frankliniella occidentalis.

Insecticides are an indispensable and important tool for agricultural production. However, the inappropriate application of insecticides can cause damage to the food chain and ecosystem. Orius similis is an important predatory and natural enemy of Frankliniella occidentalis. Imidacloprid is widely used to control pests, but will inevitably exert adverse effects on O. similis. In order to determine the effect of different imidacloprid treatments on the ability of O. similis to prey on the 2nd-instar nymphs of F. occidentalis, we determined the toxicity and predation of imidacloprid on different stages of O. similis under contact and ingestion treatments. In addition, we used the Holling disc equation to evaluate the ability of O. similis to search and exhibit predatory activity following contact and ingestion treatments. Analysis showed that the highest LC10 and LC20 values for imidacloprid contact and ingestion toxicity treatment were 17.06 mg/L and 23.74 mg/L, respectively. Both imidacloprid treatments led toa reduction in the predatory of O. similis on prey. The functional responses of the 3rd to 5th instar nymphs, along with female and male O. similis adults to the 2nd-instar nymphs of F. occidentalis were consistent with the Holling type II response following contact and ingestion with imidacloprid. However, following imidacloprid treatment, the handing time (Th) of O. similis with single F. occidentalis was prolonged and the instantaneous attack rate (a) was reduced after imidacloprid treatment. The predatory capacity (a/Th) of female O. similis adults when treated with the LC10 concentration of imidacloprid by ingestion was 52.85; this was lower than that of the LC10 concentration of imidacloprid in the contact treatment (57.67). The extent of predation of O. similis on the 2nd-instar nymphs of F. occidentalis was positively correlated with prey density, although the search effect was negatively correlated with prey density. The most extensive search effect was exhibited by adult O. similis females. Simulations with the Hessell-Varley interference model showed that an increase in the number of O. similis would reduce search efficiency regardless of whether they were treated with imidacloprid or not. Thus, O. similis, especially female adults, exhibited strong potential for controlling the 2nd-instar nymphs of F. occidentalis. The toxicity of ingestion following treatment with the same concentration of imidacloprid in O. similis was greater than that of contact treatment. When using O. similis to control F. occidentalis in the field, we should increase the number of female adults released, and prolong the interval between imidacloprid treatment and O. similis exposure. This strategy will improve the control ability of O. similis, coordinate both chemical and biological control, reduce the impact of pesticides on the environment, and improve the efficiency of agricultural production.

Predator feeding rates may often be unsaturated under typical prey densities.

Predator feeding rates (described by their functional response) must saturate at high prey densities. Although thousands of manipulative functional response experiments show feeding rate saturation at high densities under controlled conditions, it remains unclear how saturated feeding rates are at natural prey densities. The general degree of feeding rate saturation has important implications for the processes determining feeding rates and how they respond to changes in prey density. To address this, we linked two databases-one of functional response parameters and one on mass-abundance scaling-through prey mass to calculate a feeding rate saturation index. We find that: (1) feeding rates may commonly be unsaturated and (2) the degree of saturation varies with predator and prey taxonomic identities and body sizes, habitat, interaction dimension and temperature. These results reshape our conceptualisation of predator-prey interactions in nature and suggest new research on the ecological and evolutionary implications of unsaturated feeding rates.

Predator-mediated interactions through changes in predator home range size can lead to local prey exclusion.

The strength of indirect biotic interactions is difficult to quantify in the wild and can alter community composition. To investigate whether the presence of a prey species affects the population growth rate of another prey species, we quantified predator-mediated interaction strength using a multi-prey mechanistic model of predation and a population matrix model. Models were parametrized using behavioural, demographic and experimental data from a vertebrate community that includes the arctic fox (Vulpes lagopus), a predator feeding on lemmings and eggs of various species such as sandpipers and geese. We show that the positive effects of the goose colony on sandpiper nesting success (due to reduction of search time for sandpiper nests) were outweighed by the negative effect of an increase in fox density. The fox numerical response was driven by changes in home range size. As a result, the net interaction from the presence of geese was negative and could lead to local exclusion of sandpipers. Our study provides a rare empirically based model that integrates mechanistic multi-species functional responses and behavioural processes underlying the predator numerical response. This is an important step forward in our ability to quantify the consequences of predation for community structure and dynamics.

No sensitivity to functional forms in the Rosenzweig-MacArthur model with strong environmental stochasticity.

The classic Rosenzweig-MacArthur predator-prey model has been shown to exhibit, like other coupled nonlinear ordinary differential equations (ODEs) from ecology, worrying sensitivity to model structure. This sensitivity manifests as markedly different community dynamics arising from saturating functional responses with nearly identical shapes but different mathematical expressions. Using a stochastic differential equation (SDE) version of the Rosenzweig-MacArthur model with the three functional responses considered by Fussmann & Blasius (2005), I show that such sensitivity seems to be solely a property of ODEs or stochastic systems with weak noise. SDEs with strong environmental noise have by contrast very similar fluctuations patterns, irrespective of the mathematical formula used. Although eigenvalues of linearized predator-prey models have been used as an argument for structural sensitivity, they can also be an argument against structural sensitivity. While the sign of the eigenvalues' real part is sensitive to model structure, its magnitude and the presence of imaginary parts are not, which suggests noise-driven oscillations for a broad range of carrying capacities. I then discuss multiple other ways to evaluate structural sensitivity in a stochastic setting, for predator-prey or other ecological systems.

Functional data analysis with covariate-dependent mean and covariance structures.

Functional data analysis has emerged as a powerful tool in response to the ever-increasing resources and efforts devoted to collecting information about response curves or anything that varies over a continuum. However, limited progress has been made with regard to linking the covariance structures of response curves to external covariates, as most functional models assume a common covariance structure. We propose a new functional regression model with covariate-dependent mean and covariance structures. Particularly, by allowing variances of random scores to be covariate-dependent, we identify eigenfunctions for each individual from the set of eigenfunctions that govern the variation patterns across all individuals, resulting in high interpretability and prediction power. We further propose a new penalized quasi-likelihood procedure that combines regularization and B-spline smoothing for model selection and estimation and establish the convergence rate and asymptotic normality of the proposed estimators. The utility of the developed method is demonstrated via simulations, as well as an analysis of the Avon Longitudinal Study of Parents and Children concerning parental effects on the growth curves of their offspring, which yields biologically interesting results.

Variation in body size drives spatial and temporal variation in lobster-urchin interaction strength.

How strongly predators and prey interact is both notoriously context dependent and difficult to measure. Yet across taxa, interaction strength is strongly related to predator size, prey size and prey density, suggesting that general cross-taxonomic relationships could be used to predict how strongly individual species interact. Here, we ask how accurately do general size-scaling relationships predict variation in interaction strength between specific species that vary in size and density across space and time? To address this question, we quantified the size and density dependence of the functional response of the California spiny lobster Panulirus interruptus, foraging on a key ecosystem engineer, the purple sea urchin Strongylocentrotus purpuratus, in experimental mesocosms. Based on these results, we then estimated variation in lobster-urchin interaction strength across five sites and 9 years of observational data. Finally, we compared our experimental estimates to predictions based on general size-scaling relationships from the literature. Our results reveal that predator and prey body size has the greatest effect on interaction strength when prey abundance is high. Due to consistently high urchin densities in the field, our simulations suggest that body size-relative to density-accounted for up to 87% of the spatio-temporal variation in interaction strength. However, general size-scaling relationships failed to predict the magnitude of interactions between lobster and urchin; even the best prediction from the literature was, on average, an order of magnitude (+18.7×) different than our experimental predictions. Harvest and climate change are driving reductions in the average body size of many marine species. Anticipating how reductions in body size will alter species interactions is critical to managing marine systems in an ecosystem context. Our results highlight the extent to which differences in size-frequency distributions can drive dramatic variation in the strength of interactions across narrow spatial and temporal scales. Furthermore, our work suggests that species-specific estimates for the scaling of interaction strength with body size, rather than general size-scaling relationships, are necessary to quantitatively predict how reductions in body size will alter interaction strengths.

Why are biodiversity-ecosystem functioning relationships so elusive? Trophic interactions may amplify ecosystem function variability.

The relationship between biodiversity and ecosystem functions (BEFs) has attracted great interest. Studies on BEF have so far focused on the average trend of ecosystem function as species diversity increases. A tantalizing but rarely addressed question is why large variations in ecosystem functions are often observed across systems with similar species diversity, likely obscuring observed BEFs. Here we use a multi-trophic food web model in combination with empirical data to examine the relationships between species richness and the variation in ecosystem functions (VEFs) including biomass, metabolism, decomposition, and primary and secondary production. We then probe the mechanisms underlying these relationships, focusing on the role of trophic interactions. While our results reinforce the previously documented positive BEF relationships, we found that ecosystem functions exhibit significant variation within each level of species richness and the magnitude of this variation displays a hump-shaped relationship with species richness. Our analyses demonstrate that VEFs is reduced when consumer diversity increases through elevated nonlinearity in trophic interactions, and/or when the diversity of basal species such as producers and decomposers decreases. This explanation is supported by a 34-year empirical food web time series from the Gulf of Riga ecosystem. Our work suggests that biodiversity loss may not only result in ecosystem function decline, but also reduce the predictability of functions by generating greater function variability among ecosystems. It thus helps to reconcile the debate on the generality of positive BEF relationships and to disentangle the drivers of ecosystem stability. The role of trophic interactions and the variation in their strengths mediated by functional responses in shaping ecosystem function variation warrants further investigations and better incorporation into biodiversity-ecosystem functioning research.

From the distributions of times of interactions to preys and predators dynamical systems.

We consider a stochastic individual based model where each predator searches and then manipulates its prey or rests during random times. The time distributions may be non-exponential and density dependent. An age structure allows to describe these interactions and get a Markovian setting. The process is characterized by a measure-valued stochastic differential equation. We prove averaging results in this infinite dimensional setting and get the convergence of the slow-fast macroscopic prey predator process to a two dimensional dynamical system. We recover classical functional responses. We also get new forms arising in particular when births and deaths of predators are affected by the lack of food.

The green lacewing Chrysopa formosa as a potential biocontrol agent for managing Spodoptera frugiperda and Spodoptera litura.

Understanding predator-prey interactions is essential for successful pest management by using predators, especially for the suppression of novel invasive pest. The green lacewing Chrysopa formosa is a promising polyphagous predator that is widely used in the biocontrol of various pests in China, but information on the control efficiency of this predator against the seriously invasive pest Spodoptera frugiperda and native Spodoptera litura is limited. Here we evaluated the predation efficiency of C. formosa adults on eggs and first- to third-instar larvae of S. frugiperda and S. litura through functional response experiments and determined the consumption capacity and prey preference of this chrysopid. Adults of C. formosa had a high consumption of eggs and earlier instar larvae of both prey species, and displayed a type II functional response on all prey stages. Attack rates of the chrysopid on different prey stages were statistically similar, but the handling time increased notably as the prey developed. The highest predation efficiency and shortest-handling time were observed for C. formosa feeding on Spodoptera eggs, followed by the first-instar larvae. C. formosa exhibited a significant preference for S. litura over S. frugiperda in a two-prey system. In addition, we summarized the functional response and predation efficiency of several chrysopids against noctuid pests and made a comparison with the results obtained from C. formosa. These results indicate that C. formosa has potential as an agent for biological control of noctuid pests, particularly for the newly invasive pest S. frugiperda in China.

Effect of prey density on the performance of Eupeodes corollae and its predation rate against the cabbage aphid, Brevicorynae brassicae (L.).

Eupeodes corollae (F.) (Diptera: Syrphidae) is the most abundant syrphid fly which is distributed worldwide and is the sole predator of aphids. Therefore, the present study was conducted to evaluate the predation rate and functional response of E. corollae against the cabbage aphid, Brevicoryne brassicae (L.). The experiment was carried out under laboratory conditions at 25 ± 2°C with 60-70% relative humidity. The results revealed that age-specific net predation rate (qx) increased after the 4th day and a peak was recorded on the 10th day of pivotal age in the third larval instar. The stable host kill rate and finite host kill rate of E. corollae were 18.63 and 21.07, respectively, against the B. brassicae and predicted that a mean of 20.78 aphids was needed for E. corollae to produce one offspring. A negative linear coefficient (P < 0) indicated the type II functional response for all larval instars of E. corollae against the B. brassicae. At higher prey density, the prey consumption was significantly at par with second and third instar larvae of E. corollae as the prey consumption was increased with increasing the prey density, which then decreased after attaining the upper asymptote (76.40 and 81.40% consumption, respectively). The Roger's predator random equation for type II functional response was fitted to estimate attack rate (a) and handling time (Th). The maximum prey consumption was recorded for third instar of E. corollae with a higher attack rate (0.336 h-1) and lower handling time (0.514 h) against B. brassicae, followed by the second and first instar. Thus, it is concluded that the third larval instar of E. corollae was the voracious feeder and used as an efficient biocontrol agent in the IPM programme.

Fast behavioral feedbacks make ecosystems sensitive to pace and not just magnitude of anthropogenic environmental change.

Anthropogenic environmental change is altering the behavior of animals in ecosystems around the world. Although behavior typically occurs on much faster timescales than demography, it can nevertheless influence demographic processes. Here, we use detailed data on behavior and empirical estimates of demography from a coral reef ecosystem to develop a coupled behavioral-demographic ecosystem model. Analysis of the model reveals that behavior and demography feed back on one another to determine how the ecosystem responds to anthropogenic forcing. In particular, an empirically observed feedback between the density and foraging behavior of herbivorous fish leads to alternative stable ecosystem states of coral population persistence or collapse (and complete algal dominance). This feedback makes the ecosystem more prone to coral collapse under fishing pressure but also more prone to recovery as fishing is reduced. Moreover, because of the behavioral feedback, the response of the ecosystem to changes in fishing pressure depends not only on the magnitude of changes in fishing but also on the pace at which changes are imposed. For example, quickly increasing fishing to a given level can collapse an ecosystem that would persist under more gradual change. Our results reveal conditions under which the pace and not just the magnitude of external forcing can dictate the response of ecosystems to environmental change. More generally, our multiscale behavioral-demographic framework demonstrates how high-resolution behavioral data can be incorporated into ecological models to better understand how ecosystems will respond to perturbations.

Interactions between the omnivorous bug Nesidiocoris tenuis (Heteroptera: Miridae) and the tomato pests Helicoverpa armigera (Lepidoptera: Noctuidae) and Phthorimaea absoluta (Lepidoptera: Gelechiidae): predation, phytophagy, and prey preference.

Nesidiocoris tenuis (Reuter) (Heteroptera: Miridae) is a zoophytophagous bug that can derive nutrients from 3 trophic levels: plants, herbivorous arthropods, and other predators. On tomato, besides damaging the plants as they feed, might the mirid also forage on pest species and repel pests. In greenhouse and laboratory experiments, we investigated the functional response of the bug, its prey preference, and its influence on the oviposition potentials of 2 major pest species Helicoverpa armigera (Hübner) (Lepidoptera: Noctuidae) and Phthorimaea absoluta Meyrick (Lepidoptera: Gelechiidae) on tomato Solanum lycopersicum L. (Solanaceae). Nesidiocoris tenuis showed a Type II functional response to both prey species. The estimated handling time was higher for H. armigera eggs than for P. absoluta yet N. tenuis attack rates did not differ between the 2 prey species. Nesidiocoris tenuis did not show a preference for 1 species when prey eggs were provided in equal proportions. The feeding on tomato plants by N. tenuis did not affect oviposition by the 2 moth species, as neither species showed a preference for clean or N. tenuis-adult-damaged plants and clean or N. tenuis-nymph-damaged plants. This study shows that N. tenuis can prey upon eggs of both moth species as the 3 species co-occur in tomato fields. However, because of the shorter handling time of P. absoluta eggs by the predator and the higher number of eggs laid by H. armigera, the co-occurrence might be less detrimental to the H. armigera populations compared to P. absoluta.

Anthropogenic noise does not strengthen multiple-predator effects in a freshwater invasive fish.

Anthropogenic noise has the potential to alter community dynamics by modifying the strength of nested ecological interactions such as predation. Direct effects of noise on per capita predation rates have received much attention but the context in which predation occurs is often oversimplified. For instance, many animals interact with conspecifics while foraging and these nontrophic interactions can positively or negatively influence per capita predation rates. These effects are often referred to as multiple-predator effects (MPEs). The extent to which noise can modulate MPEs and thereby indirectly alter per capita predation remains unknown. To address this question, we derived the relationship between per capita predation rate and prey density, namely the functional response (FR), of single and pairs of the invasive topmouth gudgeon Pseudorasbora parva when feeding on water fleas under two noise conditions: control ambient noise estimated at 95 dB re 1 µPa and ambient noise supplemented with motorboat sounds whose relative importance over ambient noise ranged from 4.81 to 27 dB. In addition, we used video recordings to track fish movements. To detect MPEs, we compared the observed group-level FRs to predicted group-level FRs inferred from the individual FRs and based on additive effects only. Regardless of the number of fish and the noise condition, the FR was always of type II, showing predation rate in a decelerating rise to an upper asymptote. Compared to the noiseless condition, the predation rate of single fish exposed to noise did not differ at high prey densities but was significantly lower at low prey densities, resulting in an FR with the same asymptote but a less steep initial slope. Noise also reduced fish mobility, which might explain the decrease in predation rate at low prey densities. Conspecific presence suppressed the individual response to noise, the FRs of two fish (observed group-level FRs) being perfectly similar between the two noise conditions. Although observed and predicted group-level FRs did not differ significantly, observed group-level FRs tended to fall in the low range of predicted group-level FRs, suggesting antagonism and a negative effect of nontrophic interactions on individual foraging performance. Interestingly, the difference between predicted and observed group-level FRs was not greater with noise, which means that noise did not strengthen MPEs. Our results show that when considering the social context of foraging, here through the presence of a conspecific, anthropogenic noise does not compromise foraging in the invasive P. parva.

The presence of multiple parasitoids decreases host survival under warming, but parasitoid performance also decreases.

Current global changes are reshaping ecological communities and modifying environmental conditions. We need to recognize the combined impact of these biotic and abiotic factors on species interactions, community dynamics and ecosystem functioning. Specifically, the strength of predator-prey interactions often depends on the presence of other natural enemies: it weakens with competition and interference or strengthens with facilitation. Such effects of multiple predators on prey are likely to be affected by changes in the abiotic environment, altering top-down control, a key structuring force in natural and agricultural ecosystems. Here, we investigated how warming alters the effects of multiple predators on prey suppression using a dynamic model coupled with empirical laboratory experiments with Drosophila-parasitoid communities. While multiple parasitoids enhanced top-down control under warming, parasitoid performance generally declined when another parasitoid was present owing to competitive interactions. This could reduce top-down control over multiple generations. Our study highlights the importance of accounting for interactive effects between abiotic and biotic factors to better predict community dynamics in a rapidly changing world and thus better preserve ecosystem functioning and services such as biological control.

Effects of prey density and flow speed on plankton feeding by garden eels: a flume study.

Feeding by zooplanktivorous fish depends on their foraging movements and the flux of prey to which they are exposed. While prey flux is a linear function of zooplankton density and flow speed, those two factors are expected to contribute differently to fish movements. Our objective was to determine the effects of these factors for garden eels, stationary fish that feed while anchored to the sandy bottom by keeping the posterior parts of their bodies inside a burrow. Using a custom-made flume with a sandy bottom, we quantified the effects of prey density and flow speed on feeding rates by spotted garden eels (Heteroconger hassi). Feeding rates increased linearly with prey density. However, feeding rates did not show a linear relationship with flow speed and decreased at 0.25 m s-1. Using label-free tracking of body points and 3D movement analysis, we found that the reduction in feeding rates was related to modulation of the eel's movements, whereby the expected increase in energy expenditure was avoided by reducing exposure and drag. No effects of flow speed on strike speed, reactive distance or vectorial dynamic body acceleration (VeDBA) were found. A foraging model based on the body length extended from the burrow showed correspondence with observations. These findings suggest that as a result of their unique foraging mode, garden eels can occupy self-made burrows in exposed shelter-free sandy bottoms where they can effectively feed on drifting zooplankton.

Mathematical modeling of tumor-immune system interactions: the effect of rituximab on breast cancer immune response.

tBregs are a newly discovered subcategory of B regulatory cells, which are generated by breast cancer, resulting in the increase of Tregs and therefore in the death of NK cells. In this study, we use a mathematical and computational approach to investigate the complex interactions between the aforementioned cells as well as CD8+ T cells, CD4+ T cells and B cells. Furthermore, we use data fitting to prove that the functional response regarding the lysis of breast cancer cells by NK cells has a ratio-dependent form. Additionally, we include in our model the concentration of rituximab - a monoclonal antibody that has been suggested as a potential breast cancer therapy - and test its effect, when the standard, as well as experimental dosages, are administered.