Dynamics of herbivores and resources on a landscape with interspersed resources and refuges

A tradeoff between energy gain from foraging and safety from predation in refuges is a common situation for many herbivores that are vulnerable to predation while foraging. This tradeoff affects the population dynamics of the plant–herbivore–predator interaction. A new functional response is derived based on the Holling type 2 functional response and the assumption that the herbivore can forage at a rate that maximizes its fitness. The predation rate on the herbivore is assumed to be proportional to the product of the time that the herbivore spends foraging and a risk factor that reflects the habitat complexity; where greater complexity means greater interspersion of high food quality habitat and refuge habitat, which increases the amount of the edge zone between refuge and foraging areas, making foraging safer. The snowshoe hare is chosen as an example to demonstrate the resulting dynamics of an herbivore that has been intensely studied and that undergoes well-known cycling. Two models are studied in which the optimal foraging by hares is assumed, a vegetation–hare–generalist predator model and a vegetation–hare–specialist predator model. In both cases, the results suggest that the cycling of the snowshoe hare population will be greatly moderated by optimal foraging in a habitat consisting of interspersed high quality foraging habitat and refuge habitat. However, there are also large differences in the dynamics produced by the two models as a function of predation pressure.     

A field experiment on the influence of load transportation and patch distance on the locomotion velocity of <Emphasis Type="Italic">Dorymyrmex goetschi</Emphasis> (Hymenoptera,Formicidae)

Summary Locomotion velocity during foraging activities is determined by factors such as travel distance, habitat structure and load mass among others. However, few studies on foraging behavior have analyzed the influence of spatial heterogeneity and food transportation on the locomotion velocity of ants under natural conditions. In order to study the mentioned factors, we selected 20 nests of the ant Dorymyrmex goetschi (subfamily Dolichoderinae), in a lower Andes locality of central Chile. Half of the nests were offered a food patch located at 10 cm from the nest entrance, and at 20 cm for the other half. We measured the duration of trips between nest and food patch and vice versa, and the distances traveled. We also recorded spatial heterogeneity of the substratum and soil temperature. Temperature was used as a covariate in the statistical analysis. Travel speed was significantly slower when worker ants returned to the nest with a food load, compared to the velocity of foragers without load that traveled from the nest to the patch. When the food patch was located at greater distance, locomotion velocity was significantly faster. Spatial heterogeneity did not affect movement speed. The reduction in locomotion velocity in ants carrying a load of 5.6 mg represents an energetic cost of transportation equivalent to 79% of the costs involved in moving a body mass of 1.6 mg. Faster velocities at larger patch distances can be interpreted as a strategy to maintain an efficient resource exploitation, by way of decreasing the time exposed to higher predation risk.Received 28 April 2003; revised 11 November 2003; accepted 22 January 2004.     

Optimal foraging in nonpatchy habitats. I. Bounded one-dimensional resource

We present a model of optimal foraging in habitats where the food has an arbitrary density distribution (continuous or not). The classical models of foraging strategies assume that the food is distributed in patches and that the animal divides its time between the two distinct behaviors of patch exploitation and interpatch travel. This assumption is hard to accept in instances where the food distribution is continuous in space, and where travel and feeding cannot be sharply distinguished. In this paper, the habitat is assumed to be one-dimensional and bounded, and the animal is assumed to have a limited foraging time available. The problem is treated mathematically in the context of the calculus of variations. The optimal solution is to divide the habitat in two subsets according to the food density. In the richer subset, the animal equalizes the density distribution; in the poorer subset, it travels as fast as possible.     

Landscape distribution of food and nesting sites affect larval diet and nest size,but not abundance of Osmia bicornis

Habitat fragmentation is a major threat for beneficial organisms and the ecosystem services they provide. Multiple‐habitat users such as wild bees depend on both nesting and foraging habitat. Thus, they may be affected by the fragmentation of at least two habitat types. We investigated the effects of landscape‐scale amount of and patch isolation from both nesting habitat (woody plants) and foraging habitat (specific pollen sources) on the abundance and diet of Osmia bicornis L. Trap‐nests of O. bicornis were studied in 30 agricultural landscapes of the Swiss Plateau. Nesting and foraging habitats were mapped in a radius of 500 m around the sites. Pollen composition of larval diet changed as isolation to the main pollen source, Ranunculus, increased, suggesting that O. bicornis adapted its foraging strategy in function of the nest proximity to main pollen sources. Abundance of O. bicornis was neither related to isolation or amount of nesting habitat nor to isolation or abundance of food plants. Surprisingly, nests of O. bicornis contained fewer larvae in sites at forest edge compared to isolated sites, possibly due to higher parasitism risk. This study indicates that O. bicornis can nest in a variety of situations by compensating scarcity of its main larval food by exploiting alternative food sources.     

Go with the flow: water velocity regulates herbivore foraging decisions in river catchments

Foragers typically attempt to consume food resources that offer the greatest energy gain for the least cost, switching between habitats as the most profitable food resource changes over time. Optimal foraging models require accurate data on the gains and costs associated with each food resource to successfully predict temporal shifts. Whilst previous studies have shown that seasonal changes in food quantity and quality can drive habitat shifts, few studies have shown the effects on habitat choice of seasonal changes in metabolic foraging costs. In this study we combined field and literature data to construct an optimal foraging model to examine the effect of seasonal changes in food quantity, food quality and foraging costs on the timing of a switch from terrestrial to aquatic habitat by non‐breeding mute swans Cygnus olor in a shallow river catchment. Feeding experiments were used to quantify the functional response of swans to changes in aquatic plant biomasses. By sequentially testing alternative models with fixed or variable values for food quantity, food quality and foraging cost, we found that we needed to include seasonal variance in foraging costs in the model to accurately predict the observed habitat switch date. However, we did not need to include seasonal variance in food quantity and food quality, as accurate predictions could be obtained with fixed values for these two parameters. Therefore, the seasonal changes in foraging costs were the key factor influencing the behavioural decision to switch feeding habitats. These seasonal changes in foraging costs were driven by changes in water velocity; the profitability of aquatic foraging was negatively related to water velocity, as faster water required more energy to be expended in swimming. Our results demonstrate the importance of incorporating seasonal variation in foraging costs into our understanding of the foraging decisions of animals.     

Relationships between food resources, foraging patterns, and reproductive success in the water pipit, Anthus sp. spinoletta

A basic but rarely tested assumption in optimal foraging theoryis that positive relationships exist between the foraging patternof an animal, its short-term benefits in feeding, and its long-termfitness. We present evidence for these relationships for a centralplace foraging situation. We studied the foraging behavior ofadult water pipits (Anthus sp. spinoletta) feeding nestlingsin an Alpine habitat near Davos, Switzerland, with the followingresults: (1) searching effort decreases with increasing distancefrom the nest, (2) the amount of prey and the proportion oflarge items brought to the nest increases with increasing foragingdistance, (3) water pipits do not forage according to habitatavailability, but prefer vegetation types with the highest fooddensity (mainly grass and herbs) and avoid those with the lowest,and (4) this selectivity is only expressed when the birds foragemore than 50 m from the nest, i.e., usually outside the territory.Among the several potential interpretations of these results,the most parsimonious is that foraging decisions are based onprofitability, i.e., on the net energy gain per time unit. Additionally,we found that food conditions translate into fitness: the numberof fledglings per nest is related positively to the averageprey biomass at the foraging place and negatively to the averagedistance between the foraging place and the nest. Maximum economicdistances, which were predicted from this food-fitness relationship,agreed well with the actual foraging distances observed. Thissuggests a dose connection between foraging decisions and fitness.In addition to the theoretical issues, some conservation issuesare also briefly discussed.     

A dynamic habitat selection game

A patch selection game is formulated and analyzed. Organisms can forage in one of H patches. Each patch is characterized by the cost of foraging, the density and value of food, the predation risk, and the density of conspecifics. The presence of conspecifics affects the finding and sharing of food, and the predation risk. Optimal foraging theory can be viewed as a "1-person" game against nature in which the optimal patch choice of a specific organism is analyzed assuming that the number of conspecifics in other patches is fixed. In the general game theoretic approach, the behavior of conspecifics is included in the determination of the distinguished organism's strategy. An iterative algorithm is used to compute the solution of the "n-person" game or dynamic ESS, which differs from the optimal foraging theory solution. Experiments to test the proposed theory using rodents and seed trays are briefly discussed.     

Foraging-area size and food density: Some predictive models

It has been observed that when food increases in density along an environmental gradient, the size of foraging areas used by desert ant colonies decreases. Factors that could cause this inverse relationship are explored. Four models of ant foraging are developed and presented in the form of equations for calculating net foraging energy as a function of size of the foraging area. These are used to predict the optimal sizes of foraging areas under conditions of different food densities. Only one of the models predicts an inverse relationship between density of food and size of foraging area when food is the limiting factor in colony reproduction. In this model, the foraging areas of adjacent colonies are assumed to be overlapping and the number of foragers assigned to each square meter of the foraging area is constant, regardless of food density or distance from the nest entrance. Tests for distinguishing among the four models, as well as for determining whether colonies are or are not food limited, are discussed.     

华南地区典型生境中红火蚁觅食行为及工蚁召集规律

观察研究了华南地区几种典型生境中红火蚁对不同类型食物的觅食行为和工蚁召集动态规律。研究结果表明红火蚁觅食行为存在搜寻、召集及搬运等主要过程。不同生境中红火蚁对食物的搜寻时间存在一定差异,荔枝园中搜寻时间明显长于其它生境;荔枝园、荒地、路边生境中红火蚁对蜂蜜的搜寻时间明显长于其它几种食物;同一生境中红火蚁对不同重量的同种食物搜寻时间无明显变化。发现食物后召集的工蚁数量随着时间延长呈现不断增加的趋势,对于较大的食物一般30min左右召集的工蚁数量达到最大,之后趋于稳定并逐渐减少,而对于可以直接搬动的食物发现后15min左右群体召集数量达到最大并很快将其搬走。召集工蚁数量与发现后时间的关系符合二次非线性方程,建立了火腿肠、花生油和蜂蜜等食物上红火蚁工蚁召集数量与发现时间的关系模型,分别为Na=4183.91e^-0.0327T-4231.48e^-0.0346T,Na=3253.78e^-0.0233T-3314.59e^-0.0271T,Na=117.97e^-0.0131T-163.93e^-0.0808T。对于不同食物红火蚁发现后召集的最大工蚁数量间有明显差异,其中花生油上最大,平均为176．3头,火腿肠上次之,为90．4头,蜂蜜上最少,为68．0头。对于不同重量的同种食物,工蚁的召集动态规律较为一致,发现食物后25-30min左右工蚁的召集数量均达到最大值,之后缓慢减少,发现食物后时间长度和食物上工蚁数量也符合房室模型函数Na=c1×exp（-c2T）-c3×exp（-c4T）。同种食物不同重量之间同一时间召集的工蚁数量存在较大差异,呈随食物重量增大而增大趋势。不同生境中对相同质量同种食物工蚁召集数量动态总体变化规律相近,但在发现食物后工蚁数量增长的速度和最大召集工蚁的数量存在明显差异,以路边工蚁数量增长最快、工蚁总数最多,苗圃次之,荔枝园、荒地中工蚁增长速度均较低。红火蚁对不同食物种类切割、搬运耗时存在很大差异,搬运完0．5g的火腿肠需要26．23h,而黄粉虫幼虫（重量约为0．1g）仅为15．6min。不同生境中红火蚁对相同重量同一种食物的搬运耗时也不同,荔枝园要长于其它生境。     

Foraging behavior in stochastic environments

How do temporally stochastic environments affect risk sensitivity in foraging behavior? We build a simple model of foraging under predation risks in stochastic environments, where the environments change over generations. We analyze the effects of stochastic environments on risk sensitivity of foraging animals by means of the difference between the geometric mean fitness and the arithmetic mean fitness. We assume that foraging is associated with predation risks whereas resting in the nest is safe because it is free of predators. In each generation, two different environments with given food amounts and predation risks occur with a certain probability. The geometric mean optimum is independent of food amounts. In most cases of stochastic environments, risk-averse tendency is increased, but in some limited conditions, more risk-prone behavior is favored. Specifically, risk-prone tendency is increased when the variation in food amount increases. Our results imply that the optimal behavior depends on the probability distribution of environmental effects under all selection regimes.     

Hazardous duty pay and the foraging cost of predation

We review the concepts and research associated with measuring fear and its consequences for foraging. When foraging, animals should and do demand hazardous duty pay. They assess a foraging cost of predation to compensate for the risk of predation or the risk of catastrophic injury. Similarly, in weighing foraging options, animals tradeoff food and safety. The foraging cost of predation can be modelled, and it can be quantitatively and qualitatively measured using risk titrations. Giving‐up densities (GUDs) in depletable food patches and the distribution of foragers across safe and risky feeding opportunities are two frequent experimental tools for titrating food and safety. A growing body of literature shows that: (i) the cost of predation can be big and comprise the forager's largest foraging cost, (ii) seemingly small changes in habitat or microhabitat characteristics can lead to large changes in the cost of predation, and (iii) a forager's cost of predation rises with risk of mortality, the forager's energy state and a decrease in its marginal value of energy. In titrating for the cost of predation, researchers have investigated spatial and temporal variation in risk, scale‐dependent variation in risk, and the role of predation risk in a forager's ecology. A risk titration from a feeding animal often provides a more accurate behavioural indicator of predation risk than direct observations of predator‐inflicted mortality. Titrating for fear responses in foragers has some well‐established applications and holds promise for novel methodologies, concepts and applications. Future directions for expanding conceptual and empirical tools include: what are the consequences of foraging costs arising from interference behaviours and other sources of catastrophic loss? Are there alternative routes by which organisms can respond to tradeoffs of food and safety? What does an animal's landscape of fear look like as a spatially explicit map, and how do various environmental factors affect it? Behavioural titrations will help to illuminate these issues and more.     

The effect of habitat quality on foraging patterns, provisioning rate and nestling growth in Corsican Blue Tits Parus caeruleus

Many bird species face seasonal and spatial variation in the availability of the specific food required to rear chicks. Caterpillar availability is often identified as the most important factor determining chick quality and breeding success in forest birds, such as tits Parus spp. It is assumed that parents play an important role in mediating the effect of environment on chick development. A reduction in prey availability should therefore result in increased foraging effort to maintain the amount of food required for optimal chick development. To investigate the capacity of adults to compensate for a reduction in food supply, we compared the foraging behaviour of Blue Tits Parus caeruleus breeding in rich and poor habitats in Corsica. We monitored the foraging effort of adults using radiotelemetry. We also identified and quantified prey items provided to nestlings by using a video camera mounted on the nest. We found that the mean travelling distance of adults was twice as great in the poor habitat as it was in the rich. Despite the marked difference in foraging distance, the proportion of optimal prey (caterpillars) in the diet of the chicks and the total biomass per hour per chick did not differ between the two habitats. We argue that relationships between habitat richness, offspring quality and breeding success cannot be understood adequately without quantifying parental effort.     

Extended phenotypes and foraging restrictions: ant nest entrances and resource ingress in leaf‐cutting ants

Several factors may restrict the acquisition of food to below the levels predicted by the optimization theory. However, how the design of structures that animals build for foraging restricts the entry of food is less known. Using scaling relationships, we determined whether the design of the entrances of leaf‐cutting ant nests restricts resource input into the colony. We measured nests and foraging parameters in 25 nests of Atta cephalotes in a tropical rain forest. Ant flux was reduced to up to 60% at nest entrances. The width of all entrances per nest increased at similar rates as nest size, but the width of nest entrances increased with the width of its associated trail at rates below those expected by isometry. The fact that entrance widths grow slower than trail widths suggests that the enlargement of entrance holes does not reach the dimensions needed to avoid delays when foraging rates are high and loads are big. The enlargement of nest entrances appears to be restricted by the digging effort required to enlarge nest tunnels and by increments in the risk of inundation, predator/parasitoid attacks and microclimate imbalances inside the nest. The design of the extended phenotypes can also restrict the ingress of food into the organisms, offering additional evidence to better understand eventual controversies between empirical data and the foraging theory. Abstract in Spanish is available with online material.     

Nest intruders, nest defence and foraging behaviour in the Black-and-white Casqued Hornbill Bycanistes subcylindricus

The female Black-and-white Casqued Hornbill Bycanistes subcylindricus uses mud to seal herself into a nest cavity and remains there until the nesting attempt has ended. The male hornbill is solely responsible for food provisioning and external defence of the nest. Data on hornbill nests in a Ugandan rain forest were used to test Martindale's (1982) model of nest defence and central place foraging. As predicted, nest guarding by the resident male hornbill during intrusions by conspecifics altered foraging patterns; the resident male foraged closer to the nest, made a larger number of shorter visits, and brought smaller food loads. There was a significant change in size composition of fruits brought before, during, and after intrusions. For short intrusions, the volumes of food brought per unit time did not change. However, if intrusions lasted for days or weeks, food delivery rates declined. Nest-sealing by the Black-and-white Casqued Hornbill appears to function primarily to protect the nest from conspecifics rather than from interspecific predators.     

Recruitment in starved nests: the role of direct and indirect interactions between scouts and nestmates in the ant <Emphasis Type="Italic">Lasius niger</Emphasis>

In social insects, the foraging activity usually increases with the length of food deprivation. In Lasius niger, a mass-recruiting ant species, the foraging adjustment to the level of food deprivation is regulated by the scout that fed at the food source and by the response of the nestmates to signals performed by the scout inside the nest. In this study, we look at the role of these direct interactions (antennations or trophallaxes) and indirect interactions (pheromonal emission) and how they are influenced by the level of food deprivation. At the beginning of recruitment, the relative number of nestmates leaving the nest to forage increases with the level of deprivation. The nestmates’ propensity to exit the nest is not influenced by a previous trophallactic and/or antennal contact with a scout. Our results strongly suggest that the exit of nestmates is triggered by a chemical signal emitted by a scout. Deprivation lowers the response threshold of nestmates to this chemical signal resulting in a more important exit from the nest. Surprisingly, 27% of starved nestmates that receive food from the scout relay the information by depositing a chemical signal before having discovered and drunk the food source. Both phenomena boost the recruitment process. Though successful foragers returning to the nest have a significant role in the recruitment to the food source, we observed that the response of the nestmates inside the nest also greatly influence regulation of the foraging activity.     

Optimal resource allocation to survival and reproduction in parasitic wasps foraging in fragmented habitats

Expansion and intensification of human land use represents the major cause of habitat fragmentation. Such fragmentation can have dramatic consequences on species richness and trophic interactions within food webs. Although the associated ecological consequences have been studied by several authors, the evolutionary effects on interacting species have received little research attention. Using a genetic algorithm, we quantified how habitat fragmentation and environmental variability affect the optimal reproductive strategies of parasitic wasps foraging for hosts. As observed in real animal species, the model is based on the existence of a negative trade-off between survival and reproduction resulting from competitive allocation of resources to either somatic maintenance or egg production. We also asked to what degree plasticity along this trade-off would be optimal, when plasticity is costly. We found that habitat fragmentation can indeed have strong effects on the reproductive strategies adopted by parasitoids. With increasing habitat fragmentation animals should invest in greater longevity with lower fecundity; yet, especially in unpredictable environments, some level of phenotypic plasticity should be selected for. Other consequences in terms of learning ability of foraging animals were also observed. The evolutionary consequences of these results are discussed.     

Optimal foraging area: Size and allocation of search effort

A model is derived for the optimal spatial allocation of foraging effort for an animal returning with food to a central place in a uniform habitat. The forager is assumed to maximize its yield of food during a given period. Foraging effort is expended on search for food, and on transportation to the central place. It is shown that the allocation of search has been optimal if and only if the “marginal cost” of additional food is equal throughout the foraging area when the period has elapsed. The model is used to predict the optimal area radius and allocation of search time. With realistic parameter values, the optimal time per unit area roughly decreases linearly with the distance from the central place. The influence of food density and forager characteristics is examined.     

A dynamic model of hypothermia as an adaptive response by small birds to winter conditions

We present a dynamic programming model which is used to investigate hypothermia as an adaptive response by small passerine birds in winter. The model predicts that there is a threshold function of reserves during the night, below which it is optimal to enter hypothermia, and above which it is optimal to rest. This threshold function decreases during the night, with a particularly sharp drop at the end of the night, representing the time and energy costs associated with returning to normal body temperature. The results of the model emphasise the trade-off between energy and predation, not just between foraging options, but also between foraging during the day and entering hypothermia at night. The value of being able to use hypothermia represents not just energy savings, but also reduced predation risk due to changes in the optimal foraging strategy. Conditions which give a high value of hypothermia are short photoperiod, variable food supply, low temperatures, poor and scarce food supplies.     

Foraging decisions in risk-uniform landscapes

Behaviour is shaped by evolution as to maximise fitness by balancing gains and risks. Models on decision making in biology, psychology or economy have investigated choices among options which differ in gain and/or risk. Meanwhile, there are decision contexts with uniform risk distributions where options are not differing in risk while the overall risk level may be high. Adequate predictions for the emerging investment patterns in risk uniformity are missing. Here we use foraging behaviour as a model for decision making. While foraging, animals often titrate food and safety from predation and prefer safer foraging options over riskier ones. Risk uniformity can occur when habitat structures are uniform, when predators are omnipresent or when predators are ideal-free distributed in relation to prey availability. However, models and empirical investigations on optimal foraging have mainly investigated choices among options with different predation risks. Based on the existing models on local decision making in risk-heterogeneity we test predictions extrapolated to a landscape level with uniform risk distribution. We compare among landscapes with different risk levels. If the uniform risk is low, local decisions on the marginal value of an option should lead to an equal distribution of foraging effort. If the uniform risk is high, foraging should be concentrated on few options, due to a landscape-wide reduction of the value of missed opportunity costs of activities other than foraging. We provide experimental support for these predictions using foraging small mammals in artificial, risk uniform landscapes. In high risk uniform landscapes animals invested their foraging time in fewer options and accepted lower total returns, compared to their behaviour in low risk-uniform landscapes. The observed trade off between gain and risk, demonstrated here for food reduction and safety increase, may possibly apply also to other contexts of economic decision making.     

Density-dependent effects on productivity in the Griffon Vulture Gyps fulvus: the role of interference and habitat heterogeneity

Griffon Vultures Gyps fulvus in northern Spain were studied between 1969 and 1994. The number of breeding pairs increased from 221 in 1969–1975 to 1395 in 1994. The annual population growth rate decreased in the last 5 years, and this may reflect population regulation through density-dependent phenomena. Breeding success was monitored in 1994 and examined in relation to colony size, density of breeding pairs within a radius of 25 km (regional density), climate, human disturbance and food availability. We also recorded whether the year of first occupation of each nest site was before 1989 or after 1989 and whether or not the nest had a rocky shelter. The probability of successfully raising young declined as the regional density increased, which suggests that resource limitation would take place at foraging sites because the Griffon Vulture scavenges socially and no permanent feeding hierarchies are established. The other significant variable was the year of occupation of the nest; nests occupied after 1989 had a lower probability of raising a chick. The increase in the regional density of Griffon Vultures produced a decrease in the productivity at both optimal and suboptimal nest sites. This suggests that density-dependent regulation of breeding success operates through interference and that all the individuals in a colony are similarly affected. In birds of prey, prevalence of interference or habitat heterogeneity may be dependent on the social strategy of each species in space exploitation.