First Passage Time Analysis of Animal Movement and Insights into the Functional Response

Movement plays a role in structuring the interactions between individuals, their environment, and other species. Although movement models coupled with empirical data are widely used to study animal distribution, they have seldom been used to study search time. This paper proposes first passage time as a novel approach for understanding the effect of the landscape on animal movement and search time. In the context of animal movement, first passage time is the time taken for an animal to reach a specified site for the first time. We synthesize current first passage time theory and derive a general first passage time equation for animal movement. This equation is related to the Fokker–Planck equation, which is used to describe the distribution of animals in the landscape. We illustrate the first passage time method by analyzing the effect of territorial behavior on the time required for a red fox to locate prey throughout its home range. Using first passage time to compute search times, we consider the effect of two different searching modes on a functional response. We show that random searching leads to a Holling type III functional response. First passage time analysis provides a new tool for studying how animal movement may influence ecological processes.     

Optimal traits when there are several costs: the interaction of mortality and energy costs in determining foraging behavior

I analyzed the interaction of different types of costs in determiningoptimal behavior using mathematical models. The analysis concentrateson foraging behavior and asks (1) whether the cost factor thathas the greatest effect on fitness generally has the greatesteffect on optimal trait values and (2) whether increasing thesize of one type of cost makes the optimal behavior absolutelyor relatively more sensitive to that cost. The foraging costsconsidered are energy expenditure, predation risk, and othermortality factors. It is shown that increasing the magnitudeof one cost often decreases the relative and absolute sensitivityof the optimal foraging strategy to that cost. The relativefitness effects of different costs generally differ from therelative sensitivities of the optimal strategies to the costfactors. Researchers should therefore measure the shapes ofcost curves rather than their average magnitudes to determinewhich of several costs can be ignored in cost-benefit analyses.     

Minimizing errors in identifying Lévy flight behaviour of organisms

1. Lévy flights are specialized random walks with fundamental properties such as superdiffusivity and scale invariance that have recently been applied in optimal foraging theory. Lévy flights have movement lengths chosen from a probability distribution with a power-law tail, which theoretically increases the chances of a forager encountering new prey patches and may represent an optimal solution for foraging across complex, natural habitats. 2. An increasing number of studies are detecting Lévy behaviour in diverse organisms such as microbes, insects, birds, and mammals including humans. A principal method for detecting Lévy flight is whether the exponent (micro) of the power-law distribution of movement lengths falls within the range 1 < micro < or = 3. The exponent can be determined from the histogram of frequency vs. movement (step) lengths, but different plotting methods have been used to derive the Lévy exponent across different studies. 3. Here we investigate using simulations how different plotting methods influence the micro-value and show that the power-law plotting method based on 2(k) (logarithmic) binning with normalization prior to log transformation of both axes yields low error (1.4%) in identifying Lévy flights. Furthermore, increasing sample size reduced variation about the recovered values of micro, for example by 83% as sample number increased from n = 50 up to 5000. 4. Simple log transformation of the axes of the histogram of frequency vs. step length underestimated micro by c.40%, whereas two other methods, 2(k) (logarithmic) binning without normalization and calculation of a cumulative distribution function for the data, both estimate the regression slope as 1-micro. Correction of the slope therefore yields an accurate Lévy exponent with estimation errors of 1.4 and 4.5%, respectively. 5. Empirical reanalysis of data in published studies indicates that simple log transformation results in significant errors in estimating micro, which in turn affects reliability of the biological interpretation. The potential for detecting Lévy flight motion when it is not present is minimized by the approach described. We also show that using a large number of steps in movement analysis such as this will also increase the accuracy with which optimal Lévy flight behaviour can be detected.     

Mathematical modelling and computer simulation of Brownian motion and hybridisation of nanoparticle–bioprobe–polymer complexes in the low concentration limit

A wide variety of nano-biotechnological applications are being developed for nanoparticles based on in vitro diagnostic and imaging systems. Some of these systems allow highly sensitive detection of molecular biomarkers. Frequently, the very low concentration of the biomarkers makes very difficult the mathematical simulation of the motion of nanoparticles based on classical, partial differential equations. We address the issue of incubation times for low concentration systems using Monte Carlo simulations. We describe a mathematical model and computer simulation of Brownian motion of nanoparticle–bioprobe–polymer contrast agent complexes and their hybridisation to immobilised targets. We present results for the dependence of incubation times on the number of particles available for detection, and the geometric layout of the DNA-detection assay on the chip.     

Besetzungsmodelle

Starting with the classical occupancy with boxes, balls and probabilities for occupying boxes, we employ new models: a ball, which met a box, occupies this box with a probability depending on the size of box content, and - using several kinds of balls - by the composition of the content too. For that purpose several models are constructed with distinctive forms of the conditions. Dealing with these models - they are special MARKO vian chains - we pay attention mainly to the so called first passage time T_z for defined events Z; in particular for certain events Z we have to prove that T_z is a random variable, and have to set up the appropriate probability generating function.     

Predicting availability to consumers of spatially and temporally variable resources

Ecological dynamics in many aquatic communities are strongly influenced by spatial and temporal variability of key limiting resources, and the extent to which consumers can locate and exploit concentrations of those resources. Intuitively, resource concentrations that are `close' and `long-lived' should typically be more available to consumers than `distant' and `ephemeral' resource concentrations. The speed and accuracy with which consumers can locate concentrations of their resources is in part determined by their movement characteristics and sensory constraints, which vary with taxon, life-history stage, physiological state, environmental conditions, and other factors. This has motivated detailed observation and modelling of individual-level foraging behaviors in a wide variety of taxa. However, our abilities to develop this intuitive concept of availability into empirically-based, quantitative predictions for consumer–resource interactions remain limited, largely due to the complexities of formulating and simulating spatially explicit models of consumer–resource interactions, and the difficulty of understanding how specific simulation results relate to broader ecological situations. This paper presents a non-dimensional index, the Frost number, that provides a simple prediction of availability to consumers of spatially and temporally varying resource concentrations. This index incorporates characteristics of both resource distributions and consumer movement behaviors. When Frost numbers characterizing consumer–resource interactions are much less than unity, resource concentrations are typically unavailable to consumers because travel time to reach them exceeds the longevity of the resource. Conversely, when Frost numbers are much greater than unity, resource longevity exceeds travel time so that resource concentrations are available. The Frost number may provide a preliminary identification of the length and time scales at which resources are available to consumers in complex ecological systems, even when detailed spatial observations and simulations are not available.     

Predator search pattern and the strength of interference through prey depression

We develop a model of predators foraging within a single patch,on prey that become temporarily immune to predation (depressed)after detecting a predator. Interference through prey depressionoccurs because the proportion of vulnerable prey (and henceintake rate) decreases as predator density increases. Predatorsin our model are not forced to move randomly within the patch,as is the case in other similar models, but can avoid areasof depressed prey and so preferentially forage over vulnerableprey. We compare the extent to which different avoidance rules(e.g., move more quickly over depressed prey or turn if approachingdepressed prey) influence the amount of time spent foragingover depressed and vulnerable prey, and how this influencesthe strength of interference. Although based on a differentmechanism, our model produces two similar general predictionsto interference models based on direct interactions betweenpredators: the strength of interference increases with (1)increased competitor density and (2) decreased prey encounterrate. This suggests that there are underlying similarities inthe nature of interference even when it arises through differentprocesses. Not surprisingly, avoidance of depressed prey cansubstantially reduce the strength of interference comparedwith random foraging. However, we identify the region of themodel's parameter space in which this reduction is particularlylarge and show that the only system for which suitable dataare available, redshank Tringa totanus feeding on Corophiumvolutator, falls within this region. The model shows that, byadjusting its search path to avoid areas of depressed prey,a predator can substantially reduce the amount of the interferenceit experiences and that this applies over a wide range of parameterspace, including the region occupied by a real system. Thissuggests that behavior-based interference models should considerpredator search pattern if they are to accurately predict thestrength of the interference.     

圈养条件下犬蝠对陌生食物首次取食行为的研究

动物在觅食过程中,尝试取食陌生食物会给其带来潜在的风险或是利益。许多动物在首次遇到陌生食物时,不会立即对其进行取食,甚至感到恐惧而避开,这是动物应对陌生食物和环境的一种恐新行为(neophobia)。2010年10—12月,对广东省四会市圈养条件下的犬蝠Cynopterus sphinx取食行为进行研究。结果发现,在实验中犬蝠首次面对陌生食物(苹果)刺激时表现出2种不同的行为,14只实验个体中,6只在首次面对陌生食物时直接对其进行取食,定义其为探索者(explorer);而另外8只对陌生食物表现出了恐新行为,定义其为恐新者(coward)。在人为施加的环境压力下,恐新者经过反复试探,首次成功取食陌生食物后才接纳陌生食物。雌雄个体间(Mann-Whitney U test:雌性31.3 min±8.5 min,n=6,雄性122.8 min±16.2 min,n=5,U=721.0,P<0.001)及亚成体与成体间(Mann-Whitney U test:亚成体20.9 min±10.9 min,n=3,成体72.9 min±9.7 min,n=11,U=901.0,P<0.001)在首次取食行为上的差异均有统计学意义,雌性和亚成体个体更易于接受陌生食物。本文研究结果表明,犬蝠对陌生食物首次取食的这2种行为差异各自有其生态学意义,探索者的行为利于拓宽取食食物源,以应对野外多变的环境;而恐新者的行为可防止摄入过多有毒或营养过剩的食物。雌性倾向于探索陌生食物,可能与其在种群中的繁殖地位有关;亚成体积极探索陌生食物的行为则体现出其取食经验上的缺乏,同时也利于将陌生食物引入种群食谱中。行为的多样性利于种群繁衍,本文探讨了2种取食策略各自的利弊关系。     

龟纹瓢虫对棉蚜的捕食行为

为探讨天敌对害虫的捕食作用机制,充分发挥生物防治的作用,本文从捕食能学角度,系统地观测了龟纹瓢虫Propylea japonica (Thunberg)对棉蚜Aphis gossypii Glover的捕食行为及影响的因素。结果表明：龟纹瓢虫对棉蚜的捕食行为依棉蚜的密度变化而逐渐转变;它在棉蚜密度高时,搜索活动下降;而在棉蚜密度低时,则搜索活动增加。产生这种行为是由于肠胃量与棉蚜遭遇率变化的综合作用结果。因此,将瓢蚜比调控在一定水平上,可以更有效地发挥以瓢治蚜的生物防治作用。