Ecological Modelling, 57 (1991) 133 - 143 Elsevier Science Publishers B.V., Amsterdam

133

Habitat heterogeneity and foraging efficiency: an individual-based model

J o h n H. R o e s e 1, Ken L. R i s e n h o o v e r and L. J o s e p h Folse

Department of Wildlife and Fisheries Sciences, Texas A&M University, College Station, TX 77843, USA

(Accepted 11 December 1990)

ABSTRACT

Roese, J.H., Risenhoover, K.L. and Folse, L.J., 1991. Habitat heterogeneity and foraging efficiency: an individual-based model. Ecol. Modelling, 57: 133-143.

We present a rule-based, event-driven model of foraging behavior, and use it to demonstrate the influence of structure and variability of habitats in determining the foraging efficiency of an individual herbivore. The structural and distributional properties of resources were assigned based on vegetation measurements in subalpine habitats in Denali National Park and Preserve, Alaska. The forager was characterized in terms of the physical, physiological, and cognitive attributes of a moose (Alces alces). We modelled movement as a sequence of steps in response to perceived resources. Simulation of foraging behavior in the model was event-driven. Artificial habitats were simulated to evaluate the influence of biomass per plant and mean bite size of plants on the foraging efficiency of the simulated animal. The mean rate of dry matter intake, and the 24-h activity budgets simulated by the model were similar to those reported for moose by Risenhoover. Foraging efficiency varied with changes in the size and variability of plants and individual bites available in the habitat. We discuss the results of our simulations in terms of modelling at the individual level.

INTRODUCTION

Popu la t i on dynamics is a func t ion o f the in te rac t ion a m o n g individual animals and the habitat . However , d i f ferences be tween individuals within a popu la t i on are o f ten ignored or trivialized in ecological t heo ry and mode l s

(Lomnicki , 1988). F u r t h e r m o r e , the spatial loca t ion of individuals de ter -

mine the availability o f r e sources to each forager . M a n y of the e m e r g e n t p rope r t i e s of popu la t ions (i.e. age s t ructure , g rowth rate, fecundi ty , mor ta l -

I Present Address: Department of Biology and Chemistry, Lake Superior State University, Sault Ste. Marie, MI 49783, USA.

0304-3800/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved

1 3 4 J.H. ROESE ET AL.

ity, sex ratio) are directly influenced by the characteristics and spatial location of individuals within the population. Thus the movement patterns of individuals is a key component of population dynamics.

Foraging behavior is an individual rather than a population phe- nomenon, and is the result of the complex interaction between an animal and its environment. The ability of an animal to find, capture, and consume food (e.g., foraging) is critical to that individual's survival. Every animal must develop strategies and tactics that allow it to become a successful forager. Animals within a population with comparable abilities will likely forage in a similar, but not identical, manner. The natural variability of characteristics within a population and the heterogeneous nature of the environment can lead to a divergence in the efficiency with which animals forage. This is particularly true of herbivores. Herbivores must often meet requirements for absolute dry matter intake and several essential nutrients while simultaneously limiting ingestion of toxic compounds. Dietary re- quirements will differ between individuals depending on their sex, age, and physiological condition. Additionally, spatial and temporal heterogeneity, typical of the forage types used by ruminants (Hobbs, in press) will result in different opportunities for individual animals, leading to unique behavioral sequences. We present a rule-based, event-driven model of foraging behav- ior, and use it to demonstrate the significance of structure and variability of habitats in relation to the foraging efficiency of an individual herbivore. More specifically, we will examine the influence of the size and variability of individual plants and individual bites on the rate of biomass intake by moose.

MODEL DESCRIPTION

An object-oriented approach (Folse et al., 1989) was used to develop a model using the Modula-2 programming language. Modula-2 retains much of the structure of familiar programming languages such as Fortran and Pascal, yet includes some key properties required to construct object-ori- ented programs (Wegmann, 1986). Specifically, Modula-2 permits data abstraction and dynamic linkages between objects. This allows for a highly modularized, event-driven model. A graphic interface displayed simulations and provided qualitative verification of the output.

The model created two 'classes' of objects, a shrub, and a forager. There is only one 'instance' of the forager object, but several thousand 'instances' of the shrub object. During a simulation the forager and individual shrubs remained oblivious of each other until one or more of the shrubs fell within the perceptual range of the forager. When this occurred the forager received a message from the shrub regarding its value. The forager used

H A B I T A T H E T E R O G E N E I T Y AND F O R A G I N G E F F I C I E N C Y 135

this information to make decisions, and subsequently sent a message to the shrub(s) regarding how much, if any, of the shrub(s) it consumed. Once this interchange of messages occurred and the forager moved away the connec- tion between the objects disappeared.

Habitat

In foraging simulation models in which movements are explicitly repre- sented, the modeler is frequently confronted with barriers to movement imposed by the computer hardware or software. Often special rules are required to regulate movement at a boundary (Cody, 1971; Pyke, 1978). For example, Pyke (1976) observed broad-tailed hummingbirds (Selasphorus platycercus) at the boundary of a grid of flowers to determine their behavior when faced with this situation. In this case, however, the bound- ary was actually an ecotone, rather than a barrier to movement. Obviously, barriers to movement do occur in natural situations, but care must be taken to avoid computer-imposed barriers that are artifacts of the software or hardware being used.

Our model avoids artificial barriers by using the extensive storage capacity of a fixed disk. The model builds a two-dimensional matrix of cells measuring 9 m on a side. At any given moment during a simulation the cell containing the forager and the eight surrounding cells were held in the computer 's memory. As the forager moved, the program dynamically gen- erated new cells and stored information for vacated cells on the fixed disk. If the forager doubled back to a previously vacated cell, information regarding that cell was recalled. This arrangement permitted us to analyze the forager's behavior without the confounding influence of artificial barri- ers.

Within each cell the program generated hundreds of shrub objects representing the food resources in the habitat. The structural and distribu- tional properties of these shrubs were assigned on the basis of data collected by Risenhoover (1987) in Denali National Park and Preserve, Alaska. Structural characteristics considered were edible biomass per plant, available bite size, and nutritional quality. Distributional values specified were density and the mean nearest-neighbor distance between conspecifics.

For each species designated, the program used the distributional infor- mation provided to explicitly locate individual shrubs throughout the habi- tat. The number of shrubs of each species created was determined by the density. The location of each shrub was selected by randomly generating x and y coordinates from a Poisson distribution with a mean equal to the mean nearest-neighbor distance for that species. No a priori patch designa- tions were made. The model allowed for the structural characteristics of

136 J.H. R O E S E ET AL.

individual shrubs to be held constant within a species, or to be drawn from a specified distribution (i.e. uniform, normal, Poisson, etc.). Resources were considered to be non-regenerating over the course of a simulation, allowing us to investigate short-term depletion effects.

Forager

The forager was characterized in terms of physical, physiological, and cognitive attributes. The physical attributes of animals (i.e. size, locomotor abilities, etc.) can be readily measured and their influence on foraging is relatively well understood (Demment and Van Soest, 1985; Fancy and White, 1987). Physiological phenomena (i.e. digestion, metabolism, etc.) are more difficult to measure and relate to foraging ecology. The cognitive abilities of a forager (i.e. learning, memory, perception, etc.) are the most difficult to assess, yet potentially have the greatest impact on foraging performance.

We specified four physical attributes of the forager. The body size of the forager was used to calculate the amount of forage biomass required on a daily basis. Rumen capacity estimated from body size (Hudson, 1985a) constrained the amount of biomass which could be ingested before rumina- tion was necessary. Mean step length, determined from direct observations (Risenhoover, 1987), constrained the forager's locomotor ability. The con- sumptive or lateral reach of the animal constrained the distance over which the forager could consume food without taking a step.

Physiological processes have a less direct, but potentially greater influ- ence on foraging ecology than do the physical characteristics. Digestion and rumination are of special concern when modelling an animal with time constraints. Hudson (1985b) included digestive kinetics in a bioenergetics model. We modified the rumen dynamics in Hudson's model to accommo- date the event-driven nature of this model. This submodel simulated the biochemical processes of the rumino-reticulum and the lower gut.

Mechanisms regulating the duration of feeding and bedding periods are unclear. Biochemical cues and rumen distension are likely mechanisms for controlling the duration of feeding periods (Baile and Forbes, 1974; Bun- nell and Gillingham, 1985; Hudson, 1985a) but empirical evidence remains inconclusive. In our model foraging ceased and rumination was initiated when the bulk of ingesta exceeded rumen capacity. Ruminat ion time, needed to reduce the bulk of the ingesta, was a function of the amount of cell wall material in the rumen (Renecker, 1987; Risenhoover, 1987).

The ability to collect, store, and recall information significantly impacts the foraging efficiency of an animal (Smith and Sweatman, 1974; Griffiths, 1975). Unfortunately, these cognitive abilities are difficult to observe or

H A B I T A T H E T E R O G E N E I T Y A N D F O R A G I N G EFFICIENCY 137

measure. It is relatively easy to formulate a series of rules and abilities an animal might use to forage, but quite difficult to test alternatives under field conditions.

We adopted a conservative approach toward modelling the cognitive abilities of a forager. We began by providing the animal with the ability to assess biomass and time. These abilities, in combination with foraging 'rules-of-thumb', allowed the animal to make decisions between food items. For all simulations discussed in this paper the rule was simply to maximize the short-term rate of dry matter intake.

The forager was also provided with a perceptual field and the ability to estimate distance within this field. Following Sch6ne (1984), the perceptual field was cardioid-shaped. This field was defined as the area within which the animal could recognize an item as potential food. We did not provide the forager with the ability to learn or remember. Initially simulating an animal incapable of learning or remembering, and later including these abilities in future simulations, makes it possible to evaluate the value of these abilities in terms of foraging efficiency.

Movement

We modelled movement as a sequence of steps in response to perceived resources. Each step had a constant length and a turn angle drawn from a wrapped Cauchy distribution (Batschelet, 1981). This circular distribution has two parameters, the mean angle and the correlation coefficient. The mean angle was determined by the bearing to the chosen resource item. If no suitable resources were perceived the mean angle was simply the direction the forager faced at the conclusion of the previous step. The correlation coefficient represented the probability of moving in the mean direction and was approximated from observed paths by dividing the magnitude of displacement by the number of steps taken in a foraging bout. The model simulates each step by determining the orientation (mean direction) of the animal, and then drawing a random number from the wrapped Cauchy distribution to determine the actual direction of the step.

Simulation sequence

Simulation of foraging behavior in the model was event-driven. The forager in our model reacted to discrete events rather than an arbitrary time step. The animal scanned the resources within its perceptive field and oriented itself toward the most profitable item. Profitability was deter- mined as the short-term rate of biomass intake. The forager estimated the relative profitability of each plant, within the effective perceptual distance,

138 J.H. ROESE ET AL.

TABLE 1

Structural, distributional and nutritional characteristics of food resources, and the physical and cognitive characteristics of the forager, used as model inputs

Forage N G / P BS CWC DE Density NND

species (g) (g) (%) (kj/g) (stems/m 2) (m)

A. crispa 51.50 0.45 42.8 6.95 0.44 0.88 B. glandulosa 1.93 0.28 60.7 8.04 0.72 0.67 S. alaxensis 49.56 0.98 43.0 8.12 0.41 1.03 S. lanata 5.54 0.62 44.1 9.15 0.25 1.07 S. glauca 5.98 0.44 44.9 8.54 0.64 1.05 S. planifolia 5.14 0.50 42.9 6.15 0.55 0.81

See text for explanation of abbreviations.

by dividing edible biomass by the distance to the plant. The cost of moving was assumed to be proportional to distance traveled. If the selected item was not within the consumptive field, the forager took a step and the resources were re-evaluated from the new position. This process continued until a selected item was within the forager's reach. Harvest rate (b i tes /min) declined as a function of increasing mean bite size available on the selected plant (Risenhoover, unpublished manuscript). After consuming a portion (10% in these simulations) of the selected plant the animal re-evaluated resources within the effective perceptual distance. The forager continued to feed from the selected plant until it eliminated the edible biomass or perceived a more profitable plant. Thus there was a trade-off between edible biomass and travel cost. Dry matter intake rate (DMm) was calcu- lated each time the animal took a step. At the end of each simulation D M I R was averaged over five minute intervals.

MODEL VALIDATION

Characteristics of the food resources (Table 1) and the forager (Table 2) used to validate the model were based on moose foraging in sub-alpine habitats of interior Alaska (Risenhoover, 1987). Average body size, and

TABLE 2

Physical and cognitive characteristics of the forager used as model inputs

Body s i z e Rumen Stride Turn-angle Lateral Perceptual (kg) capacity length correlation reach distance

(kg) (m) coefficient (m) (m)

360 14 1.5 0.5-0.99 1.5 1.5-7.5

H A B I T A T H E T E R O G E N E I T Y AND F O R A G I N G EFFICIENCY 139

OBSERVED SIMULATED

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Fig. 1. Comparison of simulated time budget and observed time budget (Risenhoover, 1987) for foraging moose.

rumen capacity of moose were obtained from the literature (Hudson, 1985a). Stride length, correlation coefficient of the turn angle distribution, lateral reach, and effective perceptual distance were estimated from direct observations made of foraging moose (Risenhoover, unpublished data). Six food species were used to represent a variety of forage resources. Ameri- can green alder (Alnus crispa), resin birch (Betula glandulosa), feltleaf willow (Salix alaxensis), Richardson willow (S. lanata), grayleaf willow (S. glauca), and diamondleaf willow (S. planifolia) were represented in terms of the new growth per plant (NG/P), mean bite size (Bs), cell wall content (cwc), digestible energy (DE), density, and nearest-neighbor distance (NNO). The validation simulation was replicated 100 times.

Foraging efficiency is a function of many factors including the specific habitat conditions experienced by individual animals. It is difficult to replicate these conditions in a field setting. Our model allowed us to create a spatially explicit distribution of forage species based on the distributional properties of a specific habitat type. This approach allowed us to replicate the step-by-step foraging behavior of an individual animal under statisti- cally identical habitat conditions. Simulations, using the structural and distributional properties of open spruce-willow habitats, predicted 24-h activity budgets (Fig. 1), and utilization of available forage species (Table 3) similar to those reported by Risenhoover (1987) for moose in Denali National Park and Preserve.

EFFECT OF HABITAT STRUCTURE ON FORAGING EFFICIENCY

Artificial habitats were simulated to evaluate the sensitivity of the model to changes in biomass per plant and mean bite size of plants. The sensitivity of the model to variability was also examined by systematically increasing the standard deviation of biomass per plant and bite size from

140

TABLE 3

Comparison of the percent of available forage utilized by moose

J.H. R O E S E E T A L .

Species Percent utilization

Observed a Simulated

Alnus crispa 0.2+ 0.2 0.6+0.1 Betula glandulosa 8.9 + 18.0 15.8 + 2.6 Salix alaxensis 27.1 + 19.1 34.9 + 6.4 Salix glauca 8.9 + 16.6 5.8 + 1.5 Salix lanata 1.7 + 2.7 0.0 ___ 0.0 Salix planifolia 14.6 ___ 13.9 11.4 + 3.2

a Risenhoover, 1987.

zero to 50% of the mean value. The turn-angle correlation coefficient and the size of the effective perceptual distance were held constant at values which maximized OMIR in the validation trials (0.85 and 3.0, respectively). Each simulation was replicated 100 times.

In addition to providing statistical repeatability, our approach to mod- elling reveals relationships not easily observed under field conditions. The model demonstrated that DM~R was extremely variable over the course of a single foraging bout (Fig. 2) even within structurally homogeneous habitats (i.e. biomass per plant and bite size with standard deviations of zero). Variability in DMIR increased as the heterogeneity of the structural proper- ties of the habitat increased.

Our model simulated a decline in DMIR in habitats when only moderate- sized plants were available (Fig. 3). This predicted decrease in foraging efficiency emerged from our model as a function of the ratio between the size of available plants and the cost of movement to obtain the plant. When only moderate-sized plants were available the simulated forager became

~ 16- C ~ 15-

~ 14-

W 13- F-- ' ~ 12-

LaJ 11-

10- Z

5 10 1.5 20 25 30 35 40 45

BOUT DURATION (min)

Fig. 2. Simulated dry matter intake rate within a homogeneous habitat (e.g. plant size and bite size have standard deviation of 0.0) over the course of a single foraging bout.

H A B I T A T H E T E R O G E N E I T Y A N D F O R A G I N G EFFICIENCY 141

12 C

E C~

LLI I-- 10 .< Od

Ld 9-

< I-.-- Z

8 5 15 25 35

BIOMASS/PLANT (g)

Fig. 3. Simulated dry matter intake rate (_+SE) in response to increasing plant size.

more selective and consequently increased its movement costs. Varying the size of plants (SD 10-50% of the mean) within a simulation decreased the forager's efficiency. The degree of variability, however, had no impact on the forager's performance.

Our model simulated a positive, but non-linear relationship between the mean bite size available and foraging efficiency. Risenhoover (1987) ob- served a similar relationship for moose and attributed it to the increased efficiency of processing large bites. Our model predicted that DMIR should be highest when bite size was constant in the habitat. Simulated foraging efficiency declined significantly at low levels of bite size variability, but increased as the level of variability increased (Fig. 4). The model dynami- cally determined OMIR. As the variability in bite size increased, the forager's increasing efficiency at processing larger than average bites over-com- pensated for time lost processing smaller than average bites, resulting in an overall increase in DMIR.

12. c

E C~

LLI I - - 10. < n -

LLI x./ 9- <I:

Z w 8 0 10 20 30 40 50

BITE SIZE VARIABILITY (% of m e a n )

Fig. 4. Simulated dry matter intake rate (+ SE) in response to increasing the variability of bite size.

142 J .H . R O E S E E T AL.

DISCUSSION

The literature concerning foraging behavior is extensive (see reviews in Schoener, 1971; Pyke et al., 1977; Stephens and Krebs, 1986) and covers a broad range of topics. Foraging is implicitly treated as a population level phenomenon when individual variation within the habitat or population is trivialized or ignored. Conventional approaches to studying foraging strate- gies are based on evolutionary assumptions and are of limited utility for exploring tactical questions of interest to biologists and managers.

We developed a heuristic model which avoided broad-based strategic assumptions, and focused attention on the influence of temporal and spatial heterogeneity on the foraging efficiency of an individual animal. Although the model is quite simple, it includes components such as plant size and bite size that are often overlooked in foraging models. The combination of a temporally and spatially heterogeneous habitat, a conser- vative representation of the information available to the forager, and simple foraging rules produced complex behavior.

Our model demonstrated that short-term foraging efficiency is inher- ently variable. Intake rate fluctuated dramatically, even in homogeneous habitats. Spatial and temporal variability in the habitat increased the variability in foraging performance. The magnitude of this variability could be critical to the survival of time-limited foragers such as moose (Risenhoover, 1987). Our model is designed to operate at a time step short enough to capture the short-term variability in intake rate.

It is clear from our simulations that the structure and variability of resources in the environment may be critical to foraging performance. The size and variability of plants and individual bites available to the forager affected foraging performance. The significance of habitat variability is especially important from a modeling viewpoint as it emphasizes the advantages of building foraging models at the level of the individual. Because of its unique position in the environment, each individual in a population will be faced with a spatially and temporally unique distribution of resources. Models which incorporate these differences, may result in significantly different population level responses than would be predicted by a population level model in which each individual is presented with identical resources.

ACKNOWLEDGMENT

We thank Dr. William Grant and Mr. Jerry Cooke for comments and review of the manuscript.

HABITAT H E T E R O G E N E I T Y AND FORAGING EFFICIENCY 143

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