Joel S. Brown*. Department of ..... site is located near Tucson, Arizona (see Brown 1986). The ..... committee, James Brown, James Cox, Robert Holt, Thomas.
Behavioral Ecology and Sociobiology
Behav Ecol Sociobiol (1988) 22:37 47
9 Springer-Verlag 1988
Patch use as an indicator of habitat preference, predation risk, and competition Joel S. Brown* Department of Ecology and Evolutionary Biology, University of Arizona, Tucson, AZ 85721, USA Received January 28, 1987 / Accepted September 25, 1987
Summary. A technique for using patch giving up densities to investigate habitat preferences, predation risk, and interspecific competitive relationships is theoretically analyzed and empirically investigated. Giving up densities, the density of resources within a patch at which an individual ceases foraging, provide considerably more information than simply the amount of resources harvested. The giving up density of a forager, which is behaving optimally, should correspond to a harvest rate that just balances the metabolic costs of foraging, the predation cost of foraging, and the missed opportunity cost of not engaging in alternative activities. In addition, changes in giving up densities in response to climatic factors, predation risk, and missed opportunities can be used to test the model and to examine the consistency of the foragers' behavior. The technique was applied to a community of four Arizonan granivorous rodents (Perognathus amplus, Dipodomys merriami, Ammospermophilus harrisii, and Spermophilus tereticaudus). Aluminum trays filled with 3 grams of millet seeds mixed into 3 liters of sifted soil provided resource patches. The seeds remaining following a night or day of foraging were used to determine the giving up density, and footprints in the sifted sand indicated the identity of the forager. Giving up densities consistently differed in response to forager species, microhabitat (bush versus open), date, and station. The data also provide useful information regarding the relative foraging efficiencies and microhabitat preferences of the coexisting rodent species.
can be used to investigate the properties of communities. A recent example of this includes Rosenzweig's (1979 et seq.) theory of habitat selection where the behavior of individuals behaving optimally is used to predict the outcome of intra- and interspecific interactions (Rosenzweig 1981, 1985; Pimm and Rosenzweig 1981; Pimm et al. 1985). Other examples include short-term apparent competition (Holt and Kotler 1987), moose foraging dynamics (Belovsky 1978 et seq.), and resource theory (Tilman 1982, 1985). Testing models of population interactions based upon the foraging behavior of individuals often requires measuring habitat or patch use, habitat preferences, and the rejection or acceptance of patches. In this paper, I present a measuring technique to accomplish these goals. The technique uses artificial or manipulated resource patches to measure a forager's giving up density. The technique is applicable to communities of active foragers seeking comparatively immobile prey. I begin by discussing the theory which provides an interpretation of patch giving up densities. The theory is an extension of Charnov's (1976) marginal value theorem and it uses what, in economics, is called the "marginal rate of substitution" (see Russell and Wilkinson 1979) to include the effects of predation risk and alternative activities on patch use. I then give some preliminary results from applying this method to a community of four desert granivorous rodent species: Arizona pocket mouse (Perognathus amplus), Merriam's kangaroo rat (Dipodomys merriami), round-tailed ground squirrel (Spermophilus tereticaudus), and Harris's antelope ground squirrel (Ammospermophilus harrisii).
Introduction As first suggested by MacArthur and Pianka (~ 966) and Emlen (1966), optimal foraging theory Department of Biological Sciences, University of Illinois at Chicago, Chicago, IL 60680, USA * Current address:
Optimal patch use Theoretical treatments of optimal habitat use are applicable to systems where foragers are able to identify and direct their foraging efforts to subsets
38 of the environment (i.e. patches) that on average yield higher harvest rates or benefits than the environment at large. Once a habitat patch is located, a forager must decide whether to accept the opportunity to harvest the patch (Rosenzweig 1974), and it must decide how much time or effort to devote to those patches it accepts for harvesting (Charnov 1976). By varying the foraging time allotted to each patch, a forager can vary the total, average, marginal or net reward from each patch. In the simplest case of habitat utilization, an individual can only forage and has no alternative activities. Assume that resources are distributed in discrete patches and that foragers deplete the resources as they harvest a patch. However, assume also, that the distribution of resources among patches remains fixed. In other words, although the resources of a given patch are depleted by a forager while it is in the patch, the resources of the entire environment are not. Under these assumptions, the marginal value theorem (Charnov 1976) states that the rate of energy gain to a forager is maximized, and by assumption its fitness is also maximized, when the forager's quitting harvest rate in a patch equals its average harvest. The above assumptions, which lead to the marginal value theorem, are restrictive. More realistically, foraging in patches will affect not only energy gain, but also other aspects of fitness such as predation risk. Empirical work suggests that foragers balance the benefits of energetic reward and the cost of predation when making foraging decisions (Milinski and Heller 1978; Sih 1980; Grubb and Greenwald 1982; Werner etal. 1983; Lima et al. 1985). Furthermore, most organisms can engage in other fitness-determining activities besides foraging such as territorial defense, mate finding, resting, dormancy, grooming, and nest maintenance. Finally, foraging activity of individuals may not only depress the resources of a given patch but also, at least for a time, depress the resources of the entire environment. For example, following sunrise, hummingbirds and nectarivorous insects often deplete their nectar resources (Feinsinger 1976; Schaffer et al. 1979; Brown et al. 1981). In what follows, I relax these restrictive assumptions (1) by assuming that foraging activity affects both net energy gain and predation risk; (2) by permitting the foragers to engage in alternative activities; and (3) by permitting the depletion of resources over the entire environment. Let fitness, denoted by G, be a function of net energy gain from foraging, e, the probability of surviving predation while foraging, p, and a vector of inputs into fitness from engaging in any and
all alternative activites, a. I assume that the realization of fitness is discrete and occurs following a fixed amount of time T. If the individual is preyed upon during this interval its fitness is zero. The goal of the forager is to divide its time between foraging and alternative activities so as to maximize fitness. Net energy gain, e, and the probability of surviving predation, p, are functions of time spent foraging. Assume that time spent foraging is divided over m resource patches. Resource patches may vary with regard to initial resource density and predation risk. Harvest rate is assumed to be an increasing function of patch resource density. As a forager devotes harvest time to the patch, its resources are depleted and the harvest rate declines. Let t I = ( 6 , " , tin) denote the vector of times allotted to each of the m resource patches. Assume that there are s alternative activities that contribute to the other inputs into fitness, a. Let t " = ( t m + b , tm+s) be the vector of times devoted to each alternative activity. Note that alternative activities may also expend energy and incur predation risk. For accounting purposes, in what follows, I will include these in the vector of inputs into fitness from alternative activities. Let G [e (ts), p (t~), a (ta)] = p (t y) .f[e (ts), a (ta)] denote the expected per capita rate of growth (fitness) subject to the constraint that the sum of the tj's and t~'s equals T where j = 1,..., m and i = m + 1,..., m + s. Futhermore, 0 < p (t s) _ 0 (if the individual has more energy it has more to lose from being eaten). Thus, as the individual acquires more energy the MRS~p increases. We can now reconsider expression (1) which gave the quitting net harvest rate of an optimally foraging individual in any arbitrary patchj. Substituting the MRS's given by expressions (5) and (6) into (1) gives: e/~ t~= - MRSep [~p (-)/~ tj] + MRSea [8 a (')/8 ti]
(7) The first term of the right hand side of expression (7) is the cost of predation expressed in units of energy (P) and the second term is the value of alternative activities expressed in units of energy (MOC). The net quitting harvest rate can be split between the rate of harvest, H, and the energetic cost of foraging, C. Thus, the quitting harvest rate satisfies: H=C+P+MOC A forager should leave each resource patch when the patch harvest rate is no longer greater than the sum of the energetic, predation, and missed opportunity costs of foraging. The above result comes from applying an optimization criterion to a general model of patch exploitation. For illustration, the Appendix considers a specific example of a fitness function for an organism which can either forage in one of two patches or remain dormant. From the example in the appendix (or from careful consideration of the general formulation), a number of deductions can be made. First, if patches share the same risk of predation, cost of foraging and harvest rate function, then they should be foraged to the same quitting harvest rate. Second, if fitness is only a function of net energy gain and there is no predation risk, then each patch should be harvested until harvest rate just compensates for the additional cost
of foraging over remaining dormant. Third, if two patches share the same energetic cost of foraging and the same harvest rate function, then any differences in quitting harvest rates should reflect differences in patch specific risks of predation. Fourth, if two patches differ in energetic costs and in risk of predation in such a way that one is safer but energetically more costly than the other, then the forager's relative quitting harvest rates in the two patches may reflect its state. If the forager is in a state of high energy gain then it may have a lower quitting harvest rate in the less risky patch. The converse may occur if the forager is in a state of low energy gain (see McNamara and Houston 1986 for how an individual's state influences behavior). Measuring patch use Researchers have used four techniques for measuring patch use. These include measuring giving up times (Krebs et al. 1974; Hubbard and Cook 1978; Townsend and Hildrew 1980), measuring total time spent in a patch (Cowie 1977; Hartling and Plowright 1979), quitting harvest rates (Pyke 1978, 1980; Milinski 1979; Hodges 1981), and the giving up density of resources (Whitham 1977; Hodges and Wolf 1981). These authors were interested in determining foraging decision rules and seeing whether models of optimal foraging provide good characterizations of foraging behavior [see Krebs et al. (1983) and Pyke (1984) and references therein]. Here, I will advocate: 1) the use of controlled field experiments, 2) the use of giving up densities as a measure of patch use, and 3) the use of foraging behavior to investigate predation risk, habitat preferences, and interspecific competitive relationships. Controlled field experiments using artificial or manipulated resource patches offer two important advantages. First, the foragers remain in their natural environment and are faced with familiar alternative activities, competitive interactions, and predation risks. Second, the use of artificial patches permits the controlled manipulation of one or several variables of interest while the available set of alternative activities is held constant. If harvest rates are a function of patch type and resource density then giving up densities (GUD's) provide an estimate of quitting harvest rates. In many circumstances it is easier to measure G U D ' s rather than quitting harvest rates. Measuring GUD's requires assessing the remaining density of resources following use by one or several
41
foragers. On the other hand, measuring the quitting harvest rate requires an organism whose encounter and capture of prey can be observed and timed. It is particularly difficult to measure the instantaneous harvest rate of a forager as it leaves a patch. To validate the model, all four components of the model can be tested. To test for the effect of harvest rate (H) on G U D ' s requires holding C, P, and M O C constant. Adjacent manipulated resource patches in the same microhabitat should not differ in C, P, or MOC. Thus, G U D ' s in adjacent patches which differ in substrate should reflect differences in harvest rates. The patch with the 'slower' substrate should have the correspondingly higher G U D which just equalizes the quitting harvest rates in the two patches. To test for the effect of energetic costs (C) on G U D ' s requires holding H, P, and M O C constant. For endotherms, the metabolic costs of foraging should be influenced by temperature when ambient temperatures are below the forager's thermal neutral zone. Adjacent patches with the same substrate should not differ in H, P, or MOC. If one patch is rendered colder then it should have the higher G U D which just compensates the forager for its higher energetic cost of foraging in that patch. Similar tests can be used to test for the effects of P and M O C on GUD's. Increasing P (e.g. by manipulating predator densities or cues of predation) should increase GUD's. Similarly, increasing the M O C (e.g. by providing alternative resources or foraging opportunities) should increase GUD's. By manipulating patches in ways which are known to increase predation risk, harvest rate, foraging costs, or missed opportunity costs, the researcher can test whether the forager's behavior is consistent with that required to maximize G (-). The model can also be used to allow the forager to reveal its preferences and assessments of the environment. The researcher assumes that the forager's G U D is a truthful revelation of its harvest rate and foraging costs. Temporal or spatial differences in the G U D ' s of a forager reflect the effects of different habitats on missed opportunity costs, harvest rates, foraging costs, and predation risk. The researcher can investigate species and habitat specific differences in any one of these costs by holding other costs constant among habitats. Missed opportunity cost can be controlled for by ensuring that several patches are available to the same forager. If these patches are within a relatively short distance of each other, then while foraging in either patch the forager has the same set of alternative activities and thus, experiences the
same missed opportunity cost in each patch. Harvest rate can be controlled by ensuring that the structure of the artificial patches is the same with regards to factors that affect harvest rate, such as substrate and resource type. The energetic cost can be controlled by maintaining constant climatic factors across patches. Conversely, different combinations of abiotic factors such as temperature, humidity, or wind can be used to test their effects on foraging costs. Differences in the cost of predation can be measured if patches are manipulated in such a way that energetic costs, harvest rates, and missed opportunity costs remain constant. Methods I applied the approach of the previous section to a community of desert granivorous rodents in September 1983. The study site is located near Tucson, Arizona (see Brown 1986). The dominant perennial plant species in descending order of groundcover are creosote (Larrea tridentata), desert zinnia (Zinnia sp.), mouse ears (Coldenia canescens), and mesquite (Prosopsis juliflora). Total vegetation ground cover by perennials is about 20%. There are four granivorous rodent species (in parentheses : numbers and mean weights of individuals trapped): round-tailed ground squirrel, Sperrnophilus tereticaudus (18/121 g); Merriam's kangaroo rat, Dipodomys merriarni (16/37 g); Arizona pocket mouse, Perognathus amplus (55/12g); and antelope ground squirrel, Ammospermophilus harrisii, (12/104 g). Aluminum trays, measuring 45 cm on a side and 2.5 cm deep, filled with 3 g of unhusked-millet seed mixed into 3 l of soil provided resource patches. A total of 60 trays were divided over two grids. Each grid was laid out as a seven by seven small mammal trap grid with stations 25 m apart. The thirty seed trays on each grid were divided into pairs and assigned to 15 stations picked at random from the 49 trap stations. Live trapping and seedtrays were not run simultaneously. At each station with seedtrays, one tray was placed directly under the canopy of a creosote bush and the other was placed 2 4 m away from the first in the open microhabitat. Although shadowed by the canopy, the surface of trays under shrubs was unobstructed by branches or leaves up to a height of no less than 20 cm. The trays in the open were placed on bare ground at least 2 m from the nearest creosote bush. For seven mornings (9, 10, 11, 14, 15, 17, and 18 September) and afternoons (9, 10, 11, 13, 14, 15, and 17 Sept.), I collected foraging data from the seed trays (rain prevented consecutive mornings and afternoons). The morning data collection was at sunrise, a period following the cessation of activity by pocket mice and kangaroo rats and preceding the initiation of activity by ground squirrels. The afternoon data collection at sunset followed squirrel activity and preceded that of pocket mice and kangaroo rats. Thus, pocket mice and kangaroo rats had one entire night to forage the trays and squirrels had one entire day. (The rodents were very familiar with these seed trays from similar work done in the latter part of August.) Data collection from trays consisted of noting any footprints in the sired soil, sifting the soil to recover the remaining seeds, and recharging the trays with millet. The distinctiveness of footprints permitted identification of the forager down to species and sometimes to the exact individual based upon toeclips. The squirrels could be distinguished by the presence
42 Table 1. The mean G U D ' s (in grams) for the pocket mouse
Table 2. The results of two one-way ANOVA's (separate analy-
(P.a.), kangaroo rat (D.m.), and squirrel species (S.t. and A.h.)
ses for the bush and open microhabitats) showing the differences between species in GUD's. The group variables are the four species and G U D is the dependent variable (log transform of grams of millet). The column and row headings are the four species (abbreviated scientific names). Entries are the F of improvements for each pairwise comparison. Entries above and below the diagonal are for the bush and open microhabitats respectively. The error mean sum of squares for the bush and open analyses are 0.646 and 0.602 respectively. Because the six pairwise comparisons within each analysis are not orthogonal, the error rate of each test was adjusted according to the Dunn-Sidak method (Sokal and Rohlf 1981)
in the bush and open microhabitat. Bush/Open preference is determined by a sign test comparing the number of times the bush tray at a station had the lower G U D (number preceding the comma) to the number of times the open tray had the lower G U D (number following the comma). A " B " or " O " indicates whether the bush or open had the significantly lower GUD Species
Bush GUD
Sample size
Open GUD
Sample size
Bush/open preference
P. amplus D. merriami A. harrisii S. tereticaudus
0.439 0.952 0.994 0.974
121 51 39 97
0.591 0.610 1.591 1.571
103 86 32 89
51,35 14,52 36,3 81,14
B* O*** B*** B***
* P < 0 . 0 5 , *** P < 0 . 0 0 1
Species
P.a.
D.m.
S.t.
A.h.
P.a. D.m. S.t. A.h.
-
33.17"** 64.95*** 35.54***
52.82*** 0.03 0.01
30.38*** 0.06 0.02 -
0.08 75.73*** 39.71 ***
*** P 0 are constants (henceforth, when convenient, probability of surviving predation (p), maintenance (m), and energy gain (e) will be written without their arguments). The fitness function assumes that there are diminishing but positive returns to fitness from energy gain (c~ 1 or G(-)O for i=1,2. Let probability of surviving predation, maintenance, and energy gain be: p - EXP[--rltl-rzt2]
(A.la)
m=yta
(A.lb)
e = Hi(t1) + H2(t2) -- c1t I -- c2t 2 -- catd
(A.lc)
where Hi(h) is the cumulative harvest rate in patch i= 1,2.
46 To solve for the optimal patch quitting harvest rate, first calculate the MRSev and MRSem using expressions (5) and (6) : MRSe, : (1 +fle)/~flp
[1 + f l e ] E X P ( - m ) MRSem = fl[1 - E X P ( - m)] (If tl*, t2*, td* >0, the optimal values for time spent in patch 1, tl*, and 2, t2*, must satisfy condition (7).) Take the derivatives of (A.la-c) with respect to tl or td and substitute these and the MRS's into (7) to yield:
aHi(.) r~[l+fle] at, - c ~ + ~ +
7[l+fle]EXP(-m) fl[1--EXP(-m)]
ed
(A.2)
where i = 1,2. The optimal allocation of time can be obtained by solving three simultaneous equations. The first two generated by (A.2) and the third generated by the constraint: tl + t2 + ta = T. The term on the left is the quitting harvest rate, H. The first term on the right is the energetic cost of foraging in the patch, C. The second term is the cost of predation, P. And, the iast two terms are the missed opportunity costs, MOC. The first component of MOC is the foregone benefit of additional maintenance, and the second is the foregone cost of dormancy.
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