Null Models Chapter 5

8/13/2019 Null Models Chapter 5

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THE TEMPOR L NICHE

Time represents an important resource axis that may be parti t ioned by anassemblage of competing species. Die1 differences in activity times ofver tebrate predators and seasonal d if ferences in f lower ing t imes of ani-mal-pollinated plants consti tute the primary evidence for temporal parti-t ioning. For exam ple, owls and haw ks that forage at different t imes of daymay reduce competit ion for l imited food resources (e.g. , Craighead andCraighead 1956), and co-occurring plant species that flower at differenttimes of the year may reduce competition for animal pollinators (e.g.,Hein rich 1976; Stiles 19 77).Because it is both orde red and circular, the temporal niche a xis has a uniquegeometric representation, with the two orthogonal co mp onen ts of season andtime of day forming a three-dim ensional ring (Figure 5.1). Th e temporal nicheof a species represents a subset of the surface area of this ring. At the commu-nity level, we may ask if there are nonrand om pa tterns of ove rlap in the set ofsurfaces that represent a local assemblage. Because the temporal niche is bothordered an d circular, it may need to be analyzed in null m ode ls differently thandietary or microhabitat data.

Temporal partitioning is also likely to reflect different selective forces inassemblages of animals and plants. For animals that can pick up and move,migration is always a potential response to local resource competition Incontrast, plants and sessile animals must co pe with persistent competition fromclose neighbors. On the other hand, m any vertebrates must forage m ore o r lesscontinuously, whereas most plants and invertebrates can afford to wait outperiods of resource scarcity.

Under traditional models of exploitation competition (MacA rthur and Lev-ins 1967), time is not a truly indepen dent (orthogonal) niche axis (Carothersand JaksiC 1984). How ever, differences in activity time m ay allow species todirectly partition food resources in two ways. First, seasonal differences inactivity may allow predators to coexist by exposing them to different prey


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9 6 hapter 5

Figure 5 1 three-dimensional representation of the temporal niche, showing bothseasonal and diel axes. Temporal activity patterns can be represented as a subset of thesurface of this ring. Null models predict overlap patterns on this surface in the absenceof competitive interactions.

assemblages. Se cond , diel differences in activity may allow predators t o parti-t ion a rapidly renewing resource. But in many animal communit ies , thesecond mechanism is unlikely, because a predator that consumes prey atnight wo uld s t il l be competing with predators that hunt du ring the day. Forvertebrate predators such as raptors or l izards , it seem s especial ly unlikelythat prey po pulat ions can renew fast enough to permit diel food part i t ioningSchoener 1974c; Huey and Pianka 1983). m ore reasonable scenario is

that diel differences in act ivi ty evolved to minimize interference competi-t ion among foragers Carothers and JaksiC 1984). For exam ple, some antassemblages are characterized by s trong interference competi t ion and dr a-matic diel shif ts in the dominan t foraging species e .g., Klotz 1984; Ho ll-dobler 1986). Die1 foraging differences may also reduce overlap if preyactivi ty schedules are nonoverlapping .

Nevertheless, temporal partitioning may be relatively uncommon in animalcommunities. Schoener 1974a) reviewed the early literature and concludedthat animals o ften segregate food and habitat dim ensions but rarely segregatealong temporal niche axes. However, he did suggest that predators separatedmo re often by diel activity tim e of day than did o ther trophic groups. G iven thisbackground, we now review null model studies of temporal partitioning inanimal and plant comm unities.


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The Temporal iche 97

TEM POR AL PARTITIONING IN ANIMA L COMM UNITIES

On e way to analyze temporal partitioning is to treat activity time as any otherniche axis. As described in Chapter 4 Law lor's (198 0b) randomization algo -rithms RA through RA4 could be used to reshuffle observed activity data,which could then be com pared with conventional metrics for niche overlap. Forexample, Pianka et al. (1979) used RA2 to analyze extensive data on theseasonal and daily activity of desert lizards. In this algo rithm, the percentage oftime that an animal was active during a particular season (or time of day) wasreplaced by a random uniform number. Th e only restriction on this random iza-tion is that zeros were retained. In other word s, simulated activity could notoccur at times of the year or day when an animal was inactive in nature.Temporal ov erlaps in lizard assem blages did no t differ from the predictions ofthis null model, or they showed significant aggregation (high overlap). Incontrast, overlap in measures of habitat and food was often less than thatpredicted by the null m odel (see Table 4.4).

Field (1992) used R A l as a null m odel and found a significant reduction inseasonal overlap of spider-hunting pompilid w asps of Britain. How ever, RA1doe s not retain the placement of zeros in the data and consistently produces arandom com munity with a high mean and a low variance in overlap (Pianka etal. 19 79; W inemiller and Pianka 1990). Con sequently, Field's (1992) resultdoe s not necessarily suggest tempo ral resource partitioning.

Althoug h RA1-RA4 are valid null mo dels for looking at unordered dietaryor microhabitat categorie~,we think they are usually inappropriate for theanalysis of temp oral overlap. On both daily and se asonal time scales, temp oralactivity patterns sho w strong modalities, with peak activity in certain mo nths o rhours of the day. Activity curves are often not sim ple bell-shaped distributionsand may exhibit considerable skewness or multiple modes (e.g., Riechert andTracy 1975). Fo r ectotherm s, in particular, these mo des may reflect a tempe ra-ture-humidity envelope that physiologically constrains animal activity (Tracyand Christian 1986 ). Th e RA1-RA 4 algorithms destroy the shape of activitycurves, so that patterns revealed by them do not necessarily reflect temporalresource partitioning.

A better approach is to retain the shape of the activity curve and rand omizethe placement of its peak. Tokeshi (1986) followed this procedure in an analysisof nine species of chironomid larvae co -occurring in a river in eastern England.Two null models were used. In the first, activity peaks for each species werelocated randomly through the year, with the distributions overlapping circu-larly (acros s the year) if necessary. In the second, peaks were placed random lyduring nonwinter months, to reflect an obvious temperature constraint on


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activity that was unrelated to interspecific competition. Compared to both nulldistributions, overlap in the observed chironomid assemblage was significantlygreater than expected. These null models are similar to those used in theanalysis of flowering phenology (Poole and Rathcke 1979; Cole 1981), whichwe discuss later in this chapter.

An important assumption underlying the analysis of temporal activity pat-terns is that animals that feed at different times have different diets. Thisassumption can be tested by examining the correlation between activity pat-terns and diet (JaksiC 1982). For example, diurnal and nocturnal predators maydiffer in their diets and thereby face less competition for food than predatorswith identical activity profiles. The null hypothesis here is that dietary overlapbetween matched species pairs that forage at the same time (diurnal-diurnalor nocturnal-nocturnal) is no different than that for mixed species pairs thatforage at different times (diurnal-nocturnal). The alternative hypothesis is thatcompetition has promoted temporal segregation, so that matched species pairsoverlap less in diet than mixed species pairs (Huey and Pianka 1983).

JaksiC (1982) tested these hypotheses for dietary overlaps of diurnal falconi-form and nocturnal strigiform raptors. Overlaps of all possible species pairswere compared using standard nonparametric statistics. In no case was there asignificant difference in dietary overlap of mixed versus matched species pairs.Thus, temporal partitioning did not reduce exploitative competition for foodresources, although it may have alleviated interference competition (Jaksik etal. 1981).

However, conventional statistics may be unsuitable for testing the mixed-matched dietary overlap hypothesis (Pimm 1983). First, none of the pairwisedietary overlaps are independent-the overlap between species A and is notindependent of the overlap between A and C and between and C. Second, theoverlap distances are geometrically constrained so that the maximum distancebetween any pair of species is 1.0. Finally, the analysis is likely to be sample-size dependent: the more species there are in the comparison, the closer, onaverage, are the nearest neighbor distances in dietary niche space. For all thesereasons, a null model is necessary to properly test the mixed-matched dietaryhypothesis.

Suppose there are n nocturnal and m diurnal species. Then there are mnmixed comparisons and 0.5[n n 1) m m I)] matched comparisons ofspecies pairs. Pimm (1983) suggested randomly assigning the m n labels ofnocturnal or diurnal to each species and then calculating dietary overlaps ofmixed and matched pairs for this random assemblage. Repeating the proceduremany times gives the mean and sample variance of the distribution of dietaryoverlap for each nearest neighbor, which can then be compared to the actual


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The Temporal Niche 99

Figure 5.2. Dietary overlaps for syn-chronous and asynchronous lizardpredators in the deserts of Africa(upper panel) and Australia (lowerpanel). Synchronous species pairs for-age at the same time of day. The histo-grams are the results of 200randomizations, and the mangles showthe observed values. Analyses aregiven for the firjt four nearest neigh-bors in niche space. Note that synchro-nous predators show more overlap andasynchronous predators less overlapthan expected. These patterns are oppo-site to what one would expect if tempo-ral partitioning of food resources wereimportant. From Huey and Pianka(1983). Reprinted by permission of thepublisher from Lizard Ecology: Studieson a Model Orgimism R B. Huey,E R. Pianka, and T. W Schoener (eds).Cambridge, Mass.: Harvard UniversityPress. CopyrightO 1983 by the Presi-dent and Fellows of Harvard College.

3earness Rank

values. If the mixed-matched dietary hypothesis is correct, matched speciespairs should ove rlap in diet less than expe cted, and mix ed species pairs shouldoverlap more than expected. Moreover, the percentage of first nearest neigh-bors in niche space that are matched should be less than that predicted by thenull model.

Huey and Pianka (1983) used Pimm s (1983) recipe to examine dietarydifferences b etween nocturnal a nd diurnal predators in assem blage s of lizards,raptors, and water snakes. For both African (Kalah ari) and A ustralian lizards,significantly more first- and second-nearest neighbors in dietary similaritywere sy nchro nou s than w ere asyn chro nou s in their activity times. Similarly,synchronous pairs of species tended to overlap in diet more often than pre-dicted, and asynchrono us pairs less often than predicted, by the M onte Ca rlosimulation (Figure 5.2 . These patterns are opposite to the predictions of themixed-matched dietary hypothesis, suggesting that lizard food resources are


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not being partitioned by spec ies that are active at different time s of day. For alarge data set on raptor diets Craighead and Craig head 1956 ), Huey andPianka 1983) found that overlaps of synchronous versus nonsynchronouspredators did not differ significantly from predictions of the null model. Fi-nally, for dietary data on four species of water snakes Mushinsky and Hebrard1977a,b), dietary overlaps of synchronous species were higher than expected,although there w ere too few specie s in the assem blage for a statistical test.

These analyses indicate that the degree of synchrony in activity periods isunreliable as an indicator of dietary overlap. The null model simulationscontradict widely held beliefs that activity times allow vertebrate predators topartition food reso urces, and caution again st the use of time as a niche dimen-sion in competition analyses. Alternative explanations for the evolution ofnocturnal and diurnal feeding strategies include predator avoidance Lima and D ill1990), alleviation of interference com petition Carothe rs and JaksiC 1984), andphysiological thermal constrain ts Porter e t al. 1973).

Although there is little evidence for temporal partitioning by predators on adaily time scale, partitioning of food resources on a seasonal basis may beslightly m ore plausible. For exam ple, Vannote and Sw eeney 1980) hypothe-sized that competition for food within functional feeding guilds of streaminsects will lead to a temporally staggered sequen ce of maxim um reso urce useby species. Ge orgian and W allace 1983 ) tested the prediction by measurin gseasonal production of six spe cies of periphyton-grazing insects in an Appala-chian stream. Peak production for each species followed an orderly sequence ,with very little overlap between species. Based on the Poole and Rathcke1979) test described later in this chapter), production peak s for each species

showed an unusually large degree of separation p 0.1 . Overlaps based ondensity and biom ass were generally higher than those based on production.

PHENOLOGIC L OVERL P IN PL NT COMM UNITIES

Robertson 1895 ) first proposed that pollen transfer by animals was a poten -tially limiting resource that could lead to staggered phenologies of floweringplants. However, at least three hypotheses may exp lain a staggered seque nce offlowering times in a com munity Waser 1983): 1) pollinator preference, inwhich on e plant specie s attracts pollinators aw ay from othe r species, leadin g toreduced reproductive success M osquin 197 ;A. Lack 1976); 2) interspecificpollen transfer, in which pollen is exchanged between simultaneously flower-ing species, causing pollen loss, reduction of receptive stigma surfaces, andreduced reproductive success Thom son et al. 1981); 3) formation of mal-


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in this assemblage can be used as a null ex-_ _pectation for overlaps in the absence of com-

Figure 5.3. A randomly generated 20-speciesflowering phenology A). Overlap patterns

c_

adapted hybrids, in which pollen exchange between related species reducesfitness (Levin 1971). Mechanism 1) is implicit in most ecological studies of

petitive interactions. Phenology in a realassemblage is shown in (B) (see Figure 5.4).From Gleeson, S. K. 1981. Character dis-placement in flowering phenologies.Oecologia 5 :294-295, Figure 1. Copyright

1981 by Springer-Verlag CimbH Co.KG.

phenological overlap. Mech anism (2) is a form of interference competition th at

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- 9J F M A M J J A S O N D

can lead to segregation in flowering times even when pollinators are not alimiting resource, and can affect wind-pollinated species as well. All threemechanisms assume that an increase in the abundance of one plant speciesreduces pollination of other species that share common pollinators. This as-sumption notwithstanding, rare plant species may som etimes benefit from thepresence of other, com m on species acting as magnets for pollinators (Thom-son 1978; Schemske 1981).

Whereas temporal segregation of animal foragers does not necessarily reducedietary overlap, segregation of plant flowering times will reduce overlap in sharedpollinators. How ever, the con verse is not necessarily true-high overlap in tlower-ing times need not imply strong competition for pollinator visits. For example,Thomson (1982) found that overlaps in flowering times of subalpine meadowplants were unrelated to relative v isitation rates by pollinators. Thus, phenologicaloverlap was not a good indicator of competition for pollinator visits.

In spite of an extensive catalog of flowering phenology studies, the evidenc efor staggered flow ering times in most plant comm unities is weak (Waser 1983;Rathc ke and Lacey 1985; W heelright 1985). Befo re the advent of null models,staggered flowering patterns were evaluated visually, not statistically (e.g.,Heinrich 1976; Stiles 19 77). But app earance s can be deceivin g. For exam ple,Figure 5.3a looks, to our eyes, like a staggered flowering seq uenc e that might


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102 Chapter

be the result of interspecific com petition. But this sequence of flowering timeswas generated by a random draw of numbers from a uniform distribution andrepresents a pattern that might be expected in the absence of competition forpollinators (Gleeson 1981).

When flowering phenologies are com pared to appropriate null m odels, theresults may be surprising and controversial (Rathcke 1984). Poole and R athcke(1979) proposed the first statistical test of flow ering overlap patterns. T heir testconsidered the spacing of peak flowering time for each species and thereforedid not directly test for overlap. Analyses of the spacing of flowering peaks inplant com munities are identical to analy ses of the sp acing of body sizes in ananimal comm unity (Pleasants 1980), which we discuss in Chapter 6.The Poole and Rathcke (1979 ) test summ arized overlap as a single index, thesample variance of the distance between adjacent flowe ring peaks. For the firstand last flowering species in the assemblage, distance is measured from thepeak to the boundary of the grow ing season. The null hypothesis is the equiva-lent of assigning ea ch spe cies a random uniform value, ranging f rom 0.0 to 1 O,for its flowering peak within the growing season. If competition has led to aregular spacing of peak flow ering times, the observed (population) variancein the position of the flowering peaks, P, should be significantly smallerthan expected. Un der the null hypothesis, the expectation of P fo r a set of kspecies is

The ratio of observed to expected variance (PIE(P)) is an index that corre-sponds to flowering peaks that are aggregated (PIE(P ) > I), random (PIE(P) =I ) , or staggered P I E P ) 1 within the growing season. Although Poole andRathcke (1979) compared the quantity kP to a chi-squared distribution, it ismore appropriate to compare the results to a randomization test (Williams1995). De Vita (1979) developed a similar null model for analyzing resourceutilization peaks of species (see Chapter 4 . These tests ultimately d erive fromM acArthur s (1957 ) broken-stick model, in which points are randomly placedon a unit interval to simulate the relative abundance of species in an assem-blage (see Chapter 3 .

A case history illustrates the use of the Poole and R athcke (1979) test and atypical cycle of reanalysis that has accompanied many null model investiga-tions. Poole and R athcke (1979) applied their test to Stiles s (1977 ) dat a onflowering times of 11 humm ingbird-pollinated plant species in a Costa Ricanrain forest (Figure 5.4). Stiles (1977) had claime d that flowering peaks exhib-ited an orderly, staggered sequence, but the Poole and Rathcke (1979) test


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1 16

J F M A M J J A S O N D

Figure 5.4. Flowering times of 11 species of hummingbird-pollinated plants lowerpanel). Numbers denote individual plant species: 1) Helic.onia pogonatha; 2 )Passijlora vitifolia; 3) Heliconia wagneriana; 4) Jacohinia aurea; 5) Costus ruher;6)Heliconia sp. 18; 7) Heliconia sp. 16; 8) Aphelandra sinclairiana; 9) Costus

malortieanus; 10) Heliconia sp. 3; 1 1)Malvaviscus arborea. The upper panel givesthe mean and standard deviation of monthly rainfall, with symbols for each of the 4years of the study. The rainfall data were used to divide the data into wet- and dry-sea-son plants. Depending on the data partition and the null model used, this flowering se-quence has been described as aggregated Poole and Rathcke 1979), random Gleeson1981), or segregated Cole 1981). From Stiles, F. G. 1977. Coadapted competitors: theflowering seasons of hummingbird-pollinated plants in a tropical forest. Science 198:1177-1 178. Copyright O 1977 American Association for the Advancement of Science.Reprinted with permission.


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104 Chapter

revealed that flowering peaks in four consecutive years were significantlyaggreg ated, not stagg ered. However, these results ap pear to have been inaccu-rate due to a computational error (Robert W. Poole, personal communication,cited in G leeson 1981 ). Gleeson (1 981) recalculated the test and found that thepattern actually was staggered (P/E(P) I), but not significantly so. In any case,the results did not strongly sup port the o riginal claim of staggered flowering times.

Both S tiles (1979 ) and Co le (1981) argued that Poole and Rathcke s (1979 )analysis was invalid because different groups of species flowered during dis-tinct wet and dry seasons in the Costa Rican rain forest. Co le (1981) reanalyzedflowering times separately for wet- and dry-season species and found signifi-cant staggering w ith the Poole and Rathck e (197 9) test.Co le (1981) argued that the Poole and Rathc ke (1979) test was problematicfor two reasons: (1) boundaries of the grow ing season are incorporated into thedistance measure for the two terminal species of an assemblage; (2) the testmeasures not overlap in flowering times, but regularity in the spacing of peakflowering times. Species could have a regular spacing of flowering peaks butstill overlap highly in flowering times. Alternatively, species could haveclum ped flowering peaks but still have little overlap in flowering times. N ei-ther pattern w ould be revealed by the Poo le and Rathck e (1 979) test.Cole (1981) proposed a different metric, which represents the floweringperiod as a line se,ment rather than representing the flowerin g peak as a singlepoint. For the null hypothesis that the flowering period of each species occursrandomly and independently within the growing season, the expected amountof overlap between any given pair of species E d ) ) s

where is the length of the growing season, LI is the length of the firstsegment, and L is the length of the second segm ent. Th is same model has beendeveloped in the context of niche overlap (Sugihara 1986; see Chapter 4) andthe overlap of species spatial ranges (Pielou 1977; Dale 1986 ; see Chapter 9).

Statistical analysis is problematic. Cole (1981) suggested comparing ob-served and exp ected overlaps of all possible species pairs and using a binomialtest to evaluate the number of species pairs above and below the expectation.By this test, overlap for S tiles s (1 977) data was unusually low 0 = 0.02 . Thebinomial test assum es that the probability distributions are sy mm etric and thatthe species pairs are independent of one another. Cole (1981) showed by


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simulation that the symmetry assumption was not critical, but nonindepend-ence of species pairs is a serious problem. Similar comments apply to tests ofbody size ratios (Case and Sidell 1983; Schoener 1984) and co-occurrence data(Wright and Biehl 1982) that compare all possible species pairs. In contrast toCole s (1981) test, the Poole and Rathcke (1979) test has relatively weakstatistical power (Simberloff and Boecklen 198I , but it summarizes the patternof peak spacing for an entire assemblage in a single number, so it is notburdened by nonindependent comparisons of individual species pairs.

Fleming and Partridge (1984) investigated phenological overlap with a simula-tion of Cole s (1981) model. They assumed that the flowering period for eachspecies was fixed in length, and then randomly placed each interval on a lineTegment. The end points of this line segment corresponded to the observed begin-ning and end of the flowering season. In addition to painvise overlap, Fleming andPartridge (1984) measured the n-wise overlap of each species with the aggregatephenology of the remaining n 1 species. The n-wise overlap might provide abetter measure of the effects of diffuse competition (Pianka 1974) than the painviseoverlap. Both measures gave similar results, although the null hypothesis wasrejected more often with painvise overlap. Using these methods, Fleming andPartridge (1984) analyzed a variety of published phenologies and found thatrandom or aggregated patterns were the rule. Their test has subsequently been usedto assess phenological overlap of other tropical plant assemblages (Fleming 1985;Murray et al. 1987), the timing of seedfall in a guild of ant-dispersed herbs(Kjellsson 1985), and the spatial distribution of parasitic helminths along bat guts(Lotz and Font 1985), all of which were random or aggregated.

However, these measures of phenological overlap may be misleading. Pleas-ants (1990) tested the statistical power of the pairwise and n-wise overlapmeasures against a hypothetical phenology that was strongly segregated. Theseindices did not reveal significance for assemblages that were obviously struc-tured by competition (Type I error), whereas low overlap was revealed for ahypothetical assemblage that was not ordered by competition (Type I error).Rather than comparing individual species pairs, Plcasants (1990) recommendedcalculating the average pairwise overlap for the entire assemblage and compar-ing this single number to the values emerging from the simulation. This is thesame metric used in niche overlap studies (Inger and Colwell 1977; Pianka1980), and it did not suffer from Type I and Type I1 errors. As we noted for thePoole and Rathcke (1979) test, mean pairwise overlap avoids nonindependentcomparisons. Mean pairwise overlap may not reveal some low-overlap patterns(Thomson and Rusterholz 1982), but if both the mean and the variance ofoverlap are calculated, comparisons with null models will usually be valid(Winemiller and Pianka 1990).


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106 Chapter

Ashton et al. (1988) pointed out a more serious problem with Monte Carlosimulation s of C ole's (1981) model. If the boundaries of the flowering seaso nare determined by the observed first and last flowering species (which isusually the case), the simulated flowering season will always be too shortbecause the segm ents are thrown randomly between these two boundaries. Thisedge effect (Haefne r et al. 19 91) biases the test toward findin g staggered

(low-overlap) pattems. It is therefore noteworthy, and worth repeating, thatmost simulation studies have detected random or aggregated pattems, whichare in the opposite direction of this inherent bias.

Ashton et al. (1988) suggested a simple scaling procedure that adjusts thesimulated flowering phenologies to the correct growing season. First, random-ize the placement of the flowering peaks within the line segment, as in thePoole and Rathcke (1979) test. Then expand the scale of the segment toencom pass the starting time of the first species and the ending time of the last.This scaling ensures that the simulated flowering times are randomly placedwithin the growing season. Overlap in the null assemblage can then be com-pared to the real data. Using this procedure, Ashton et al. (1988) detected asignificant staggering of flowering times in tropical dipterocarps. An additionalnull model showed that mass flowering years were associated with droughtsand the occu rrence of El Niiio events.

Staggered flowering times have also been detected in meadow plant com mu -nities of the Rocky Mountains. Pleasants (1980) divided the assemblage intoguilds based on the identity of the dominant species of bumblebee pollinator.Of 11 guild comparisons, mean pairwise overlaps were significantly less thanexpected in five, and marginally less than expected (0.05 p 0.15) in fiveothers. However, these simulations followed Cole's (1981) procedure, so theywere biased against the null hypothesis (Ashton et al. 1988). In addition,previous null model tests of flowering times in a different set of sites in theRocky Mountains did not reveal a significant reduction in temporal overlap(Thomson 1982).

Pheno logical studies indirectly assess competition fo r pollinators by assum-ing it is more severe with increasing temporal overlap. Armbruster (1986)addressed competition m ore directly by exam ining species co-occurrence andshared pollinators in assemblages of the eupho rb Dalechampia His study is abotanical analog to the mixed-matched dietary hypothesis for predator assem -blages. Arm bruster's (1986) analysis is notew orthy for its use of both ecolog-ical and evolutionary null hypotheses. Th ese null hypotheses are similar inspirit to tests for mechanisms of ecological assortm ent and evolutiona ry diver-gence (Case and Side11 1983) in produc ing patterns of character d isplacem ent(see Chapter 6). The ecological null hypothesis was that sympatric species


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NUMBER OFOVERL PS

> .LU

O.lnL L

Figure 5.5. Frequency distribution of pollinator niche overlaps generated by a null modelfor Australian triggerplants Stylidiurn). rom Armbmster et al 1994),with permission

Observed number < 99.7 01 runs)

were assembled at random with respect to the pollinator species utilized. Theevolutionary null hypothesis was that each population evolved pollinator asso-ciations at random with respect to those of sympatric congeners. A mixedmodel contained elements of both ecological and evolutionary models. Overall,there was a marginal tendency toward reduced overlap in shared pollinators,although the results depended on the type of null model used, whether sourcepool species were equiprobable colonists or not, and how local sympatry wasoperationally defined.

A similar analysis revealed much more striking patterns in an assemblage of31 species of triggerplants Stylidium spp.). At 25 sites in western Australia,there was only one overlap of discretely defined pollinator niches for 86comparisons of sympatric species pairs Armbruster et al. 1994). In contrast,the ecological, evolutionary, and mixed null models generated an expectationof approximately four to seven pollinator niche overlaps Figure 5.5 . Ninespecies of Stylidium in this assemblage exhibited intraspecific variation incolumn reach, which determines pollen placement. A significant pattern ofcharacter displacement in the presence of sympatric congeners also suggestedthat competition for shared pollinators structured this assemblage.

These examples of reduced overlap in pollinators or flowering times areexceptional. Most tests have revealed aggregated or random phenologicaloverlap, compared to the null hypothesis of equiprobable flowering periodswithin a uniform growing season. Detailed studies of phenology in temperateParrish and Bazzaz 1979; Anderson and Schelfhout 1980; Rabinowitz et al.

1981) and tropical Wheelright 1985) plant communities have not revealedunusually low temporal overlap. For example, Rathcke 1988a) measured theflowering periods of 14 species of temperate shrubs over five years. Flowering

O . O + 0 2 4 6 8 1 I 2 14


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phenologies were significantly aggregated within a season and consistentacross years. Althoug h ag gregation migh t increase competition for pollinators,field experiments showed that seed production of only four of the 14 specieswas limited by pollination, and of these, only one was likely to have sufferedcompetitive effects (Rathcke 1988b).

CONSTR INTS

The independent placement of species flowering times within a uniform grow-ing season is the appropriate null hypothesis fo r tests of phenological ov erlap.However, even within an appropriately defined growing season, there may beother types of constraints on flowering phenology. For exam ple, the floweringinterval for a species may be correlated with the time of the flowering peak inthe growing season (A shton et al. 1988), and null m odels might be m ade m oresophisticated by incorporating such constraints. Divergence in flowering timesmay also e constrained by plant mating systems (Lindsey 1982; Flanagan andM oser 1985), seed predators (Augsburger 1981), seed production (Roach1986), and pollinator attraction (A ugsburger 1980). So m e of these forces m aypromote convergence rather than divergence of flowering times.

A more fundam ental l imitation to f lowering phenology may be inherentphylogenetic constraints on flowering time. Independent of ecological forces,the flowering time of a species may fall within certain limits that arecharacteristic of its clade. Koch me r and Handel (1986) used phylogeny as anull hypothesis in a com para tive study of flow ering times of animal-pol-

l inated angiosperms of North and South Carolina and temperate Japan.Flowering times were similar on the two continents but differed signifi-cantly for species in different plant families. Each plant family had acharacteristic f lowering time and skewn ess, and there w ere negative corre-lations between skewn ess and mean family f lowering times. These phyloge-netic fingerprints we re more pronounced than differences in flow eringtimes am ong plant life forms (e.g., trees versus shrubs). Th e results sug gestthat, regardless of local com petitive pressures, the flow ering times of plantspecies were limited by phylogeny. Within these limits, phenology may stillbe shaped by competition, mutualism, and other ecological interactions,although K ochm er and Handel 's (1986) analyses w ere too coarse to evalu-ate such effects. In any case , the use of phylogeny as a null hypothesis is apromising avenue for future studies of phenology and other community-level patterns (Harvey an d Page1 1991).


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Th e Temporal iche 109

NONEQ UILIBRIUM N LYSESThe preceding analyses all make the imp licit assumption that flowering timesor activity periods of species have reached an ecological or evolutionaryequilibrium. The equilibrium assumption underlies much of the deterministicmathe matics of comm unity ecology theory (e.g., M acArthur 1972), but itsrelevance to many real communities is questionable (e.g., Boecklen and Price1991 ). Equilibrium and nonequilibrium com mu nities may be structured bydifferent mechanisms (Wiens 1984). For example, predictable patterns ofresource availability may lead to specialization and resource partitioning bycompetitors in an equilibrium comm unity (Schoener 1974a). In phenologicalstudies, equilibrium com mu nities would exhibit the sa me patterns of temporaloverlap from one year to the next (e.g., Stiles 1977; Rathcke 1988a). Incontrast, if the availability of resources fluctuates through time, competitiveeffects may be intermittent and may only be important during occasionalresource crunches (Wiens 1977). For pheno logical studies, nonequilibrium

communities would be characterized by variable patterns of temporal overlapand sets of shared pollinators.

W hat w ould constitute a valid null model for assessing the equilibrium statusof a community? In Chapter 10, we consider this problem in the context ofcom mu nity stability and food w eb models. H ere, we address a more restrictedquestion: Do co-occurring species exhibit compensatory fluctuations in abun-dance, activity, or phenology? Compensatory change might suggest competi-tive interactions as species covary negatively in abundance. Alternatively,positive c ovariation migh t result if species tracked shared resources that fluctu-ate in abundance (Schluter 1984).

Th e data for such an analysis wou ld consist of a matrix w ith rows represent-ing species and co lumn s representing census dates. The entries in the matrix arethe abun dance (or activity) of each species at each census. Patterns of covaria-tion in this matrix can be quantified by comparing the sum of the individualspecies variances to the variance of their sums (Pielou 1972a; Robson 1972).The latter variance includes the average covariation between species pairs,which is a good m easure of compensatory fluctuations. The ratio of the secondvariance to the first, V reveals whether species are fluctuating independently( V = I) , concordantly (V > 1) or compensatorily (V 1). Ja vi ne n (1979)calculated the reciprocal of V for censuses of avian communities at differentlatitudes. T his index was not consistently different for northern versus southernassemblages, contradicting the hypothesis that compensatory fluctuations sta-bilize species-rich tropical communities (McNaughton 1977).


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110 hapter

mp t y b it Las ius pa l l i t a r s i sr e m a t o g a s t e r p u n c t u l a t a P h e i d o l e d e n t a t a

M o n o m o r i u m m i n i m u mFigure 5.6. Spatial and temporal segregation of common grassland ants as measuredby the variance ratio Schluter 1984).Each matrix shows the species occurrences at 25tuna-fish baits placed in a 5 x 5-m grid that were censused for 4 consecutive hours inCaddo County, Oklahoma, July 1992.The variance ratio indicates significant spatialpartitioning at certain times of the day. Symbols indicate the presence of particular spe-cies at individual baits. Unpublished data from Marc C. Albrecht.

James and Boecklen 1984) refined this approach in an analysis of sevenyears of breeding bird census data from M aryland w oodlands. To estimate thevariance components, they assumed that individual birds were distributedaccordin g to a Poisson process. V fo r this assemblage w as 0.65, which was inthe direction of negative cov ariation, although still within the limits expectedby chance p 0.28). The covariance matrix revealed one pair of speciesCardinal-Red-eyed Vireo) with a large positive covasiation, follo we d in ord er

of decreasing magnitude by pairs with positive or negative covasiation. Al-


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though the abu ndan ces of particular pairs of spec ies were correlated , there wasno evidence over the 7-year study for strong com pensatory fluctuations in theassem blage as a whole.

Schluter (1984) developed significance tests for the variance ratio. Theproduct of the variance ratio and the number of censuses VT) has an approxi-mate chi-squared distribution with T degrees of freedom. Simulated datashowed an acc eptable fit to the chi-squared distribution, so the variance ratiocan be evaluated without the use of a simulation. McCulloch (1985) showedthat, for presence-absence data, the variance ratio is a mu ltiple of C ochran s Qstatistic (Coch ran 1950 ), which has been used a s a null hypothes is to testequiprobable colonization of aquatic taxa in experimental ponds (Wilbur andTravis 1984). Hastings (1987) found that the variance ratio did not alwaysreveal significant patterns for a simp le competition model in which the proba-bility of extinction was proportional to sp ecies richness. The varian ce ratio w illreveal cases where the average pairwise correlation between species is negative(McC ulloch 1985 ), althoug h, like all statistical tests, the va riance ratio issensitive to sample size and samp ling error. Perhaps fo r this reason, a literaturesurvey of spec ies co-occurrenc e matrices revealed m ostly random o r ag gre -gated spatial patterns as measured by the variance ratio (Schluter 1984).An interesting exception can be found in the co-occurrence pattern of ant speciesat tuna-fish baits in an Oklahom a grassland (Marc C. Albrecht, unpublished data).Spatial occurrence, as measured by the variance ratio, was strongly negative.However, the spatial pattern changed on an hourly basis, as different associationsof species emerged because of die1 foraging patterns (Figure 5.6). Most authorshave used the variance ratio as an index of spatial co-occurrence (see Chapter 6),and more long-term commun ity studies such as James and Boecklen s (1984) areneeded to evaluate the com pensatory fluctuations hypothesis.

RECOMMEND TIONSTo compare the diets of synchronous and asynch ronous predators, we recom -mend Pim m s (1983) Monte C arlo simulation of the mixed-ma tched dietaryhypothesis. Th e Poole and R athck e (1979) test, with mod ifications by Williams(1995), is acceptable for simple analyses of flow ering peaks, although so me ofthe character displacem ent tests described in Chapter 6 may be m ore powerful.If the data consist of flowering intervals for each species, we recomm end themodification of Cole s (1981) test by Ashton et al. (1988). The variance ratio(Schluter 1984) is appropriate for testing the hypothesis of compensatoryfluctuatio ns of abund ance or activity throu gh time.


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Null Models Chapter 5

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