a simulation model of mexican long-nosed bat (leptonycteris nivalis) migration

Ecological Modelling 134 (2000) 117–127

A simulation model of Mexican long-nosed bat(Leptonycteris ni6alis) migration

Arnulfo Moreno-Valdez *, William E. Grant, Rodney L. HoneycuttDepartment of Wildlife and Fisheries Sciences, Texas A&M Uni6ersity, College Station, TX 77843-2258, USA

Received 5 July 1999; received in revised form 1 February 2000; accepted 4 February 2000

Abstract

We (1) describe a model that simulates migration of the Mexican long-nosed bat (Leptonycteris ni6alis) based onthe flowering phenology (nectar–pollen production) of agaves (Agavaceae) and hypothesized ‘rules’ governing batmovements; (2) evaluate the model by comparing simulated seasonal and spatial patterns of nectar production andconsumption, and bat movements and densities, to patterns observed in the field; and (3) use the model to examinevarious hypotheses concerning factors that control migration. A nectar production sub-model represents the floweringphenology of agaves in terms of the daily availability of nectar within each of four latitudinal intervals between 18and 29°N. A bat migration sub-model represents the number of bats present within each latitudinal interval each day,with bat movements from one site to another depending on availability of nectar and season. Simulated patterns ofnectar consumption are similar to observed patterns of nectar production based on the number of flowering plantspecies present at different latitudes. Simulated patterns of bat movements are similar to general patterns observed inthe field for Leptonycteris curasoae and L. ni6alis. Simulated fluctuations of bat density at the southernmost latitudeexhibit the same general annual cycle observed at a southern roost of L. curasoae. The seasonal representation ofnectar production in the model corresponds well with patterns of nectar production observed over a 2-year period ata site in northern Mexico, although nectar production in the model begins somewhat earlier. Simulations examiningfactors hypothesized to control migration indicate that predicted migration patterns correspond well with fieldobservations only when model rules assume that both food availability and season limit migration, and that all batswith access to sufficient energy during the correct season migrate. © 2000 Elsevier Science B.V. All rights reserved.

Keywords: Mexican long-nosed bat; Leptonycteris ni6alis ; Migration; Agaves (Agavaceae); Food availability; Simulation model

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1. Introduction

Migration is an important component of thelife history of many organisms (Rankin, 1985).Not only does migration permit escape from unfa-vorable conditions, but it also allows exploitationof habitat created by spatial and temporal

* Corresponding author. Tel.: +1-979-8455777; fax: +1-979-8453786.

E-mail address: [email protected] (A. Moreno-Valdez).

0304-3800/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved.

PII: S0304-3800(00)00253-2

A. Moreno-Valdez et al. / Ecological Modelling 134 (2000) 117–127118

changes in the environment (Dingle, 1996).Among mammals some species of ungulates, pin-nipeds, cetaceans, and bats exhibit long-rangemovements (Orr, 1976). Bat migration has beendocumented for both tropical and temperate spe-cies (Fenton and Thomas, 1985). In North Amer-ica, migratory bats are represented by manyspecies of temperate vespertilionids that move sea-sonally between breeding colonies and hibernatingroosts, north temperate tree bats that move southduring the winter, and tropical bats that migratenorth to give birth (Griffin, 1970; McNab, 1982).The best examples of tropical migrants in NorthAmerica are the insectivorous Mexican free-tailedbat (Tadarida brasiliensis) and the nectarivorouslong-nosed bats (Leptonycteris ni6alis and Lep-tonycteris curasoae ; Barbour and Davis, 1969).Mexican free-tailed bats show high altitude migra-tions (Constantine, 1967), whereas long-nosedbats move through nectar corridors (Fleming etal., 1993). Nectar corridors have important con-servation implications for the federally endan-gered long-nosed bats because elimination of foodplants along the corridor jeopardizes both bat andplant populations (Fleming et al., 1993). How-ever, due to the spatial and temporal variability inabundance of both bats and their food resources,it is difficult to determine if recent observations oflow bat densities should be attributed to eitherhabitat destruction or naturally occurring varia-tion in flowering plant density.

In this paper we (1) describe a model thatsimulates migration of the Mexican long-nosedbat (L. ni6alis) based on the flowering phenology(nectar–pollen production) of agaves (Agavaceae)and hypothesize ‘rules’ governing bat movements,(2) evaluate the model by comparing simulatedseasonal and spatial patterns of nectar supply andbat densities to patterns observed in the field, and(3) use the model to examine various hypothesesconcerning the factors controlling migration.

2. Background information

The genus Leptonycteris is represented by twospecies, L. ni6alis and L. curasoae (Mexican andlesser long-nosed bats, respectively). L. ni6alis isknown from central Mexico to the Big Bend areaof Texas, and Hidalgo County, New Mexico (Fig.1; Arita and Humphrey, 1988), whereas L. cura-soae has two disjunct populations, one distributedfrom southern Arizona and New Mexico to Cen-tral America, and the other in northern SouthAmerica (Koopman, 1981; Arita and Humphrey,1988). Both species are sympatric in central andnorthern Mexico (Arita and Humphrey, 1988).

Mexican and lesser long-nosed bats have beenconsidered as migratory species based on theirseasonal absence from the American southwest(Fenton and Kunz, 1977). Additionally, Cockrum(1991) provided evidence of seasonal variation inthe northwestern distribution of L. curasoae, andFleming et al. (1993) indicated the presence offeeding corridors along the migratory path of L.curasoae. Also, genetic data reveal migrationroutes for this species (Wilkinson and Fleming,1996). Even though scarce, some data suggest thatL. ni6alis migrate north in early spring from as farsouth as Morelos, Mexico, to their northern rangeand then back south in late summer (Schmidly,1991; A. Moreno-V., unpublished data), indicat-ing that they may travel as far as 1200 km. Thebreeding season in L. ni6alis appears to be re-stricted to April, May, and June (Wilson, 1979).Lactating females and their young arrive at BigBend National Park in June and leave the area bythe end of August (Schmidly, 1991).

Fig. 1. Geographical distribution of the Mexican long-nosedbat (L. ni6alis).

A. Moreno-Valdez et al. / Ecological Modelling 134 (2000) 117–127 119

Fig. 2. Conceptual model representing effects of food availability on migration of Mexican long-nosed bats. Boxes represent statevariables, large arrows represent material transfers, small arrows represent information transfers, circles represent driving variables(SEASON), auxiliary variables (FS), or constants (ER, D). Names of system components correspond to those defined in the text.

3. Model description

The model, which represents the seasonal mi-gration of the Mexican long-nosed bats fromCuernavaca (18°N 92°W), Morelos, Mexico, toBig Bend National Park (29°N 103°W), Texas(USA), consists of two sub-models that represent(1) nectar production and (2) hypothesized ‘rules’governing bat migration (Fig. 2). The nectar pro-duction sub-model represents the flowering phe-nology of agaves in terms of the daily availabilityof nectar (NAt) from January 1 to December 31within each of four latitudinal intervals, 18–20,21–23, 24–26, and 27–29°N. The amount ofnectar available at a given site is a function of thedaily nectar production (NP) minus the volumeconsumed by bats (NC) minus the nectar con-tained in flowers that have senesced (NS):

NAt+1=NAt+ (NP−NC−NS)Dt (1)

The bat migration sub-model represents the num-ber of bats present (BPt) within each latitudinalinterval each day from January 1 to December 31.The number of bats present changes as a functionof immigration from the north (IN) and from thesouth (IS) and emigration toward the north (EN)and toward the south (ES):

BPt+1=BPt+ (IN+IS−EN+ES)Dt (2)

Bat movements from one site to another dependon availability of nectar and season.

The model is formulated as a discrete-timecompartment model based on difference equa-tions with a 1-day time step. Simulations are runusing STELLA® (High Performance Systems,1998). Spatial relationships are represented im-plicitly in the model by assuming that 24 sites arelocated along a 1200-km latitudinal gradient fromsouth (Cuernavaca) to north (Big Bend NationalPark) at 50-km intervals (Fig. 1).


3.1. Nectar production sub-model

3.1.1. Nectar productionThe flowering season of paniculate agaves is

from January to December between 18 and 23°N,March to November between 24 and 26°N, andApril to November between 27 and 29°N (Gentry,1982) (Fig. 3(a)). Daily nectar production (NP) isarbitrarily considered to be normally distributedduring the appropriate flowering season (FS) de-

pending on latitude (Fig. 3(b)), with the totalannual nectar production at each site assumedequal. Specific energetic data are not available foragave nectar–pollen production or for consump-tion of nectar–pollen by L. ni6alis. Thus, NP isrepresented in arbitrary units, with one unitdefined as the energy required for one bat to fly 1km. Because bats are considered K-selected ani-mals (Findley, 1993) whose populations are at ornear carrying capacity of their environments (Pi-

Fig. 3. (a) Flowering months of agaves (shaded) distributed within the range of the Mexican long-nosed bat (L. ni6alis) at fourlatitudes (Gentry 1982) and (b) relative seasonal distribution of nectar production at different latitudes as represented in the model(Fig. 2).


anka, 1994), total annual nectar production(1 000 000) is adjusted to represent the amount offood required for a hypothetical population of2472 bats to complete the 1200-km round-tripmigration.

3.1.2. Nectar consumptionIn the model daily nectar consumption (NC)

represents only that portion of food consumedthat is required for flight, not for other physiolog-ical requirements. NC at each site is a function ofnectar production (NP) at that site and energyrequired (ER, arbitrary units with one unitdefined as the energy required for one bat to fly 1km) by the bat population (BPt) to fly a givendistance (D, km). D is held constant at 50 km forsimulations in this study.

NC=BPtDER if NP]BPDER (3)

NC=NP if NPBBPDER (4)

3.1.3. Nectar senescenceWe assume that nectar available on a given day

is either consumed by the nectar-feeding commu-nity or senesces. In the model, we lump these two‘non-bat’ causes of nectar disappearance as nectarsenescence (NS):

NS=NP – NC (5)

3.2. Bat migration sub-model

Nectarivorous bats have high metabolic rates(McNab, 1982) and rarely have excess energy thatcan be stored as fat deposits (Fleming, 1988). Assuggested for some hummingbirds (True, 1993), itis risky to use all available energy in a straightflight. Due to the uncertainty of finding the nextfood patch along the migratory route, successful(in an evolutionary sense) migrants probably re-turn to a known food patch after they have usedapproximately half of their available energy. Be-cause L. curasoae can fly roughly 100 km per dayin search of food (T. H. Fleming, personal com-munication), in our model bats must acquire 100units of energy (enough to fly 50 km away andback again) for migration to continue. If there issufficient energy produced at a given site during a

given day for all the bats at that site to migrate,then all the bats migrate either north or south,depending on the season. Northward migrationbegins on March 1 and southward migration onSeptember 1. Thus at each site:EN=BP

if NA]BPDER and 60BDOYB244

otherwise EN=0 (6)

ES=BP if NA]BPDER and DOY]244

otherwise ES=0 (7)

where DOY is day of year (1 is January 1; 365 isDecember 31). IN and IS for each site are equalto EN from the adjacent site to the north and ESfrom the adjacent site to the south, respectively.

4. Model evaluation

We evaluated the model by comparing: (1) sim-ulated seasonal and spatial patterns of nectarconsumption to observed patterns of nectar pro-duction; (2) simulated patterns of bat movementsto observed movement patterns in the field; (3)simulated seasonal patterns of bat density to den-sity patterns observed at a southern roost; and (4)the seasonal representation of nectar productionin the model to observed patterns in northernMexico.

Simulated patterns of nectar consumption (Fig.4(a)) are similar to observed patterns of nectarproduction based on the number of floweringspecies present at different latitudes (Fleming,1992) (Fig. 4(b)). Although the latitudes fromwhich data are available fall outside the range ofsimulated latitudes, at more northern latitudesthere is one flowering peak during the middle ofthe year, and at more southern latitudes there aretwo peaks, one in late spring and the other inearly fall. These observations suggest the presenceof two flowering seasons in central Mexico (be-tween 18 and 23°N), rather than one set in themodel. Two flowering seasons seem reasonablebecause it is not advantageous for plants to pro-duce nectar and pollen when their pollinators arenot present.

Simulated temporal patterns of bat movements(Fig. 5(a)) are similar to general patterns observed


Fig. 4. Comparison of (a) simulated seasonal patterns of nectar consumption and (b) observed seasonal patterns of nectarproduction (Fleming, 1992) at northern and southern extremes of bat migration routes.

in the field for L. curasoae (Cockrum, 1991; Ce-ballos et al., 1997) and L. ni6alis. Mexican long-nosed bats arrive at the northern site (Big BendNational Park) as early as April (DOY 91–120)(L. Ammerman, personal communication), returnsouth during September (DOY 244–273)(Schmidly, 1991), and arrive at the southern site(Cuernavaca) during October (DOY 274–304) (A.Moreno-V., unpublished data).

Simulated temporal patterns of bat density ex-hibit the same general annual cycle observed at asouthern roost of L. curasoae (Wilkinson andFleming, 1996; Ceballos et al., 1997): density de-

creases more than 75% during spring as batsmigrate northward, remains at low levels for anextended period of time (\100 days), and in-creases to previous levels during fall as south-ward-migrating bats return (Fig. 6). However,simulated changes in density occur more rapidlyduring both spring and fall, due primarily to thehomogeneous distribution of food and the lack ofinter specific competition in the model. Althoughrepresentation of the seasonal distribution of nec-tar production at a given site seems adequate (seenext paragraph), obviously nectar sources are nei-ther equidistant nor equally productive in the real


Fig. 5. Simulated seasonal patterns of bat migration in which (a) 100%, (b) 50%, and (c) 33% of the bats have access to sufficientenergy for migration to occur.


world. Also, other nectar feeding species surelycompete to some degree with bats rather thansimply ‘cleaning up’ nectar not consumed by bats,as currently represented in the model.

The seasonal representation of nectar produc-tion in the model corresponds well with patternsof nectar production observed over a 2-year pe-riod in northern Mexico (A. Moreno, unpublisheddata), although nectar production in the modelbegins somewhat earlier (Fig. 7). Nectar produc-tion is a driving variable, which was quantifiedbased on more general information (described

earlier) before these recent, local data were avail-able. Thus, these data provide an excellent, inde-pendent point of comparison at one specific sitealong the migration route that was simulated bythe model.

5. Examination of hypothesized rules governingmigration

We examined the parsimony of model structureby eliminating or modifying each of three key

Fig. 6. Simulated seasonal patterns of bat density and patterns observed at a southern roost of L. curasoae, modified from Fig. 2of Ceballos et al. (1997).

Fig. 7. Relative seasonal nectar production observed in northern Mexico (25°N), as indicated by both the number of floweringagaves and the representation of nectar production in the model.


Fig. 8. Simulated patterns of bat migration with (a) no seasonal restrictions on migration (assuming that food availability limitsmigration and that all bats with access to sufficient energy migrate) and (b) unlimited food supply (assuming that all bats with accessto sufficient energy during the correct season migrate).

factors (one behavioral and two environmentalhypotheses) that control migration. We ran aseries of simulations that: (1) no longer requiredall bats with access to sufficient energy during themigration season to migrate (still assuming thatboth season and food availability limit migration);(2) removed seasonal environmental restrictionson migration (assuming that 100% of the batswith access to sufficient energy migrate); and (3)

removed food availability restrictions on migra-tion (assuming that season limits migration).Compared to baseline data (Fig. 5(a)), when ei-ther 50 or 33% of the bats migrate, fewer batsarrive at the northern site and numbers peak laterin the year (see population at 27–29°N on DOY182, Fig. 5(b) and (c)), whereas fewer bats returnto the southern site (see population at 18–20°Non DOY 365, Fig. 5(b) and (c)). Simulations with


no seasonal restrictions on migration do not pro-duce recognizable migration patterns in that batsdo not return to the southern site (see populationat 18–20°N on DOY 365, Fig. 8(a)). Simulationswith unlimited food availability do not producerecognizable migration (Fig. 8(b)). Thus, cur-rently, we are unable to reject any of these behav-ioral or environmental hypotheses. Therefore, wehypothesize that all bats achieve migration if theyhave access to sufficient energy during the rightseason.

6. Discussion

We developed a simulation model of the Mexi-can long-nosed bat migration, and simulated pat-terns of migration are consistent with publisheddata and field observations. We hypothesize thatall bats with access to sufficient energy during theright season migrate, because the model does notproduce recognized migratory patterns when oneof these three factors is eliminated. However, aclear relationship is observed between nectaravailability and bat migration. For this reason itis important to study other patterns of nectardistribution.

It is not known if annual fluctuations in Mexi-can long-nosed bat populations at Big Bend Na-tional Park are natural or caused by man.Easterla (1972) proposed that this is a ‘spill-over’colony formed during years of high populationand/or low food supply in Mexico. These hy-potheses are not supported with our model be-cause the number of bats moving northward is afunction of food availability. Because model pre-dictions and field data (Easterla, 1972) showhigher variation in bat numbers in northern sitesin response to food availability, it is important tostudy population trends on the winter grounds incentral Mexico.

We believe our model provides a starting pointfor studying complex ecological phenomena suchas bat migration. Systems analysis and simulationmodels are cost-effective tools to study large-scaleecological phenomena for which it is virtuallyimpossible to generate a complete empirical data-

base, and for which efforts to collect new fielddata must be targeted well. Results of the presentmodel suggest that more detailed field data relat-ing population dynamics to food availability at aspecific locality are a high priority (Moreno-V.unpubl. data) to increase the usefulness of themodel for evaluating the potential impact of habi-tat fragmentation on migratory patterns of bats.

Acknowledgements

The first author wishes to thank Consejo Na-cional de Ciencia y Tecnologıa and Instituto Tec-nologico de Cd. Victoria Tamaulipas, Mexico, fortheir financial support.

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a simulation model of mexican long-nosed bat (leptonycteris nivalis) migration

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