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PHYSIOLOGICAL AND CHEMICAL ECOLOGY

Modeling Temperature-Dependent Range Limits for the Fire AntSolenopsis invicta (Hymenoptera: Formicidae) in the United States

MICHAEL D. KORZUKHIN,1 SANFORD D. PORTER,2 LYNNE C. THOMPSON,3

AND SUZANNE WILEY3

Environ. Entomol. 30(4): 645Ð655 (2001)

ABSTRACT We predict the future range of the Þre ant Solenopsis invicta Buren within the UnitedStates based on climate and its current extreme distributions. To reach that goal, a dynamic modelof colony growth with two time steps per day was formulated that operates by colony area, S, andalate production, a. Colony growth rate depended on daily maximum and minimum soil tempera-tures. Temperature records at 4,537meteorological stationswithin the current (near 1.5million km2)and potential range of S. invictawere obtained fromNOAAÕsNational ClimaticDataCenter. At eachstation, a colony was allowed to grow and lifetime female alate production was calculated. Estimatedalate production was then examined at current extremes of the Þre ant distribution at selectedlocations in Arkansas, Tennessee, and Oklahoma. Estimates from these locations were used to deÞnefour zones of colony proliferation success: certain, possible, undemonstrated, and improbable. Anannual precipitation limit (510 mm) was selected to indicate regions where arid conditions mayprohibit growth in areas without supplemental water sources. Results of the model predict that S.invicta will likely move 80Ð150 km north in Oklahoma and Arkansas. It will also likely continueexpanding into portions of Virginia, Maryland, and Delaware in the east and New Mexico, Arizona,California, Oregon, Nevada, and maybe even Washington and Utah in the west.

KEY WORDS Solenopsis invicta, biogeographical range, modeling, distribution, United States,quarantine

THERE ARE TWO major reasons to model range limits ofthe Þre ant Solenopsis invicta Buren. First, S. invicta isan important economic pest (Thompson et al. 1995)and knowledge of its potential range limits will indi-cate where quarantine efforts are most needed. Thesecond reason is that Þre ant biology and ecology arecomparatively well known (Wojcik and Porter 2000)making the effort very interesting and tractable froma scientiÞc standpoint. ImportedÞreants arecurrentlydistributed across much of the southern United Stateswhere they occur across a wide range of temperatureand precipitation.

The problem of determining the range limits ofinvading species is an issue that has attracted theattention of researchers working with many kinds ofplants and animals throughout the world (Worner1994, Sutherst et al. 1999, Baker et al. 2000). Severalattemptshavebeenmade topredict theultimate rangeof imported Þre ants in the United States. The earliestestimates (Anonymous 1972, CAST 1976) were basedon plant hardiness isolines (USDA 1941). Severalother isoline predictions have also been published(Vinson and Sorensen 1986, Vinson 1997). To date,there are no worldwide estimates of the future range

of S. invicta even though recent discoveries of this pestin Australia and New Zealand indicate that this infor-mation could greatly help target quarantine efforts.

Three attempts to model Þre ant range limits in theUnited States are reported in the literature. A statis-tical-based work by Pimm and Bartell (1980) usedthree monthly mean climatic variables (rainfall andnumber of cold and hot days) at a spatial resolution ofone degree. The authors calculated Þre ant propaga-tion rate and applied it to the situation in Texas. Theyaccurately predicted that Þre ants were beginning toreach the northern limits of their range. However,they seriously overestimated the rate of western ex-pansion (see Stoker et al. 1994 for a map of the 1993distribution in Texas) apparently because dry condi-tions are a limiting factor, a possibility that Pimm andBartell (1980) warned of in their paper.

Stoker et al. (1994) developed a mechanistic modelto Þnd a ÔreproductiveÕ border, which is a point inspace where a queen during its life produces exactlyone queen surviving to maturity. This mechanisticmodel describes the joint dynamics of a population ofcolonies and operates using seven ant developmentalstages; it describes queen fecundity, mating ßights,and dependence of developmental rates andmortalityon air temperature. The model operated with daily airtemperatures normally distributed around monthlymeans. The model was applied to a transect in north-ern Texas and did not show a distribution limit thatmatched reality.Matingßights tookplace andcolonies

1 Institute ofGlobalClimate andEcology,GlebovskayaStreet, 20-b,107258 Moscow, Russia.

2 Center for Medical, Agricultural and Veterinary Entomology,USDA-ARS, P.O. Box 14565, Gainesville, FL 32604.

3 School of ForestResources,University ofArkansas, P.O. Box 3468,Monticello, AR 71656.

0046-225X/01/0645Ð0655$02.00/0 q 2001 Entomological Society of America

grew even up to the northern boundary of the Texaspanhandle and probably beyond. We see two meth-odological deÞciencies of the approach: Þrst the ap-plication of a population-level model when a singlecolony model is sufÞcient and secondly no attemptwas made to adjust the model to match reality. Addi-tional problems were that the model did not deal withwinter kill and did not use realistic estimates forworker mortality.

The third work (Killion and Grant 1995) tried toÞnd a ÔgrowthÕ border, that is a point in space wherea Þre ant colony ceases to grow. The temperaturescenario used was similar to that taken by Stoker et al.(1994). The mechanistic model described the growthof a single colony and operated using Þve ant devel-opmental stages. It gave an approximate location forthe Þre ant geographical limit, but in very low reso-lution (three points along a Texas-Kansas-Wyomingtransect and one point in Alabama). So, actually onlyone point on the Þre ant range border was estimated.The model was fairly sophisticated and generally dida good job of simulating seasonal variability in colonygrowth, but prediction of thermal range limits wereunreliable because the estimate of winter kill used inthe model was not based on empirical data. A secondproblem was that workers in the model died tooquickly at cool temperatures (see Calabi and Porter1989).

From our point of view, the two last models wereoverly complicated and contained featureswhich pre-vented realistic results. Many details about colonygrowth are known with low accuracy, and their in-corporation into a model does not improve modelquality because it makes the model less stable withrespect to parameter variations. As we understand theproblem, model development needs to rely not on thedescription of a ÔrealÕ colony, with more and moredetails, but on a search for an idealized case that is justsufÞcient to solve the problem. While an ecologistusually tries todescribehis object indetail inordernotto loose the reality, a modeler tries to get the desiredeffects by minimum means. Our variant, offered be-low, was developed with a minimum of assumptionsand with parameters Þtted to provide a realistic out-come.

Materials and Methods

Soil temperature Ts is the key ecological factorwhich determines colony metabolism and activity(Markin et al. 1973; Porter and Tschinkel 1987,Tschinkel 1993; Porter 1988), therefore it was usedbelow as the primary ecological factor.

The most biologically sound way to Þnd a stableborder would be to evaluate the “basic reproductiverate,” R0, equal to the average number of queen prog-eny surviving to adulthood, in the absence of intra-speciÞc competition. Then, the needed border isfound from the equation

R0~Ts! 5 1, [1]

(Birch 1948, May 1974, Cooksey et al. 1990, De JongandDiekmann 1992,Hochburg et al. 1992). ToÞndR0,one needs to know with sufÞcient accuracy the ratesfor queen fecundity, colony alate production, andqueen mortality. All three values need to be given asfunctions of colony size, andecological factors like soiltemperature, maybe precipitation, and competitionwith other species of ants. This seems to be too muchfor the current state of knowledge, so several assump-tions were made to simplify the approach.

First, colonies were described by two dynamic vari-ablesÑcolony size as describedby territory area, S(t),and daily alate production, a(t). Increases and de-creases in colony size were governed by soil temper-ature. Instead of using equation 1 to Þnd the border,we calibrated themodel to adjust the calculated rangeto the furthermost points in the present distribution.Northward movement of this area has been very slowover the last 10 yr, indicating that the northern limitsof the range are being reached, as predicted by Pimmand Bartell (1980). To calibrate the model, the totalnumber of alates produced by a colony, a 5 Sa(t)wasconsidered a free parameter. In short, ourmodel func-tions at two levels: the Þrst is an ecophysiologicalmodel of the effects of temperature on colony growthand mortality; the second level is a geographic pre-diction of future range limits based on estimated life-time alate production calibrated to current extremelimits of S. invicta’s range. AmpliÞcation of this ap-proach is given below.

Model Construction. We assumed that the numberof workers in a colony is proportional to the area of itsterritory, S (see Appendix, Tschinkel et al. 1995, alsoplease note that capital “S” is used to indicate territorysize and should not be confused with subscript “s”which is used to designate soil temperature). Conse-quently, the size of a colony at age t is given by colonyarea, S(t) in m2. From this we calculated colony alateproduction, a(t), females per day. Because we hadmaximum and minimum temperature values for eachday, we also used two time steps per day. Parts of thismodel grew out of a spatial model of Þre ant territorialcompetition (Korzukhin and Porter 1994).

ColonyAreaDynamics.Within ourmodel, twopro-cesses determine dynamics of S, the production ofworkers and the death of workers. The rates of theseprocesses depend on temperature and were deter-mined from empirical laboratory observations (Porter1988, Calabi and Porter 1989).

We distinguished two temperature intervals, eachwith its own speciÞc colony dynamics (Fig. 1A).When Ts . Ts1, the balance of birth and death ispositive, and S(t) is growing with the speciÞc growthrate r(Ts) per day. When Ts # Ts1, temperatures aretoo cold to grow (Porter 1988) and so the colony diesoffwith a rate 1/L(Ts), whereL(Ts), in days, isworkerlongevity given by the empirical curve shown in Fig.1B. The curve indicates cold-stress or cold-coma mor-tality for Ts , 48C (S.D.P. and T. Macom, unpublisheddata).

Colony Alate Production. After reaching the repro-ductive size, Srep, m2, a colony splits its growth re-

646 ENVIRONMENTAL ENTOMOLOGY Vol. 30, no. 4

sources between worker and alate production(Tschinkel 1993, Fig. 1C). The share of resourcesdirected to alate production is givenby a function f(J)referred to later as the “alate production scenario,”where J is Julian date. The share f(J) is directed toalate production, while the rest 1 2 f(J) is directed toworker production. The function f(J) changes from 0to 1; f(J) 5 1 corresponds to zero worker productionand100%alateproduction,while f(J)50correspondsto the opposite situation.

The above considerations were expressed formallyin the system of equations for two dynamic variablesfor T $ T1 and S , Srep:

S~Ts,t 1 1! 5 S~Ts,t! 1 r~Ts!S~Ts,t!@1 2 S~Ts,t!/Smax]

and a~t 1 1! 5 0 [2a]

for T $ T1 and S $ Srep:

S~Ts,t 1 1! 5 S~Ts,t! 1 @1 2 f~t!#r~Ts!S~Ts,t!

z @1 2 S~Ts,t!/Smax#

and a~t 1 1! 5 qf~t!r~Ts!S~Ts,t! [2b]

for T , T1:

S~Ts,t 1 1! 5 S~Ts,t! 2 S~Ts,t!/L~Ts!

and a~t 1 1! 5 0, [2c]

where t is colony age, in days, andTs 5 Ts(t) is currentsoil (s) temperature (in 8C); functions r(Ts), f(t), andL(Ts) were described above; q is a parameter provid-ing correspondence between colony size, S, measuredin square meters, and alate production, a, measured innumbers. As one can see, colony area growth is re-stricted with the maximum colony area, Smax. (SeeAppendix for these and other parameter values.)

For the sake of simplicity, we assumed that Smax

does not depend on temperature; this justiÞes thespeciÞc form of equation 2Ñunder any positive r(Ts),we have S(Ts,t) going to Smax mandatory while in acase of the general equation like

S~Ts,t 1 1! 5 S~Ts,t! 1 r~Ts!S~Ts,t! 2 q~Ts!S2~Ts,t!

we would get temperature dependent Smax(Ts) 5r(Ts)/q(Ts).

A queen establishes the nest at a given Julian date,J0, with initial colony area S0 5 S(J0), and lives amaximum L days. A shrinking colony dies when itreaches some critical area Smin that can happen eitherafter t . L or after a long period of cold temperature.

The main output variable was the total number ofalates produced, a, by a colony during its lifetime

a 5 Sa~t!. [3]

Temperature Data. Data were taken from the Na-tional Ocean and Atmosphere Administration CD-ROMs (NOAA 1994); the last year available was 1993.Twenty-four states were selected including 15 whereÞreantpopulationshavebeendocumented(Alabama,Arizona, Arkansas, California, Florida, Georgia, Lou-isiana,Mississippi,NewMexico,NorthCarolina,Okla-homa, South Carolina Tennessee, Texas, and Virgin-ia), andnine adjacent stateswhereÞre ant infestationshave not yet been reported (Delaware, New Jersey,Nevada, Oregon, Kansas, Kentucky, Maryland, Mis-souri, and Washington). After eliminating stationswith heavily damaged data, 4,537 stations were left formodel runs. Average interstation distances ranged be-tween 26 and 38 km for the different states. Conse-quently, each station represented 660Ð1,440 km2 (Vir-ginia and Oregon, respectively). Two types ofmeasurements were used:

(1) Direct soil daily maximum and minimum tem-perature values at 10 cmdepth,Ts

min,Tsmax, were used

(comprising '96% of the available soil temperaturedata). All soil temperature records started from 1982or later. So, we had maximum soil temperature recordlengthof 12yr.Among137 stations left for the analysis,112 had 12 yr long records, whereas 25 others hadintervals varying from 3 to 11 yr.

(2)Dailymaximumandminimumair temperatures,Ta

min, Tamax, 4,537 stations in total (including 137 ÔsoilÕ

stations). Missing values within the year (near 5% oftotal dates) were substituted by averages; missingyears were not reconstructed.

Fig. 1. Three empirical curves used in the model. (A)speciÞc colony growth rate r(Ts), 1/day (Porter 1988); (B)worker longevity L(Ts), day (Porter 1988, Calabi and Porter1989); (C) alate production scenario, f(J) # 1 (Tschinkel1993). T1, T2, T3 are temperature parameters (see text andAppendix for explanations).

August 2001 KORZUKHIN ET AL.: MODELING FIRE ANT RANGE LIMITS 647

Temperature values Tsmin, Ts

max, Tamin and Ta

max

from 137 ÔsoilÕ stations were used for Þnding the re-gressions, Ts

min(Tamin, Ta

max) and Tsmax(Ta

min, Tamax)

for the rest of 4,400 stations. We applied the formulasof Chang et al. (1994) and Kluender et al. (1993) tocalculate soil from air temperatures. Our results are asfollows:

Tsmin~ J! 5 7.30 1 0.403Ta

min~ J! 1 0.193Tamax~ J!

2 1.98 sin~ z! 2 3.78 cos~ z!

Tsmax~ J! 5 7.63 1 0.154Ta

min~ J! 1 0.533Tamax~ J!

2 1.52 sin~ z! 2 4.50 cos~ z! [4]

where z 5 2p(J/365), J is a Julian date. Statisticalcharacteristics of the regressions are as follows:R2

min 5 0.908, standard deviation smin 5 2.56, numberof empirical points nmin 5 511,832; R2

max 5 0.882,smax 5 3.40, nmax 5 511,740. nmin, nmax were less thanpossible maximum N 5 137 3 12 3 365.25 5 600,471because of trajectory incompleteness in 25 ÔsoilÕ sta-tions. For the 137 ÔsoilÕ stations, we used the originalsoil measurements for model runs.

Soil temperature values for 10 cm were then cor-rected to mimic thermoregulatory movements of col-ony population that gave the model ÔworkingÕ tem-peratures somewhat warmer than the original ones.SpeciÞcally, maximum temperatures at 10 cm (Ts

max)were increased to account for warmer mound tem-peratures during the day (Tsm

max) using the formulaTsm

max 5 0.09211.28Tsmax. This adjustment added

3Ð98C to daily maximum temperatures based on ob-servations that the degree of difference betweenmound and soil temperature increases with increasingsoil temperature (S.D.P., unpublished data). Also, soiltemperatures below 48C were adjusted to soil tem-peratures at 30 cm to account for movement of theworkers to this depth during periods of cold weather(S.D.P., unpublished). This was done by adding 1.48Cto Ts

min and subtracting 0.78C from Tsmax. In north

Florida, the majority of workers never move below 30cm no matter how cold (S.D.P., unpublished data).We assume that this is the case in other parts of theirrange, but this needs to be veriÞed along the northernlimits of their range. Estimated minimum and maxi-mum soil temperatures below 08C were set equal to08C (see parameter T3 on Fig. 1b) because plots ofNOAA soil temperatures at 20 cm against air temper-atures showed that soil temperatures at this depthnever fall below08Cevenwhen air temperatureswereextremely cold. Apparently the process of freezingalmost always truncates soil temperatures at 08C, atleast, in regions along the northern boundary of theÞre ant range.

Technically, for each station, we took the most re-cent trajectories, fromY 5 3 to 12 yr long forTs

min andTs

max values. Then this original set was used to get anine year long extension. One 9 yr long portion fromthe beginning was added to the end for Y 5 9Ð12; twoportions were added for Y 5 5Ð8, and three portionsfor Y 5 3Ð4. The Þrst Y years were used in sequenceto start the growth of Y colonies, while the remaining

9 yr served for continuation of the last coloniesgrowth. Average lifetime female alate production, A,was the main output variable (ak 5 individual colonyproduction)

A 5 Sak/Y [5]

Model Adjustment. Persistence of ants at a locationrequires that a queen produce, during her life, no lessthan some critical number of female alates, A0, whichresults in precisely one queen surviving to the matu-rity, so the equality [1] will be satisÞed. A0 is deter-mined by alate survivorship probability and by colonyalate production during its lifetime; empirical valuesfor these curves are poorly known. For example, Þeldobservations give a total female alateproduction rangefrom several hundred to ten thousand (Markin et al.1973,Morrill 1974). Because of this,wedecided toÞndA0 from the empirical Þre ant distribution; in otherwords, the model was calibrated using the observedmost northerly distributions. Five infested regions inOklahoma (2), Arkansas (2), and Tennessee (1) wereselected for this purpose (“calibration areas” are de-picted as circles on Fig. 2).

The procedure consisted of the following. To ac-count for considerable inter-station variability in alateproduction, we took Þve circles (radius 5 58 km,corresponding to an average of 10 stations in the cir-cle), and found the average alate production withineach of them; number of covered stations varied from10 to 11. The minimum value among these averages

A01 5 min~ Ak!,k 5 1. . .5, [6]

appeared in the Tennessee circle, A01 5 3900 (theother values were 4700 and 4600 for Arkansas, and4300 and 5200 for Oklahoma). This number has animportant ecological meaning. Being found for theinfested area, it gives anestimateof theminimumalateproductionnecessary for a queen to reproduceherselfunder Þeld conditions. All currently noninfested areasthat had greater alate production, that is

A . 3,900, [7]

are the Þrst candidates for infestation. So, we refer tothis area as a zone of “certain” colony proliferationsuccess. This is a conservative forecast because it isbased on the current Þre ant range and average alateproduction in the calibration area rather than ex-tremes. We may need to repeat the adjustment pro-cedure and zone of certain colony proliferation suc-cess if Þre ants continue invading colder sites.

To reßect the uncertainty in infestation data, andinter-station temperature variations, we estimated an-other, more liberal, critical value of alate production,A02, which gives a wider “possible” zone of futureinfestation. Among several conceivable ways to getthis estimate, the following was used: We found thevalue of A02 equal to the average of minimum valuesfound in each calibration area. With the exception oftwo very low values (in Arkansas A 5 25, and inOklahoma A 5 0) that are naturally explained bymountain region heterogeneity, this procedure gaveA02 5 2,100. So we take


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as another minimum estimate for alate production.The last approach can be considered as an alterna-

tive to the one which leads to Þnding A01. Obviously,usage of average circle alate production will alwaysgive greater critical values for A0 than the valueneeded to infest all the individual locations, thereforethe inequality

A01 . A02 [9]

is always true. This justiÞes the name liberal for A02

and “possible” for the corresponding infestation zone.Regions with alate production values less than A02 arereferred to as “undemonstrated.” If S. invicta havereachedor arenear their northern limits inTennessee,then most or all of the “undemonstrated” sites will notbe occupied by S. invicta.

It is important to note that Þre ant colonies in this“undemonstrated” region, and even in the “possible”

region, may not actually be able to produce the num-bersof alatespredicted if persistentwinterkills reducetheir ability to competewithnative ants that arebetteradapted to cooler climates. Sites with zero alate pro-duction (A 5 0) are obviously considered “improba-ble” locations for future invasion by the S. invicta. Thisdesignation, of course, depends on the accuracy of ourestimates of cold coma mortality for the red importedÞre ant, S. invicta. We do not yet have estimates forcold coma mortality of black imported Þre ants (So-lenopsis richteri Forel) or hybrid Þre ants (S. invicta 3S. richteri). Consequently, we did not use sites inTennesseewithblackorhybridÞreants for calibrationof the model. If black or hybrid Þre ants have a highertolerance for cold temperatures, it seems likely thatthey will be able to move further north. However, thefact that infestations of black and hybrid Þre ants arestill not known fromKentucky suggests that these antsdo not have a dramatically higher cold tolerance thanthe S. invicta.

Arid or semiarid conditions should also hamper theÞre ant advance because of low habitat productivityand possible direct affects on colony founding. Thereare no reliable data of this kind, so we took a precip-itation threshold of P 5 510 mm/yr as a reasonablevalue limiting Þre ant range. This value corresponds toa semiarid region in southern Texas (near Laredo)where Þre ants have been reported to survive in nat-ural mesquite scrub lands (L. E. and R.J.W. PatrockGilbert, personal communication). However, Þre antsare known to do well in arid areas that are irrigated oradjacent to natural water sources (Anonymous 1999,Frank 1988, MacKay and Fagerlund 1997).

Results and Discussion

Potential Fire Ant Range. The model was run in all4,537 station locations and average alate production[5]wascalculated foreachpoint.Fig. 2 shows the totaltheoretical range with several insets for regions ofparticular interest. The red circles indicate sites of“certain” infestation. The green circles are sites of“possible” infestation. The dark blue circles depictsites in themodelwith cold temperatures atwhichÞreants have not demonstrated their ability to survive(beyond our “certain” and “possible” estimates forsurvival). Light blue circles correspond to sites withno alate production where success is very “improba-ble”.

What can be seen Þrst, is a full coverage of thecurrent Þre ant quarantine zone with red circles thatconÞrms our selection of a calibration area in themostextreme limit of the current range.

Green circles occur primarily in a transitional zonewhere red, green, and blue stations are mixed. Thereason for this “fuzzy border” is the spatial heteroge-neity of weather (temperature). At what degree it iscaused by the intrinsic temperature spatial variability,and at what by the heterogeneity of the habitat (veg-etation, attitude, aspect) is another question. The ex-istence of the fuzzy border is also the reason for the“certain” and “possible” estimates discussed above.

Fig. 3. (A) estimated percent winter kill of workers inSolenopsis invicta colonies at 4,537 sites plotted against meanminimum winter air temperatures (DecemberÐFebruary).Each point is the yearly average of Y 5 3Ð12 trial colony runsover the life of the colony. (B) Mean lifetime female alateproduction of trial colonies from 4,537 sites plotted againstmean minimum winter air temperature (DecemberÐFebru-ary). Each point is the average of Y 5 3Ð12 trial colony runs.


For the S. invicta, the “certain” estimate is best if thecurrent distribution has reached or nearly reached itsmaximumlimits.The “possible”estimate isbetter ifÞreants have only just invaded the most southerly loca-tionsalong this fuzzyborderatwhich theycan survive.Red imported Þre ants still appear to bemoving north-ward at a slow rate in Oklahoma, Arkansas, and prob-ably Tennessee; consequently, the “possible” estimatemay provide a better estimate of the ultimate Þre antdistribution.

With the “certain” success zone, our model predictslarge range extensions of the S. invicta in several re-gions of theUnited States (Fig. 2). Themodel predictsa 120Ð150 km northern extension in Oklahoma, thesame size extension inArkansas, and80Ð100kmnorth-ern extension for Tennessee, except most of Tennes-see is occupied by black or hybrid Þre ants so themodel may not apply well to this state. The CAST(1976) report used the 212.28C (108F) mean annualminimum air temperature isoline (USDA 1941) topredict the potential imported Þre ant range in theUnited States based on their northern expansion until1976. Our results (Fig. 2), adjusted to the 1999 distri-bution of imported Þre ants, indicates that the 2158C(58F) isoline (see USDA 1941, Vinson 1997) would bemore accurate in the southeastern United States.However, mean annual minimum temperature iso-

lines may not work well in the PaciÞc Northwest,because cool summer temperatures limited the abilityof colonies in our model to produce sexuals (Fig. 2).Range estimates using the 217.88C (08F) isoline (Kil-lionandGrant 1995,Anonymous1972)werenotbasedon empirical data and currently appear overly liberal.In any case, any attempts to apply “temperature iso-line-based” range predictions will be essentially cor-relative so generally one cannot expect that they willwork successfully for the whole range.

For the whole Þre ant range (Fig. 2), the modelpredicts considerable expansion of the current rangeto the northeast and to the west, mainly in maritimeparts of Virginia, western parts of Texas, and wideregions of New Mexico, Arizona, California, and Or-egon. Even Washington, Delaware, Maryland, Ne-vada, and Utah may be able to support Þre ant pop-ulations at some sites. Areas around SanFrancisco andSacramento, CA, appear to be especially good habitatbecause of moderate temperatures and adequateprecipitation. Low precipitation values will almostcertainly restrict Þre ant propagation in most unir-rigated sites between western Texas and easternCalifornia (Fig. 2). However, areas along watercourses and hundreds of thousands of hectares ofirrigated land in urban and agricultural areas aresusceptible.

Fig. 4. Geographic distribution of colony winter kill predicted by the model. Each dot indicates the percentage of trialcolonies at each site that did not grow large enough to produce sexuals during their lifetime because of winter kill. Trialcolonies were run sequentially each year for 3Ð12 yr, depending on the length of weather data (maximum/minimum air orsoil temperatures).


Mechanics of Range Limit. As detailed earlier, ourestimates of future range limits are based on a coreecophysiologicalmodel of alateproduction.Alatepro-duction and population survival is, of course, a bal-ance between the effects of cold kill in the winterand colony growth in the warmer months. Our es-timates of winter kill caused by extended periods ofcold induced immobility or cold coma (tempera-tures , 48C; S.D.P. and T. Macom, unpublisheddata) was the principle factor limiting colony sur-vival in the model.

Figure 3A plots the predicted percent reduction incolony size during the winter months (December2February) against themeanminimumair temperaturefor those months. Colony size at sites with mean min-imum temperatures between '28C and 108C declined10Ð20% during the winter months, mainly due to lownatural mortality when brood was not produced. Col-onies at siteswithmeanminimum temperatures above108C actually grew during the winter months as indi-catedby thenegativepercent reductions.However, asmean minimum temperatures declined from 2 to288C, the percent reduction in colony size increasedrapidly to 100%, due to the estimated effects of pro-longed periods of cold coma. Below about 288C mostsites showed 100%winter kill. Althoughnot clear fromFig. 3A, colonies at 423 sites suffered 100% wintermortality in the Þrst year of all 12 trial runs.

Total lifetime female alate production was stronglycorrelated with mean minimum winter temperatures(Fig. 3B). From 188C to '28C, alate production de-clined gradually. But below 28C, alate productiondropped dramatically, generally reaching zero atmean minimum temperatures between 23 and 278C.Colonies at 1,155 of the 4,537 sites never grewlarge enough to produce sexuals. Below 23 to 278C,colonies were generally killed outright (Fig. 3A), sosexual production was zero. The scatter of 50Ð70points to the right of the main cluster was mainly(.90%) west coast sites (California, Oregon, Wash-ington) that are apparently unusually warm in thewinter but cooler than normal in the summer; con-sequently these sites suffered little or no winter killbut lower than expected sexual production duringthe warmer months. A comparison of Fig. 3A andFig. 3B indicates that average winter mortality of50Ð70% is required to drive sexual production downbelow the critical level (A01 or A02) for sustaining apopulation.

Fig. 4 shows the percentage of trial colonies at eachsite that were unable to grow to maturity and producealate queens. Without winter kill, almost all colonieswould have been capable of growing to maturity atalmost all sites. The distribution of winter-kill limitedcolonies (Fig. 4) is reasonably consistent with theavailable empirical data. Winter kill of exposed colo-nies has been reported from north central Georgia(80Ð100%, winter 1976Ð1977; Morrill et al. 1978) andLubbock, TX (60%, winter 1986Ð1987; Thorvilson etal. 1992). However, little or no winter kill occurred atthese same times for other years. DifÞe et al. (1996)followed colonies for 5 yr (1985Ð1990) in north and

north central Georgia without Þnding clear evidenceof winter mortality, so it seems likely that the winterkill reported for 1976Ð1977 (Morrill et al. 1978) mayhave been a fairly rare event. Callcott et al. (2000) ata site in southeastern Tennessee reported high winterkills for the winters of 1993Ð1994 (88% of colonies),1994Ð1995 (61%), and 1995Ð1996 (79%). They furtherreported that these kills were best correlated to thenumber of consecutive days with maximum temper-atures below 1.18C, a measure that is congruent withour method of estimating cold coma mortality. Hope-fully, future studies will be able to directly test ourpredictions of winter kill (Fig. 4) by linking directmeasurements of soil temperatures with colony sur-vival at speciÞc sites.

The slow northerly expansion of S. invicta alongtheir northern border (Callcott and Collins 1996)combined with evidence of strong and frequent win-ter kill in Tennessee (Callcott et al. 2000) stronglyindicates that S. invicta is reaching the northern limitsof its potential range (Pimm and Bartell 1980). Redimported Þre ants will probably require 30Ð40 yr tocomplete their invasion of sites within the city ofGainesville, FL (Wojcik 1994). If the invasion processis so slow in an area with prime thermal conditions,then it may require Þre ants several hundred years toÞll in all of the marginal sites where Þre ants cansurvive along a fuzzy (heterogeneous) northern bor-der.

This model was calibrated to the most northernlocations where Þre ants are known to survive in ruralenvironments. Fire ants will likely survive in colderclimates in urban environments and other areas withsolar heat sinks and artiÞcial heat sources (Thorvilsonet al. 1992). In these areas Þre ants will generally notbe landscape pests; however, they may be able totemporarily infest the landscape during warm yearsfrom nearby refugia. Our range estimates were pri-marily based on 1982Ð1992 weather data. Globalwarming could also cause Þre ants to expand furthernorth than expected (Patz et al. 1998).

Acknowledgments

Dana Focks read the manuscript and provided a numberof helpful suggestions. This research was made possible inpart by grants from the United States Department of Agri-cultureÕs Animal and Plant Health Inspection Service (Nos.98-0810-0229 GR and 99-0810-0229 GR) to L.C.T. Approvedfor publication by the director of the Arkansas AgriculturalExperiment Station, Fayetteville.

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Received for publication 23 October 2000; accepted 27 April2001.


Appendix. Primary model parameters and standard values

Standard model parameters, units (source)Parameter

values

Colony sizeMax territory area, Smax, m2 (Markin et al. 1975) 100Territory area at which worker mortality causes colony death, Smin, m2 a 0.01Initial territory area, S0, m2 b 0.02Minimum area for colony production, Srep, m2 c 10

Max colony growth rate, rmax, 1/d (Markin and Dillier 1971, Porter 1988) 0.03286Temp when colony growth begins, T1 (Porter 1988) 218CTemp for maximum growth rate, T2 (Porter 1988) 328CLower limit for effective soil temperature, T3 08CQueen longevity, L, days (Tschinkel 1987)d 3000Colony proliferation parameter, qe 89Julian date of colony founding, J0 165

a Corresponds to '15 workers.b Estimated from mean worker density (1/m2), Wilson et al. 1971, and the number of workers in new postclaustral colonies (Porter and

Tschinkel 1986).c Estimated from average empirical colony age when proliferation begins.d We chose this value because it is somewhat larger than that estimated by Tschinkel (1987) on the assumption that rates of sperm depletion

would be a bit less in cooler climates.e Estimated from Markin et al. 1973, Morrill 1974, and our adjustment of alate production model (unpublished data).


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