Modeling Effects of Harvest on Firefly Population Persistence

Home , Allee effect, Pyractomena lucifera

Ecological Modelling 256 (2013) 43–52

Contents lists available at SciVerse ScienceDirect

Ecological Modelling

jo urnal homepage: www.elsevier.com/locate/ecolmodel

Modeling effects of harvest on ﬁreﬂy population persistence

a,∗ b a c a

Carolyn M. Bauer , Gösta Nachman , Sara M. Lewis , Lynn F. Faust , J. Michael Reed

Department of Biology, Tufts University, Medford, MA 02155, USA

Department of Biology, Section of Ecology and Evolution, University of Copenhagen, Denmark

11828 Couch Mill Road, Knoxville, TN 37932, USA

a r t i c l e i n f o a b s t r a c t

Article history: North American ﬁreﬂies in the genus Photinus are commercially harvested to extract the enzyme

Received 15 February 2012

luciferase, despite the availability of a synthetic recombinant enzyme. Our goal was to examine the poten-

Received in revised form 12 February 2013

tial effects of harvesting on Photinus population persistence. Using estimated demographic parameters

Accepted 18 February 2013

for Photinus, we developed a stochastic simulation population model to understand combined effects

of demography, harvest rate, delayed larval development, and environmental stochasticity on popula-

Keywords:

tion persistence of ﬁreﬂies. With no harvest and low environmental stochasticity, modeled populations

Fireﬂy

tended to reach carrying capacity. We found that average population size of adult ﬁreﬂies decreased

Insect conservation

Luciferase with increasing harvest rate and increasing environmental stochasticity. At the highest modeled growth

Overharvest rate ( = 2.8) the population failed to persist only when environmental stochasticity was high and har-

≥

Population persistence vest rate was 60%. Once harvest was introduced, only populations with high growth rates consistently

Population viability analysis persisted. Long-term, sustainable Photinus harvest rates based on survey data suggest that harvest rates

Wildlife exploitation >10% are acceptable only if > 1.6. Our modeling results suggest that Photinus populations might toler-

ate low harvest levels, although in the absence of more precise data on vital rates and the amount of

environmental stochasticity, the exact level is unknown. To further examine sustainability, harvest rates

should be monitored and standardized surveys conducted to document ﬁreﬂy population changes.

1. Introduction insect groups harvested for taxonomic collections, such as birdwing

butterﬂies, Papilionidae (Marshall, 1982; Owen, 1971) and bee-

One of the most common causes of current species extinctions tles, Coleoptera (New, 1995). However, effects of such harvest on

is overharvest, or overkill (Brook et al., 2008; Yiming and Wilcove, population persistence have seldom been quantiﬁed, and current

2005). The effect of harvest on population viability is central to insect harvest practices are considered by some to be unsustain-

hunting and other sustained yield programs and has been well able (e.g., butterﬂies, Kurdna, 1986; Petanidou et al., 1991; USFWS,

studied for species of commercial concern, mostly vertebrates and 1997).

trees (e.g., Ellner and Fieberg, 2003; Gustafson, 1996; Taylor et al., Fireﬂies (Coleoptera: Lampyridae) are charismatic insects that

2005). Many efforts have been made to determine sustainable attract considerable public attention. Fireﬂy harvesting has been

harvesting practices for species commonly collected or exploited virtually ignored, despite recent concerns about their conserva-

by human commerce, such as wild ﬁsh (Conover and Munch, tion status (Takeda et al., 2006). The bioluminescent displays of

2002), parrots (Beissinger and Bucher, 1992), and sharks (Gallucci certain synchronously flashing fireflies appeal to ecotourists (e.g.,

et al., 2006). Sustainable harvest practices for invertebrates have Photinus carolinus in Great Smoky Mountains National Park, USA

received less attention (Dunn, 2005). Most invertebrate harvest- (Faust, 2010), Pteroptyx tener in Kuala Selangor, Malaysia (Wong

ing studies have focused on commercial species that humans use and Yeap, 2012)). There have been widespread reports of declin-

as food or bait, such as abalone, oysters, crabs, tunicates, sponges, ing ﬁreﬂy populations (Khoo et al., 2009; Wong and Yeap, 2012;

and annelids (New, 1995; Reynolds et al., 2001). There are many L.F. Faust, unpubl. data), although the lack of systematic monitor-

ing means that most evidence is anecdotal. Although purported

ﬁreﬂy declines might be partially attributed to habitat destruc-

tion, pesticides, and light pollution, overharvest may also have a

substantial impact. In the USA, ﬁreﬂies are harvested commer-

∗

Corresponding author. Current address: Department of Biology, Tufts University,

cially to extract luciferase (Howes, 1993; Sigma-Aldrich, 2010), an

Dana Hall, 163 Packard Ave., Medford, MA 02155, USA. Tel.: +1 617 627 2757;

enzyme that catalyzes light production when adenosine triphos-

fax: +1 617 627 3805.

E-mail address: [email protected] (C.M. Bauer). phate (ATP) is present. Until 1985, luciferase could be obtained

44 C.M. Bauer et al. / Ecological Modelling 256 (2013) 43–52

only by harvesting live ﬁreﬂies (mainly Photinus spp. in the USA), 2.2. Deterministic model

but once the Photinus pyralis luciferase gene was cloned (de

Wet et al., 1985) synthetic luciferase could be produced in large The number of eggs produced by Af adult females in year t is

quantities. denoted E(t), and the expected number of young larvae that will

Although it is no longer necessary to harvest ﬁreﬂies to extract develop from these eggs is

luciferase, commercial ﬁreﬂy harvesting continues. For example,

L0(t) = peE(t) (1)

during the summer of 2008 collectors in one Tennessee county

reportedly harvested 1584 g of ﬁreﬂies (The Oak Ridger, 2008).

where pe is the probability that an egg develops into a larva.

At approximately 40 mg wet weight per Photinus individual (S.

The probability that a larva survives the ﬁrst year is denoted pl0.

Lewis, unpubl. data), this represents approximately 40,000 male

We determined that a proportion of surviving larvae do not pupate

fireflies. Harvesting has the potential to impact Photinus firefly

and therefore start on their second larval year (denoted b). Larvae

populations in the USA, but no studies have evaluated what harvest

that do not emerge after the second year die. Thus, the number of

levels these insect populations can sustain. Here we use a pattern-

larvae that are approximately one-year old in the following year

oriented modeling approach (e.g., Grimm et al., 1996; Wichmann becomes

et al., 2003) to examine the potential effects of harvest on ﬁreﬂy

L (t + 1) = pl L (t) (2)

population size and persistence. Because stochasticity affects pop- 1 0 0

ulation persistence, we ﬁrst developed a deterministic model to

while the number of two-year old larvae in year t + 1 is the number

allow us to investigate the effects of variation in demography and

of one-year old larvae that remain larvae and survive for an extra

harvest rate on population growth and equilibrium population size.

year, i.e.

We then included demographic stochasticity but kept the environ-

L t + = p b L t

ment constant, followed by adding environmental stochasticity to 2( 1) l1 1 1( ) (3)

determine the combined inﬂuence of both sources of stochastic-

or, in general, for individuals spending i + 1 year in the larval stage

ity on population persistence. We next examined how different

larval development strategies might affect population persistence.

Finally, we performed a sensitivity analysis to evaluate which of

L t + = p b L t

i+1( 1) li i i( ) (4)

our estimated parameters has the greatest impact of population

persistence. We assumed that the probability of a larva surviving from one

year to the next declines with larval density due to intraspeciﬁc

interactions such as competition for resources and cannibalism

2. Methods (Evans, 1991; Inouye, 1999; Lee and Seybold, 2010; Miller, 1964;

Peckarsky, 1991). A general model for the decrease in survival rate

2.1. The model of larvae during their ith year is ⎛ ⎞

We developed a stage-structured model of an insect popula- ⎝ ⎠

pli = pmi exp − cijLj (5)

tion that has a single reproductive period per year, after which

adults die. The model includes harvest of adults of both sexes, 0

although in some species of Photinus only the males are har-

where pmi is the survival rate of age i larvae in the absence of

vested. Eggs usually develop into adults within a single year, but

intraspeciﬁc competition. cij expresses the inﬂuence of competi-

the model allows for prolonged larval development, as seen in

tion on survival rate exerted by larvae of age j on larvae of age

some species, where some larvae take more than one year to

reach adulthood (e.g., Hovestadt et al., 2007). Because we used

Larval competition may prolong development time (Danks,

the model to analyze the consequences of extending the larval

1992; Gerber, 1984), so the proportion of larvae taking an extra

stage beyond a single year, only a fraction of larvae become adults

year to develop will increase with population size. We modeled

after one year. We used the model to investigate how popula-

the proportion of larvae postponing pupation as

tion persistence is affected if larvae postpone development with a ⎛ ⎞

ﬁxed probability, e.g. as a diversiﬁed bet-hedging strategy (Philippi

and Seger, 1989), and if the delayed larval development is a ⎝ ⎠

bi = 1 − (1 − bmi) exp −ıi cijLj (6)

result of phenotypic plasticity caused by environmental signals

j=0

(Danforth, 1999; Danks, 1992). Finally, the model incorporates the

probability that adult females become mated, to allow us to inves-

where bmi is the proportion of larvae of age i that do not pupate

tigate one type of Allee effect when population density becomes ı

in the absence of intraspeciﬁc competition and i is a constant

low.

expressing the effect of competition on development of larvae. Note

As the purpose of the model is to investigate the risk of pop-

that by varying bmi and ıi, Eq. (6) can model delayed larval develop-

ulation extinction due to harvesting, we included demographic

ment as a ﬁxed proportion of all larvae (when bmi > 0 and ıi = 0), as a

stochasticity by considering population size as a discrete stochas-

variable proportion dependent on larval density (when bmi = 0 and

tic variable affected by probabilistic demographic events. We ı

i > 0), as a mixture of the two strategies (when bmi > 0 and ıi > 0),

added increasing levels of environmental stochasticity to the

or as the absence of developmental delay (when bmi = 0 and ıi = 0).

model, thereby enabling us to explore whether prolonged larval

In year t + 1, expected recruitment of adults comes from larvae

development is a beneﬁcial strategy in an unpredictable environ-

that have spent one or more years in that stage. The probability

ment.

that a larva survives pupation and reaches reproductive maturity

In our model, we considered three developmental stages in the

is denoted pa, so the expected number of adults in year t + 1 is

life cycle of ﬁreﬂies: eggs (E), larvae (L) and adults (A). Adults con-

sist of females (A ) and males (Am), and larvae consist of those that A t + =

f ( 1) (1 − bi)paLi(t + 1) (7)

i=1

have spent approximately i years in the larval stage (Li), so that

L =

L , −

i=1 i where is the maximum number of years an individ- of which Af(t + 1) = fA(t + 1) are females and Am(t + 1) = (1 f)A(t + 1)

ual can spend in the larval stage. are males (0 ≤ f ≤ 1).

C.M. Bauer et al. / Ecological Modelling 256 (2013) 43–52 45

The maximum number of eggs a female can produce under opti- The total number of eggs produced is assumed to be Poisson dis-

mal conditions is denoted Fm. It declines if the number of males is tributed i.e.

inadequate to ensure that all females lay their full compliment of

E t + = Poisson F t + A t +

( 1) ( ( 1) ( 1)) (15)

eggs. We used Holling’s (1959) disc equation to model the expected f

number of matings per male (m) during a breeding season of length

aTAm

F t + = F − − T, i.e. where ( 1) m 1 exp +at A

1 m f

a(1 − (1 − )h )A T Environmental stochasticity can affect the values of the model’s m f f

= (8)

parameters, so instead of regarding them as ﬁxed values, they can

1 + atm(1 − (1 − )hf )Af

be replaced by probability distributions. However, we incorporated

where Af is the number of adult females emerging in a given year, stochasticity into only the parameters we considered important for

a is a constant expressing how efﬁcient the males are in ﬁnding the dynamics of a species. For instance, in the case of Photinus pyralis

females, and tm is the time needed per copulation. a, the efﬁciency we assumed that the most critical phase in the species’ life cycle

of males ﬁnding females, can be affected by a variety of factors is during summer, when males search for females to mate with.

including population density, operational sex ratio, temperature, In ‘poor’ breeding seasons, which are characterized by cold, rainy

wind, and precipitation (Faust, 2012). hf is the proportion of females weather during early summer or hot, dry weather during late sum-

harvested, and is the timing of harvest. Thus, would be 0, 0.5, or 1 mer, activity of males declines causing fewer females to be mated

if harvesting takes place before, during, or after the mating season, (Faust, 2010, 2012; S. Lewis pers. obs.). As mating rate depends on

respectively. For our purposes, we only modeled = 0. We deﬁne the parameter a in Eq. (8), we can let a vary stochastically from year

the effective harvest rate, i.e. the impact harvest has on the number to year. In poor summers, a may be close to 0 and in ‘good’ sum-

h = − h .

of reproductive females, as f (1 ) f Likewise, we deﬁne the mers (‘good’ referring to high mating success) it may be close to its

effective harvest rate of males as hm = (1 − )hm where hm is the maximum value denoted am. Assuming that a varies randomly and

proportion of adult males being harvested. As the total number of symmetrically around a mean (or median) value (denoted ¯ ), we

matings is m(1 − hm)Am, the mean number of matings per female can replace am with 2¯ and model the actual value of a in year t as

therefore becomes eε eε

a t = a = a < a t < a

( ) m ε 2¯ ε (0 ( ) m) (16)

m − h Am a − h Am

+ e + e = (1 m) (1 m) 1 1

= (9)

− h A

+ at − h A

(1 f ) f 1 m(1 f ) f

where ε is a normally distributed stochastic variable with zero

mean and standard deviation . Each year is characterized by a

We assume that a mated female can produce up to Fm eggs,

new random value of ε.

while unmated females produce none. The proportion of unmated

Likewise, if the parameter subject to environmental stochastic-

females is calculated from the 0-term of the Poisson distribution

−␮ ity is a probability rather than a rate, and therefore constrained to

as e . The mean fecundity per female is assumed to increase with

fall between 0 and 1, the time-speciﬁc probability in year t can be

the proportion of females that have mated at least once during their

−␮ modeled as

lifetime, i.e. 1 − e . Thus, the expected fecundity per female is peε

− ¯

F t p t = < p t <

( + 1) = Fm(1 − e ) (10) ( ) ε (0 ( ) 1) (17) + p e

1 ¯ ( − 1)

yielding the expected total number of eggs in year t + 1 as p

where ¯ denotes the median value of p(t). The median and the

p = . .

E t + = F t + − h mean values of p(t) will be the same if ¯ 0 5 This environmental

A t +

( 1) ( 1)(1 f ) f ( 1) (11)

stochasticity can be caused by increased rainfall, low temperatures,

or drought, which can interrupt or shorten the mating season (Faust

2.3. The stochastic version of the model

and Weston, 2009; Kaufmann, 1965).

Demographic stochasticity was incorporated by replacing

2.4. Applying the model to ﬁreﬂy populations

expected values with integer values obtained from probability dis-

tributions. Hence, the number of newly hatched larvae in year t is

Although many Photinus species are harvested for commercial

found as

purposes, vital rates were obtained from the relatively well-studied

L species Photinus ignitus (Cratsley and Lewis, 2005; Rooney and

0(t + 1) = Bin(pe, E(t)) (12)

Lewis, 2002). Along with most Photinus species, P. ignitus is found

which means that the number of larvae is generated from a bino- throughout eastern North America during summer months (Faust

mial distribution with parameters pe and E(t) by means of Monte and Weston, 2009; Lloyd, 1966). Females lay their eggs in the soil

Carlo simulation. The number of larvae surviving to the next year and larvae hatch after about two weeks. Singly mated females lay

is generated as an average of 18.5 ± 3.2 (SD) eggs; increasing the number of mates

increases the number of eggs laid (Rooney and Lewis, 2002). Egg

t + = Bin p , L t i = , , . . . ,

i+1( 1) ( li i( )) for 0 1 3 (13)

survival has only been estimated in the lab, and that was 88–93%

(Rooney and Lewis, 2002). This hatching rate is similar to the 93%

Of surviving larvae, the number of pupating larvae is generated as

egg survival rate reported in captive Photuris fulvipes (Rosa, 2007).

Bin(1 − bi+1, Li+1(t + 1)) and the number of adults (A(t + 1)) is gener-

Larvae then spend one to two years underground, subsisting on

ated from a binomial distribution with survival probability pa.

earthworms and soft-bodied insect larvae, but nothing is known

The numbers of reproducing adult males and females are

about survival rates during this stage. Danks (1992) found that

modeled as

prolonged development can be caused by scarcity of food, but envi-

m(t + 1) = Bin(1 − hm, Am(t + 1)) (14a) ronmental factors such as temperature, photoperiod, and humidity

may also be involved (Buschman, 1988; McLean et al., 1972; Rosa,

and 2007).

Pupation typically takes two weeks (Lewis and Lloyd, 2003),

t + = Bin − h , A t +

f ( 1) (1 f f ( 1)) (14b)

after which adults emerge and immediately begin breeding. The

46 C.M. Bauer et al. / Ecological Modelling 256 (2013) 43–52

∗

Photinus ignitus adult lifespan is about two weeks (Cratsley et al., Finally, once l has been obtained from Eq. (21), the default

2003; Lewis and Wang, 1991). value of c is found from Eq. (19) is

Adult Photinus population sizes are extremely variable from

1 pm

= year-to-year, but generally do not appear to exceed several thou- c ln (22)

∗ ∗ p∗

(1 + p b)L

sand individuals across an area ranging from 10 to 100 hectares (S. l 0 l

Lewis, unpubl. data), so in our simulations we set carrying capac- ∗

p = . ,

As the default parameter values yield l 0 1128 we get the

ity at 6000 adults, i.e. A(t + 1) = A(t) = A* = K. Likewise, at equilibrium

default value of c as 0.0000087.

we have E(t + 1) = E(t) = E*, and L(t + 1) = L(t) = L*. This means that the

The proportion of larvae spending two years in the soil (b) is

number of eggs produced per year at equilibrium can be found as

modeled according to Eq. (6) as

∗ ∗

= − − b −ıc + p b L

a(1 − f )KT b 1 (1 m) exp( (1 )

E∗ − l 0

= Fm(1 − e )Af = Fm 1 − exp − fK (18)

1 + atmfK

where ı expresses the effect of larval competition on the devel-

opmental rate of larvae. If the developmental strategy is ﬁxed, we

From the published literature, we estimate that females, on aver-

set ı = 0, so that b = bm = 0.2. On the other hand, if it is either purely

age, are responsible for an average of 28 eggs (F) over the course of

ﬂexible or mixed, ı can be obtained as

their lifetime. This value was calculated by taking into account the

− b

average number of matings a female receives (Cratsley et al., 2003), 1 1 m

ı = ∗ ∗ ln (bm < 1) (23)

c + p b L − b

the probability of mating with males that have already mated (1 l ) 0 1

(mating history inﬂuences spermatophore size), and the aver-

If we assume that delayed larval development is purely ﬂexible so

age fecundity of females receiving large or small spermatophores

that it occurs only when larvae compete for resources, we can set

(Rooney and Lewis, 2002). The average male has two successful

bm = 0. Consequently, if 20% of the larvae spend an extra year in the

matings over the course of his lifetime (Cratsley et al., 2003), so

soil when the population is at equilibrium, the default value of ı is

we set m = 2. Furthermore, if we assume that the sex ratio is even

0.3899.

(f = 0.5), and since = (m(1 − f)/f), we ﬁnd = 2. Setting T equal to

one mating season, tm should be 0.333 if a male maximally mates

2.5. Model scenarios

three times during its lifespan (Rooney and Lewis, 2002). Finally,

setting a(1 − f)KT/(1 + atmfK) = 2 yields a = 0.002 per mating season.

− −2 To solve the model numerically it was converted into a

Finally, E* = Fm(1 − e )fK = 28(1 − e )0.5 × 6000 = 72, 632 eggs.

computer simulation model and implemented in Delphi 2009

We set the survival probability from egg to larval stage (p ) at

e ®

(Embarcadero ). An executable version of the model, called Fire-

89%, based on data from captive, laboratory individuals (Rooney

ﬂies, is available by emailing [email protected].

and Lewis, 2002), so the number of young larvae at equilibrium

∗ ∗ To estimate allowable harvest rate under a variety of condi-

L = peE = , .

becomes 0 64 642

tions, we varied , environmental stochasticity, and harvest rate.

The default parameter values associated with the larval stage

is deﬁned as the ﬁnite growth rate of the population when there

were obtained by making following assumptions: (i) When a pop-

are no limiting factors for growth; that is, all females reproduce

ulation is at equilibrium, 20% of the larvae spend an extra year in

maximally (F = Fmax), food is unlimited (pl = pm), there is no harvest

the soil (i.e. b1 = b = 0.2); (ii) Larvae can maximally spend two years

(h = 0) and no environmental stochasticity ( = 0). In this situation,

in the soil ( = 2); (iii) The competition factor (cij) is the same for

from the deterministic version of the model,

all larvae irrespective of age (i.e. cij = c). From Eq. (5) we ﬁnd the

equilibrium value of p as + = p

l A(t 1) epm(1 − b)pafFmA(t) + pepmbpafFmA(t − 1) (24)

⎛ ⎞

The probabilities p , p , and p can be combined into a joint

e m a

≤ ≤

p∗ ⎝ ⎠ probability denoted as P = pepmpa (0 P 1). Thus, P expresses the = p − c L

l mi exp ij j

probability that an individual survives from the egg stage to the

j=0

adult stage if development takes a single year. Eq. (24) can therefore

∗ ∗ ∗

be written as

= p −cL t − cp bL t − = p −c + p b L

m exp( 0( ) l 0( 1)) m exp( (1 l ) 0)

+ = P − b fF A t + p

A t PbfF A t −

(19) ( 1) (1 ) m ( ) m m ( 1)

As = A(t + 1)/A(t), we can ﬁnd as the largest positive root of

We assume that the survival probability of a larva staying one year

in the soil without competition with other larvae is 20%, i.e. the P(1 − b)fFm ± (P(1 − b)fFm) + 4pmPbfFm

= (25)

default value of pm is 0.2. 2

The number of larvae becoming adults is

If b = 0 (i.e., life history is strictly univoltine), we get = PfFm.

We varied vital rates to yield ’s approximately equal to 1.2,

A∗ ∗ ∗ ∗ 2 ∗

= p pa(1 − b)L + (p ) bpaL = K (20)

l 0 l 0 1.6, 2.0, 2.4, and 2.8. To limit the number of combinations, we only

changed pm and Fm (Supplementary Materials) while the remaining

p∗

which means that can be obtained as the largest positive root of

l parameters took their default values (Table 1). Irrespective of , the

carrying capacity of the population was ﬁxed to K = 6000 adults.

− 2 ∗ The values of c and necessary to keep the number of adults at a

− b ± − b + bK/ paL

(1 ) (1 ) 4 ( 0)

∗ carrying capacity for a given combination of p and F were found p = (21) m m

l b

2 by solving Eqs. (22) and (23).

We also investigated the effect of larvae with a strictly univoltine

∗ K

p = ∗

ı when 0 < b < 1, while for b = 0 or b = 1, Eq. (20) reduces to l paL lifecycle, i.e. b = 0, with an unconditional strategy (bm > 0 and = 0),

∗ K and with a purely conditional (density-dependent) strategy (i.e. b

p = ∗

and l paL , respectively. As we have no knowledge of pa we

0 m = 0 and > 0).

will use pa = 1 as the default value, but Eq. (21) shows that lower The effect of harvest was modeled by varying the proportion

∗

h , values of pa will increase l . of adult males being removed from the population ( m) whereas

C.M. Bauer et al. / Ecological Modelling 256 (2013) 43–52 47

Table 1 Table 2

Default parameter values used in the simulation model. Values are estimated at Standard and experimental values used in sensitivity analysis. Because the standard

population equilibrium. value of pa is 1.0, we only investigated a 10% decrease in this parameter. 1/tm is the

maximum number of mates for each male.

Parameter Description Value(s)

symbol Variable Standard 10% below 10% above

K Carrying capacity of adults 6000 pm 0.2 0.18 0.22

pe Hatching probability of eggs 0.89 pa 1.0 0.9 N/A

pm Maximum survival probability of 0.2 Fm 28 25.2 30.8

larvae pe 0.89 0.801 0.979

c Effect of larval competition on survival 0.00000866 c 0.00000866 0.000007794 0.000009526

probability b 0.2 0.18 0.22

pa Probability of surviving pupation 1.0 1/tm 3.0 2.7 3.3

b Proportion of larvae with delayed 0.2 h 0.05 0.045 0.055

pupation 0.5 0.45 0.55

bm Proportion of larvae with a ﬁxed 0, 0.2

bet-hedging strategy

Effect of larval competition on 0, 0.3899 by assuming that all larvae in year 0 were newly hatched; that is,

developmental rate

the number of larvae from the previous year was set to 0. With

***

a Efﬁciency of adult males to ﬁnd and 0.002

the default parameter values this means that the number of newly

mate with females

*** hatched larvae must be 66,980 in order to produce 6000 adult ﬁre-

tm Time per mating 0.333

Fm Maximum number of eggs produced 28 ﬂies in the following year, while 1500 larvae will stay in the soil

per female

for an extra year. The population was then projected for the next

f Proportion of females 0.5

50 years. Each combination of parameter values was replicated 100

h Harvest rate 0

times.

Timing of harvest 0

Standard deviation of environmental 0.5

stochasticity 2.6. Allowable harvest rate based on survey data

c is obtained from Eq. (22) to ensure that larval mortality will keep population

−1

at equilibrium; units are larvae . Since detailed life-history data are generally unavailable for ﬁre-

A ﬁxed (unconditional) strategy corresponds to bm = 0.2 and ı = 0, while a ﬂexible

ﬂies, it might be useful to generate a simple harvest model for a

(conditional) strategy corresponds to bm = 0 and ı = 0.3899. ı is obtained from Eq

population exposed to environmental stochasticity. We modeled

(23) to ensure that the proportion of larvae with delayed development is b when

environmental conditions for ﬁreﬂies in a given year as either good

the population is at equilibrium.

***

Units are area/time. Time unit is the duration of one mating season, i.e. T = 1. or bad, with reference to the number of adults produced. The prob-

ability of a bad year is denoted is ˇ (0 ≤ ˇ ≤ 1). In a good year, the

ﬁnite per capita growth rate is ( > 1) and in a bad year it is

f is 0 as only adult males of the genus Photinus are collected. If ≤

B , where B deﬁnes the effect of a bad year on (i.e. 0 B < 1).

harvest rate is sustainable, the number of males at equilibrium

∗ We further assumed that is reduced due to harvest by a factor

will be Am = (1 − f )K(1 − hm), while the equilibrium number of

− h h ≤ h ≤

∗ ∗ 1 m where m (0 m 1) expresses the effective harvest rate

A = f

females will be K. Thus, at a sustainable level of harvest the

f of males. The expected net growth rate over a longer period of time

A∗

= − h − f K,

number of adults will be [1 m(1 )] which shows that is therefore

A* < K when harvest takes place. Consequently, the mean fecundity

E = − ˇ − h

[ ] (1 ) (1 m) + ˇB(1 − hm) (27)

of females (F) will decline with increasing harvest rate of males

according to Eq. (8)

As ﬁreﬂy population dynamics are strongly affected by weather

conditions (e.g., Yuma, 2007) we set B = 0.3, which represents the

a(1 − f )KT(1 − hm)

F = Fm − −

1 exp (26)

+ at qualitatively estimated decrease in population size associated with

1 mfK

a bad year (Faust, unpubl. data). The probability of a bad year (ˇ)

Therefore, if the harvest rate goes up, the decline in mean fecun- was estimated as 21% using qualitative population data gathered

dity of the females may no longer be sufﬁcient to produce enough over 19 years from a single population of P. carolinus, a syn-

◦

males in the next generation for complete female mating, which chronously flashing firefly, in Elkmont, Tennessee, USA (35 39 13

◦

would further exaggerate the effect of harvest. Consequently, har- N, 83 34 50 ) (Supplementary Materials). Long-term persistence in

vest may impose an Allee effect (Allee et al., 1949) on ﬁreﬂy a stable environment requires that E[] ≥ 1, which implies that the

dynamics, which makes the species vulnerable to extinction when maximum sustainable harvest can be obtained when hm is

harvest rate exceeds a certain threshold. Because harvest reduces

= −

the density of mature males, the likelihood that a female will max 1 (28)

(1 − ˇ(1 − B))

become mated can decrease (Robinet et al., 2007), unless the

remaining males can compensate (at least partly) by increasing Using this equation, we estimated the maximum sustainable har-

their mating success. As the parameter a expresses the efﬁciency of vest rate for a range of s > 1, and for different combinations of B

males to mate with females, we analyzed the extinction threshold and ˇ.

for three different values of a (a = 0.002, 0.01, and 0.1).

To investigate how stochasticity affects population persistence 2.7. Sensitivity analysis

of ﬁreﬂies, we used the stochastic version of the model for two

levels of environmental stochasticity ( = 0.5 and 1.0) and four har- Because vital rates and other parameter values used in our

vest rates ( m = 0, 0.2, 0.4, and 0.6). We used this wide range of model were estimated from a small number of sources, the

harvest rates because the typical harvest rate of ﬁreﬂy popula- real-world application of our model conclusions are uncertain.

tions is unknown. Rates of 40% and 60% might seem high, but these Therefore, we performed a sensitivity analysis to determine which

rates are plausible because fireflies are conspicuous, slow-flying model parameters have the greatest impact on population persis-

insects that form dense mating aggregations. Default values of the tence and therefore have the highest priorities for further research

remaining parameters are given in Table 1. All simulations were ini- for more accurate assessments. We explored the sensitivity of nine

tiated with a population size close to equilibrium. This was achieved difference parameters by varying them each, one at a time, 10%

48 C.M. Bauer et al. / Ecological Modelling 256 (2013) 43–52

a) to reach carrying capacity (Fig. 2a). At the lowest growth rate

1400 ( = 1.2), population size decreased to zero in every scenario with

a = 0.1

1200 harvest. Conversely, at the highest growth rate ( = 2.8), average

1000 a= 0.01 population size never declined to zero under any scenario, but

800 it showed more variability when environmental stochasticity

a = 0.002

600 ( = 1.0) and harvest rate (h = 0.6) were high (Fig. 2h). At high

harvested

400 harvest rates, only populations with higher growth rates per-

No. of adult males

200 sisted, even with low environmental stochasticity (Fig. 2e and g).

0 Increasing environmental stochasticity in the presence of harvest

0 0.2 0.4 0.6 0.8 1

had the same qualitative effect as when there was no harvest.

That is, average population sizes were much lower, and decreased

Harvest rate (h)

more rapidly over time, with the greatest decreases at the highest

7000 harvest rates (Fig. 2d, f and h). The population trajectories in Fig. 2,

6000 however, tell only part of the story. For all trajectories except those

5000 that attained equilibrium, uncertainty increased over time. This

4000 is because the average values depicted include populations that

3000 have gone extinct, as well as those that remained near equilibrium.

2000 With larger environmental stochasticity and harvest rates, there is

1000 increasing extinction risk over time, although higher growth rates

No. of adults (A*)

0 increased the probability of population persistence (Fig. 3a–b).

0 0.2 0.4 0.6 0.8 1

3.3. Effect of larval developmental strategy

Harvest rate (h)

We compared developmental strategies when a population is

Fig. 1. (a) The predicted harvest and (b) number of adults (A*) in the population

h = .

when exposed to harvest rate (h) for different values of mating efﬁciency (a). A* is exposed to moderate harvest ( m 0 4) in a stochastically variable

equal to the carrying capacity (K) when no harvest takes place. This is under the

environment ( = 1.0) (Fig. 4). When larval development cannot be

assumption that males are harvested before they have the chance to mate.

prolonged (when b = 0), 92% of the simulated populations persisted

after 50 years. This percentage tends to increase with b for the ﬂexi-

above and below their standard value (see Table 2 for parame- ble conditional (density-dependent) strategy but decreases sharply

ter values) and examined their effects on the number of males at for the ﬁxed (unconditional) strategy. This clearly indicates that

equilibrium (A*). the ﬂexible developmental strategy is much more robust against

extinction than is the ﬁxed strategy (Fig. 4). The difference between

3. Results the two strategies is exaggerated in the more unpredictable envi-

ronment.

3.1. Maximum sustainable harvest

3.4. Allowable harvest rate based on survey data

Using the deterministic model with male-only harvest before

mating ( = 0), we found that the sustained yield increased with har- For estimating allowable harvest rate when all one has is survey

vest rate up until a threshold, at which point the population crashed data, we needed the probability of bad years and the effect of a bad

(Fig. 1). Whereas the maximum sustainable harvest is relatively year on population size (Eq. (27)). Using the data available to us,

independent of mating efﬁciency (a) at lower harvest rates (h < 0.2), the maximum sustainable harvest rates for a range of s > 1 and a

the extinction threshold decreases the lower the mating efﬁciency. range of environmental variances ( ≥ 0), are shown in Fig. 5. Maxi-

Thus, when mating efﬁciency is high (i.e., a = 0.1) the harvest peaks mum harvest rates based on survey data for P. carolinus suggest that

when about 60% of the males are harvested (Fig. 1a), while a harvest effective harvest rates >10% are sustainable only if > 1.4, and that

rate of about 75% will drive the population to extinction (Fig. 1b). higher environmental variance decreases the average maximum

If mating efﬁciency is ten times lower (i.e., a = 0.01), the maximum sustainable harvest rate (Fig. 5).

sustainable yield is only slightly reduced but the population will

go extinct if harvest rate exceeds 65%. At the lowest modeled mat- 3.5. Sensitivity analysis

ing efﬁciency (a = 0.002), the maximum sustainable harvest rate is

h = 0.35, but the population goes extinct when h = 0.46. If a = 0.002, The parameters that caused the greatest changes in equilibrium

males in an unexploited population at equilibrium adult popula- population size were larval survival probability (pm), maximum

tion size will, on average, mate twice, which is in agreement with number of eggs per female (Fm), and egg hatching probability (pe)

empirical data (Cratsley et al., 2003). (Table 3). There were also strong asymmetric effects of pupation

survival probability (pa) and larval competition’s effect on sur-

3.2. Demographic and environmental stochasticity vival probability (c); decreases in the former had a strong effect in

decreasing equilibrium population size, while increases in the lat-

We found that the average population size of adult ﬁreﬂies and ter caused a strong increase. When changed by 10%, all parameters

time to extinction decreased with increasing harvest rate and with with the exception of the effect of larval competition on survival

increasing environmental stochasticity (Fig. 2a–h). Because the probability (c), had a greater effect on decreasing the population

simulations were started with the equilibrium number of young than on increasing the population.

L∗

larvae ( 0), the number of larvae increases with a decrease in .

Low values of also increased the time it took to reach a stable 4. Discussion

number of adults (A ), although a stable level is attained only

for the lowest value of (1.2) when no harvest takes place and Habitat loss and degradation have contributed to declining ﬁre-

environmental stochasticity is low ( = 0.5). With no harvest and ﬂy populations in some regions (Khoo et al., 2009; Wong and Yeap,

low environmental stochasticity, average population size tended 2012). In Japan, the well-documented decline of Luciola cruciata

C.M. Bauer et al. / Ecological Modelling 256 (2013) 43–52 49

a) Harvest=0, ES=0.5 b) Harvest=0, ES=1.0

9000 9000 8000 8000 7000 7000 6000 6000 5000 5000 4000 4000 3000 3000 2000 2000 1000 1000

0 0

0 10 20 30 40 50 0 10 20 30 40 50

c) Harvest=0.2, ES=0.5 d) Harvest=0.2, ES=1.0

9000 9000 8000 8000

Number of Number Adults 7000 7000 6000 6000 5000 5000 4000 4000 3000 3000 2000 2000 1000 1000

0 0

0 10 20 30 40 50 60 0 10 20 30 40 50

e) Harvest=0.4, ES=0.5 f) Harvest=0.4, ES=1.0

9000 9000 8000 8000 7000 7000 6000 6000 5000 5000 4000 4000 3000 3000 2000 2000 1000 1000

0 0

0 10 20 30 40 50 0 10 20 30 40 50

g) Harvest=0.6, ES=1.0 h) Harvest=0.6, ES=1.0 2.8 9000 9000 2.4

Number of Number Adults 8000 8000 2 7000 7000 1.6 6000 6000 1.2 5000 5000 4000 4000 3000 3000 2000 2000 1000

1000 0

0 0 10 20 30 40 50

0 10 20 30 40 50

Years

Fig. 2. Predicted mean number and 90% confidence intervals of adult fireflies over a time horizon of 50 years. Each graph represents a different combination of environmental

stochasticity (ES) and harvest rate (h). Graphs in the left column represent an environmental stochasticity of 0.5 with a harvest rate of 0% (a), 20% (c), 40% (e), and 60% (g).

Graphs in the right column represent an environmental stochasticity of 1.0 with a harvest rate of 0% (b), 20% (d), 40% (f), and 60% (h). Each line represents a different value

of (1.2, 1.6, 2, 2.4, 2.8). Each case was replicated 100 times.

has been attributed to habitat destruction, light pollution, com- declining populations no matter what growth rate was assumed.

mercial harvest, and water pollution (Katoh et al., 2009; Ohba, A population could tolerate higher harvest rates under lower envi-

2004; Yajima, 2007; Yuma, 2007). In some parts of the world ronmental stochasticity, but only the highest growth rates enabled

ﬁreﬂies are harvested, and regardless of a species’ life history, a the modeled population to persist for 50 years. Because of the

sufﬁcient harvest rate can cause population declines. The big ques- widespread availability of recombinant luciferase, it is no longer

tion is what harvest rate causes declines for a particular species? necessary to harvest ﬁreﬂies to obtain luciferase. Although our

Results from our stochastic simulation model suggest that Photi- model was able to predict sustainable levels of harvest for Photinus

nus ﬁreﬂy populations can sustain only moderate levels of male populations, its validity is dependent on the accuracy of our esti-

harvest. Speciﬁcally, in our models, high environmental stochas- mates of Photinus vital rates. Because not even qualitative data are

ticity coupled with high harvest rates invariably led to rapidly available on ﬁreﬂy harvest and growth potential, the applicability

50 C.M. Bauer et al. / Ecological Modelling 256 (2013) 43–52

Table 3

Relative rank of each variable’s effect on decreasing and increasing the number of males at equilibrium (A*). A* = 4118 under standard conditions.

Decrease equilibrium population size (A*) Increase equilibrium population size (A*)

Variable A* % change Variable A* % change

pm 2907 29.4 pm 4974 20.8

pa 2969 27.9 c 4653 13.0

Fm 3499 15.0 Fm 4459 8.3

pe 3499 15.0 pe 4459 8.3

c 3674 10.8 b 4313 4.7

b 3914 5.0 1/tm 4207 2.2

1/tm 3997 2.9 h 4147 0.7

h 4094 0.6 4123 0.1

4114 0.1

of our results cannot be validated at this time. As population per- 100

sistence was highly inﬂuenced by growth rate estimates, this is one 90

of the most important areas for future ﬁreﬂy research. Better esti- 80

mates of population sizes, and how they change across years, are 70

also necessary for accurately determining persistence likelihood 60

and sustainable harvest rates of ﬁreﬂies. 50 Fixed

To determine biologically sustainable commercial harvest rates 40

Flexibl e

for any ﬁreﬂy species, we recommend that statistically valid survey 30

plots be established to document the relationship between har- 20

Persistence (%) Persistence

vest rate and ﬁreﬂy population sizes across a range of ecological 10

conditions, and better and more accurate vital rates need to be 0

Probability of Population Probability

determined for effective harvest. Lessons might be extrapolated 0 0.2 0.4 0.6 0.8

from successful harvest programs for other taxa (e.g., Breitburg

et al., 2000; Emanuel et al., 2005; Punt and Smith, 2000). In addition, b

Fig. 4. Population persistence as a function of percent of larvae postponing

pupation. The ﬁxed strategy assumes that the percent of larvae with prolonged

development is independent of larval density (i.e. ı = 0) while the ﬂexible strategy

a) assumes that it is density-dependent (i.e. ı > 0). Environmental stochasticity () is

ES = 0.5

set to 1.0 and the effective harvest rate of males (h m) is set to 0.4. See Table 1 for

100 the remaining parameters.

based on our sensitivity analyses, we encourage researchers to

gather more demographic data in the ﬁeld. Speciﬁcally, it would

40 be particularly important to determine values for probabilities

of larval survival (pm), pupation survival (pa), and egg hatching

20 probability (pe), as well as maximum eggs produced per female

(Fm). We realize that this will be challenging and possibly expen-

0 sive, and that the methods might not yet exist to determine values

0 0.2 0.4 0.6 0.8 for some species. For example, virtually nothing is known about the

fraction of larvae spending more than one year in the soil under

natural conditions; similar cryptic life stages are present in other

species of ﬁreﬂy as well (e.g., Luciola cruciata, Takeda et al., 2006). b) ES = 1.0

100 0.7

80 0.6 2.8 60 2.4 ) 0.5 2 max 40 1.6 0.4 1.2 20 0.3

0.2 harvest (h harvest

ProbabilityPopulation of Persistence (%) 0

0 0.2 0.4 0.6 0.8 0.1 Maximum sustainable Maximum

Harves t 0.5 1 1.5 2 2.5 3

Net growth rate ( )

Fig. 3. Effect of different annual harvest rates (h) on the probability of modeled adult

ﬁreﬂy populations persisting over the course of 50 years with an environmental Fig. 5. Estimated average allowable harvest rate using only data on growth rate

ˇ stochasticity () of 0.5 (a) or 1.0 (b). Each line represents a different value of (from (Eq. (28)), probability of a bad year ( = 0.21), and effect of a bad year on growth rate

1.2 to 2.8). Each case was replicated 100 times; means are plotted without error bars (B = 0.30). Environmental stochasticity ( ) at 0 (bold line), 0.5 (dashed line), and 1.0

for clarity. (dotted line) are presented for a range of s > 1.

C.M. Bauer et al. / Ecological Modelling 256 (2013) 43–52 51

Determining some of these values even in captivity might be chal- the Great Smoky Mountains National Park (Faust, 2010; Faust and

lenging. Weston, 2009) Allegheny National Forest, PA (Faust et al., 2012)

One interesting result from our model is the importance of the and Congaree National Forest, SC (Faust, pers. comm). Because of

larval emergence strategy. Because adults only live for a single sea- their popularity with the public, fireflies might also benefit from

son, a population without a risk-spreading strategy (b = 0) faces data gathered by a citizen science program. As an example, “Fireﬂy

extinction if bad weather in one year prevents females from repro- Watch” is a citizen science initiative sponsored by the Boston

ducing. When we allowed larvae to postpone pupation, we found Museum of Science (https://www.mos.org/ﬁreﬂywatch/, accessed

that a ﬁxed (unconditional) strategy performed worse than did a 21.06.2010) that provides one approach to collecting and managing

strict one-year lifecycle. Spending an extra year in the soil, a ﬂexible, such data. This program encourages citizens across North America

density-dependent strategy, was superior with respect to buffer- to monitor the number of ﬁreﬂies appearing in their backyards dur-

ing environmental uncertainty, despite increased mortality due to ing the spring and summer months. This approach might not be as

intraspeciﬁc competition and cannibalism (Fig. 4). The proximate statistically rigorous as other survey designs, but in their absence

cause of this increased persistence is that between-year variation in it would provide useful data on ﬁreﬂy abundance and distribution.

number of adults is stabilized, because in a year with many larvae,

a relatively large fraction postpones pupation to the following year, Acknowledgments

while the opposite will be the case in a year with few larvae. Such

a mechanism reduces the risk that the number of adults in a given We thank C. Cratsley, K. Demary, and A. South for information

year will reach a critical threshold below which the population is concerning ﬁreﬂy life history parameters, S. Levine for providing

likely to go extinct (see below). This relationship could be mediated modeling advice, and R. Kamada for Japanese translation services.

by body size, as increased density results in increased food compe- We also thank R. Steidl and one anonymous reviewer for comments

tition, and many insect species delay pupation until they reach a on an earlier draft of this manuscript.

certain body size (Beaudoin et al., 1992; Matsuo, 2006; Teng and

Apperson, 2000). Appendix A. Supplementary data

Although our model shows that the ﬁxed developmental strat-

egy seems to be unable to buffer environmental stochasticity, this Supplementary data associated with this article can be

does not imply that a bet-hedging (ﬁxed development) strategy found, in the online version, at http://dx.doi.org/10.1016/

cannot occur in this species. If prolonged development is balanced j.ecolmodel.2013.02.018.

by some advantages, it could be maintained. Thus, in our simula-

tions we assumed that larvae staying two years in the soil suffered References

higher larval mortality than did those staying only a single year. This

may not be the case if prolonged larval development is caused by Allee, W.C., Emerson, A.E., Park, O., Park, T., Schmidt, K.P., 1949. Principles of Animal

Ecology. W.B. Saunders Co., Philadelphia.

diapause (e.g. Danks, 1992; Menu et al., 2000), as diapausing larvae

Beaudoin, L., Geri, C., Allais, J.P., 1992. The effects of photoperiodicity, temperature,

do not compete for resources and therefore are not at risk from food

food and endogenous processes on the determination of diapause of Diprion pini.

shortages. At the same time, diapausing larvae would not exert a Bulletin de la Societe Zoologique de France- Evolution et zoologie 117, 351–363.

Beissinger, S.R., Bucher, E., 1992. Can parrots be conserved through sustainable har-

negative inﬂuence on the non-diapausing larvae. There is evidence

vesting? BioScience 42, 164–173.

from laboratory studies that ﬁreﬂy larvae can enter diapause during

Breitburg, D.L., Coen, L.D., Luckenbach, M.W., Mann, R., Posey, M., Wesson, J.A., 2000.

periods of low food availability (McLean et al., 1972). This differ- Oyster reef restoration: convergence of harvest and conservation strategies.

Journal of Shellﬁsh Research 19, 371–377.

ence between active and inactive larvae could be modeled via the

Brook, B.W., Sodhi, N.S., Bradshaw, C.J.A., 2008. Synergies among extinction drivers

competition coefﬁcients cij in Eq (5). Another possibility is that lar-

under global change. Trends in Ecology and Evolution 23, 453–460.

vae with postponed development continue to grow, which may Buschman, L.L., 1984. Larval biology and ecology of Photuris ﬁreﬂies (Lampyridae,

Coleopetera) in northcentral Florida. Journal of the Kansas Entomological Society

explain why both small and large larvae can be found at the same

57, 7–16.

time (Buschman, 1984; McLean et al., 1972). If adults that hatch

Buschman, L.L., 1988. Larval development and its photoperiodic control in the ﬁre-

from larger larvae have higher reproductive success than do the ﬂy Pyractomena lucifera (Coleoptera Lampyridae). Annals of the Entomological

small larvae, it could offset a higher mortality encountered during Society of America 81, 82–90.

Conover, D., Munch, S., 2002. Sustaining ﬁsheries yields over evolutionary time

prolonged larval development. In contrast, a phenotypically plastic

scales. Science 297, 94–96.

larval development response could increase population persistence

Cratsley, C.K., Rooney, J.A., Lewis, S.M., 2003. Limits to nuptial gift production by

if it buffered environmental stochasticity (Grimm et al., 2005). male ﬁreﬂies, Photinus ignitus. Journal of Insect Behavior 16, 361–370.

Cratsley, C.K., Lewis, S.M., 2005. Seasonal variation in mate choice of Photinus ignitus

Another aspect of ﬁreﬂy life history that needs further empiri-

ﬁreﬂies. Ethology 111, 89–100.

cal investigation is the relationship between the number of adult

Danforth, B.N., 1999. Emergence dynamics and bet hedging in a desert bee, Perdita

males and the chance that females become mated. Mating proba- portalis. Proceeding of the Royal Society B: Biological Sciences 266, 1985–1994.

Danks, H.V., 1992. Long life cycles in insects. The Canadian Entomologist 124,

bility likely decreases with population size, in particular with the

167–187.

number of adult males. Low mating success can exert an Allee

de Wet, J.R., Wood, K.V., Helsinki, D.R., Deluca, M., 1985. Cloning of ﬁreﬂy luciferase

effect (Gascoigne et al., 2009; Yamanaka and Liebhold, 2009), thus cDNA and the expression of active luciferase in Escherchia coli. Proceedings of

the National Academy of Sciences of the USA 82, 7870–7873.

making small populations more vulnerable to extirpation. Fig. 1

Dunn, R.R., 2005. Modern insect extinctions, the neglected majority. Conservation

indicates that the separation between maximum sustainable har-

Biology 19, 1030–1036.

vest and extinction caused by harvest is rather narrow, especially if Ellner, S.P., Fieberg, J., 2003. Using PVA for management despite uncertainty: effects

of habitat, hatcheries, and harvest on salmon. Ecology 84, 1359–1369.

a is small. Consequently, stochastic events may push a population

Emanuel, P.L., Shackleton, C.M., Baxter, J.S., 2005. Modelling the sustainable harvest

that is harvested at close to the maximum sustainable rate, into the

of Sclerocarya birrea subsp. caffra fruits in the South African lowveld. Forestry

unstable region and eventual extinction. Ecology and Management 214, 91–103.

Of the field data needed for firefly population viability and har- Evans, E.W., 1991. Intra versus interspecific interactions of ladybirds (Coleoptera:

Coccinellidae) attacking aphids. Oecologia 87, 401–408.

vest rate assessment, standardized monitoring (Kirton et al., 2012;

Faust, L.F., 2010. Natural history and flash repertoire of the synchronous firefly Phot-

Takeda et al., 2006) would be the most readily achievable. From

inus carolinus (Coleoptera: Lampyridae) in the Great Smoky Mountains National

these time-series data one could calculate annual variation in pop- Park. Florida Entomologist 93, 208–217.

Faust, L.F., 2012. Fireﬂies in the snow: observations on two early-season arboreal

ulation size and growth rates (), which could provide estimates of

ﬁreﬂies Ellychnia corrusca and Pyractomena borealis. Lampyrid 2, 48–71.

the amount of environmental stochasticity these animals are facing.

Faust, L.F., De Cock, R., Hall, K.S., Marion, Z., Sander, S., 2012. Allegheny

Monitoring and management programs have been established in National Forest June 201 Fireﬂy Survey Forest and Warren Counties,

52 C.M. Bauer et al. / Ecological Modelling 256 (2013) 43–52

PA. In cooperation with the U.S. Forest Service, Department of Agri- Menu, F., Roebuck, J.P., Viala, M., 2000. Bet-Hedging diapause strategies in stochastic

culture, Allegheny National Forest. Under the Secure Rural Schools Act, environments. American Naturalist 155, 724–734.

P.L.110-343 and Forest Service Agreement 12-DG-11091900-011. Available Miller, R.S., 1964. Larval competition in Drosophila melanogaster and D. simulans.

from http://org2.democracyinaction.org/o/6155/p/salsa/web/common/public/ Ecology 45, 132–148.

content?con.tent item KEY=10747 New, T.R., 1995. An Introduction to Invertebrate Conservation Biology. Oxford Uni-

Faust, L.F., Weston, P.A., 2009. Degree-day prediction of adult emergence of Photinus versity Press, New York.

carolinus (Coleoptera: Lampyridae). Environmental Entomology 38, 1505–1512. Ohba, N., 2004. Mystery of ﬁreﬂies. Yokosuka City Museum Special Exhibition Man-

Fireﬂy Watch, 2010. Museum of Science, Boston [Internet]. Available from ual (in Japanese).

https://www.mos.org/fireflywatch/ (cited 21.06.2010). Owen, D.F., 1971. Tropical Butterflies. Clarendon Press, Oxford.

Gallucci, V.F., Taylor, I., Erzini, K., 2006. Conservation and management of exploited Peckarsky, B.L., 1991. Mechanisms of intraspeciﬁc and interspeciﬁc interference

shark populations based on reproductive value. Canadian Journal of Fisheries between larval stoneﬂies. Oecologia 85, 521–529.

and Aquatic Sciences 63, 931–942. Petanidou, T., Vokou, D., Margaris, N.S., 1991. Panaxia quadripunctaria in the highly

Gascoigne, J., Berec, L., Gregory, S., Courchamp, F., 2009. Dangerously few liasons: a touristic Valley of Butterﬂies (Rhodes Greece): conservation problems and reme-

review of mate-ﬁnding Allee effects. Population Ecology 51, 355–372. dies. Ambio 20, 124–128.

Gerber, G.H., 1984. Effects of starvation in the ﬁrst instar larva on growth, develop- Philippi, T., Seger, J., 1989. Hedging ones evolutionary bets, revisited. Trends in

ment and survival in the red turnip beetle, Entomoscelis americana (Coleoptera; Ecology and Evolution 4, 41–44.

Chrysomelidae). The Canadian Entomologist 116, 529–536. Punt, A.E., Smith, A.D.M., 2000. The gospel of maximum sustainable yield in ﬁsheries

Grimm, V., Frank, K., Jeltsch, F., Brandl, R., Uchmanski, J., Wissel, C., 1996. Pattern- management: birth, cruciﬁxion and reincarnation. In: Reynolds, J.D., Mace, G.M.,

oriented modelling in population ecology. Science of the Total Environment 183, Radford, K.H., Robinson, J.G. (Eds.), Conservation of Exploited Species. Cambridge

151–166. University Press, Cambridge, pp. 41–66.

Grimm, V., Revilla, E., Groeneveld, J., Kramer-Schadt, S., Schwager, M., Tews, J., Wich- Reynolds, J.D., Mace, G.M., Redford, K.H., Robinson, J.G., 2001. Conservation of

mann, M.C., Jeltsch, F., 2005. Importance of buffer mechanisms for population Exploited Species. Cambridge University Press, Cambridge.

viability analysis. Conservation Biology 19, 578–580. Robinet, C., Liebhold, A., Gray, D., 2007. Variation in developmental time affects

Gustafson, E.J., 1996. Expanding the scale of forest management: allocating timber mating success and Allee effects. Oikos 116, 1227–1237.

harvests in time and space. Forest Ecology and Management 87, 27–39. Rooney, J., Lewis, S.M., 2002. Fitness advantage from nuptial gifts in female ﬁreﬂies.

Holling, C.S., 1959. Some characteristics of simple types of predation and parasitism. Ecological Entomology 27, 373–377.

Canadian Entomologist 91, 385–398. Rosa, S.P., 2007. Description of Photuris fulvipes (Blanchard) immatures (Coleoptera,

Hovestadt, T., Mitesser, O., Elmes, G.W., Thomas, J.A., Hochberg, M.E., 2007. An evolu- Lampyridae Photurinae) and bionomic aspects under laboratory conditions.

tionary stable strategy model for the evolution of dimorphic development in the Revista Brasileira de Entomologia 51, 125–130.

butterfly Maculinea rebeli, a social parasite of Myrmica ant colonies. American Sigma-Aldrich, 2010. Luciferase from Photinus pyralis (firefly) [Internet] (accessed

Naturalist 169, 466–480. 07.05.2010). Sigma Aldrich. Available from http://www.sigmaaldrich.com/

Howes, N., 1993. Catching fireflies for fun and profit. Old Farmer’s Almanac 1993, catalog/ProductDetail.do?l.ang=en&N4=L5256 SIGMA&N5=SEARCH CONCAT

158–160. PNO|BRAND KEY&F=SPEC

Inouye, B.D., 1999. Estimating competition coefﬁcients: strong competition among Takeda, M., Amano, T., Katoh, K., Higuchi, H., 2006. The habitat requirement of

three species of frugivorous flies. Oecologia 120, 588–594. the Genji-firefly Luciola cruciata (Coleoptera: Lampyridae), a representative

Katoh, K., Sakai, S., Takahashi, T., 2009. Factors maintaining species diversity in endemic species of Japanese rural landscapes. Biodiversity and Conservation

Satoyama, a traditional agricultural landscape of Japan. Biological Conservation 15, 191–203.

142, 1930–1936. Taylor, M.K., Laake, J., McLoughlin, P.D., Born, E.W., Cluff, H.D., Ferguson, S.H., Rosing-

Kaufmann, T., 1965. Ecological and biological studies on Ilie West African ﬁreﬂy Asvid, A., Schweinsburg, R., Messier, F., 2005. Demography and viability of a

Luciola disciollis (Coleoptera: Lampyridae). Annals of the Entomological Society hunted population of polar bears. Arctic 58, 203–214.

of America 58, 414–426. The Oak Ridger, 2008. Area lightning bug collectors catch 465 grams this year.

Khoo, V., Nada, B., Kirton, L.G., Phon, C., 2009. Monitoring the population of the Sept. 9 [Internet]. Available from http://www.oakridger.com/community/

ﬁreﬂy Pteroptyx tener along the Selangor River, Malaysia for conservation and x1056109090/Area-lightning-bug-collectors-catch-465-grams-this-year

sustainable ecotourism. Lampyrid 2, 162–173. (accessed 25.06.2010).

Kirton, L.G., Nada, B., Khoo, V., Phon, C.K., 2012. Monitoring populations of biolumi- Teng, H.J., Apperson, C.S., 2000. Development and survival of immature Aedes

nescent organisms using digital night photography and image analysis: a case albopictus and Aedes triseriatus (Dipter: Culicidae) in the laboratory: effects of

study of the ﬁreﬂies of the Selangor River Malaysia). Insect Conservation and density, food and competition on response to temperature. Journal of Medical

Diversity 5, 244–250. Entomology 37, 40–52.

Kurdna, O., 1986. Butterflies in Europe. Aspects of the Conservation of Butterflies in USFWS, 1997. Recovery Plan for Mitchells Satyr Butterfly (Neonympha mitchelli

Europe, vol. 8. Aula-Verlag, Wiesbad. mitchelli French). USFWS, Fort Snelling, MN.

Lee, L.C., Seybold, S.J., 2010. Host acceptance and larval competition in the Banded Wichmann, M.C., Johst, K., Moloney, K.A., Wissel, C., Jeltsch, F., 2003. Extinc-

and European bark beetles, Scolytus schevyrewi and S. multistriatus (Coleoptera: tion risk in periodically ﬂuctuating environments. Ecological Modelling 167,

Scolytidae): potential mechanisms for competitive displacement between inva- 221–231.

sive species. Journal of Insect Behavior 23, 19–34. Wong, C.H., Yeap, C.A., 2012. Conservation of congregating ﬁreﬂy zones (CFZs) in

Lewis, S.M., Wang, O.T., 1991. Reproductive ecology of two species of Photinus ﬁre- peninsular Malaysia. Lampyrid 2, 174–187.

flies (Coleoptera: Lampyridae). Psyche 98, 293–307. Yajima, M., 2007. Breeding fireflies at tama zoo: an ecological approach. Der Zoolo-

Lewis, S.M., Lloyd, J.E., 2003. Summer flings: firefly courtship, sex, and death. Natural gische Garten 77, 84–95.

History 112, 44–49. Yamanaka, T., Liebhold, A.M., 2009. Mate-location failure, the Allee effect,

Lloyd, J.E., 1966. Studies on the flash communication systems of Photinus fireflies. and the establishment of invading populations. Population Ecology 51,

University of Michigan Museum of Zoology 130, 1–95. 337–340.

Marshall, A.G., 1982. The butterﬂy industry of Taiwan. Antenna 6, 203–204. Yiming, L., Wilcove, D.S., 2005. Threats to vertebrate species in China and the United

Matsuo, Y., 2006. Cost of prolonged diapause and its relationship to body size in a States. BioScience 55, 147–153.

seed predator. Functional Ecology 20, 300–306. Yuma, M., 2007. Effect of rainfall on the long-term population dynamics of the

McLean, M., Hanson, F.E., Buck, J., 1972. Culture and larval behavior of Photurid aquatic ﬁreﬂy Luciola cruciata. Entomological Science 10, 237–244.

ﬁreﬂies. American Midland Naturalist 87, 133–145.