a number of stressors 
 have been implicated in honeybee losses in 
 many parts of the world , including habitat 
 loss ; viral diseases ; parasites such as varroa destructor , which can be a disease vector ; and use of pesticides . because these stressors may interact , it is difficult 
 to predict how they change the colony dynamics separately and in combination . 
 moreover , because of the many feedback mechanisms in honeybee colonies , 
 understanding the relationship between the effects on individuals 
 and the colony level effects is not straightforward .
ecological 
 modeling enables us to disentangle these interactions and explore 
 them both separately and in combination , in fully controlled simulations . 

an innate difficulty in studying the effect of pesticides on honeybee 
 colonies is the level of replication needed to capture low - level effects 
 at the field scale .
the european food 
 safety authority ( efsa ) has described specific protection goals for 
 honeybee colonies , stating ,  the magnitude of effects on colonies 
 should not exceed 7% reduction in colony size  . to assess
whether this level of impact is occurring 
 a minimum of 60 pairs ( control and treatment ) of colonies and fields 
 are needed for each study . if multiple 
 stressors are to be studied even higher numbers would be needed .
ecological 
 models can help in designing and targeting empirical studies , generating 
 specific hypotheses that later may be tested experimentally , and can 
 be used to assess the risk of environmental chemicals to honeybees .
there have been many laboratory , semifield , 
 and field studies showing 
 both acute and chronic effects of pesticides on adult honeybees and bee larvae .
for example , pesticides 
 have been shown to affect foraging via acute mortality , or alternatively from sublethal effects .
other effects , such as reduced learning acquisition , decreased rate of learning from olfactory cues , and reduced communication for recruitment to 
 foraging have also been shown to occur , 
 but the realism of these exposures is unclear . in this study , we will concentrate mainly on hypothetical 
 direct lethal effects on different life stages and reduced egg laying 
 rate that could result from sublethal effects on the queen .
this does not capture the complexity of real 
 exposure events , but it is important to compare the sensitivity of 
 the colony to mortality of different cohorts at different times of 
 the year in a controlled way . as pesticides can affect individuals 
 in a number of ways , determining 
 the colony level impact of an individual effect
feedback 
 loops may compensate for moderate stresses ( e.g. , earlier onset of 
 foraging if food stores are low ) or exacerbate 
 other processes ; for instance , less comprehensive care of brood as 
 a result of high in - hive worker mortalities .
the beehave model is a suitable tool to investigate this complexity 
 because it integrates in - hive processes and foraging activities to 
 simulate interactions between colony and environment .
the model consists 
 of four modules : ( 1 ) a landscape module , 
 allowing the user to define a landscape of nectar and pollen in food 
 patches ; ( 2 ) a colony module , an age - based cohort model including 
 processes such as nursing and care of brood ; ( 3 ) a foraging module , 
 an individual - based model calculating 
 the foraging activities on a particular day and the quantity of both 
 nectar and pollen brought back into the hive ; and ( 4 ) a varroa and virus module simulating the population 
 dynamics of the varroa mite and the transmission of viruses . the large 
 number of procedures and feedback loops allow a comprehensive view 
 of the impacts of stressors on the honeybee colony . here
, we report simulations using the beehave model to explore the colony - level impact of altering 
 the mortality of a number of honeybee life - stages and reducing the 
 egg - laying rate of the queen at different times of the year .
because such simulations enable the user to examine a whole variety 
 of stressors on individual bees , and the effects on the colony , finding 
 a standard way of comparing the responses of the colony would be useful 
 in risk assessment .
for environmental chemicals the ld50 is the standard index used to describe the median lethal dose of 
 a toxin i.e. that resulting in 50% subject mortality .
here , we present an index to compare the impact of different 
 imposed stresses on colony survival , the lis50 , describing 
 the  lethal imposed stress  level resulting in a 50% 
 colony mortality as predicted using the beehave model
. we also present 
 the lis10 , which predicts 10% colony failure from an imposed 
 stress .
we argue that these indices will be useful for comparing the 
 impact of imposed stressors at colony level and could also inform 
 the setting of pesticide protection goals in the future , once the 
 indices have been applied to a wider variety of stressors and their 
 variability has been quantified .
the beehave model ( beehave - model version 
 2014 - 03 - 04 , free to download 
 at www.beehave-model.net ) was modified to increase the 
 daily mortality of different life stages of bees in the colony from 
 a defined day for a defined period to simulate potential effects of 
 an exposure event ( where exposure is defined as the period when toxic 
 effects are imposed ) .
we used the default setting as described in 
 becher et al . , altering the landscape 
 as explained below .
modifications to the model for the treatments 
 below are outlined in the supporting information ( appendix 2 ) .
the simulations started from first january with 
 10  000 worker bees in a colony and ran for 3 years , and each 
 year had an identical annual weather cycle ( based on maximal temperature 
 and hours of sunlight at rothamsted research , hertfordshire , u.k . 
 in 2009 ) .
the colony was free from varroa and disease , as the purpose 
 of the simulations was to look at effects of singular events increasing 
 mortality in isolation .
on the last day of each year , if fewer than 
 4000 adult bees were present , the colony is assumed to die due to 
 winter mortality . at the end of each 
 three - year simulation
the number of bees alive in the colony , or alternatively 
 whether the colony had failed , was recorded .
beehave 
 allows users to define a dynamic 
 landscape , giving values for the distance of each food patch to the 
 colony , and the nectar quantity ( l ) , nectar quality ( sucrose concentration 
 ( mol / l ) ) and pollen quantity ( kg ) for each food patch on each day 
 of the year .
the simulations were set up in a very simplified and 
 stylized modeled landscape : a single food patch was 1 km away from 
 the hive offering 20 l of nectar and 1 kg of pollen each day of the 
 year ( although not representing the complexity of real landscapes , 
 this enables tests of potential  exposure  in each month 
 of the year in a controlled manner ) .
we ran simulations to contrast the effects 
 of five different imposed stresses : reduced egg laying rate ( elr ) 
 of the queen , increased daily larval mortality , increased daily in - hive 
 worker mortality , and increased forager mortality , applied daily or 
 applied on each foraging trip . in reality
, an exposure event may affect 
 a combination of life stages over varying timeframes via different 
 routes ( nectar , pollen , honey , wax ) , but to specifically examine the 
 sensitivity of different life stages , we chose a simplified set of 
 simulations : examining increased mortality of individual life stages , 
 during single exposure periods , when that exposure is assumed to be 
 direct via consumption of nectar and pollen .
we also ran the simulations 
 for one combination of daily life stage mortalities ( larvae , in - hive 
 workers , foragers ) .
pupal mortality was not tested , as the pupae are 
 in capped cells and do not receive food and therefore are unlikely 
 to be exposed directly via nectar and pollen . in each simulation , 
 a single stressor was applied for a continuous 30 day period each 
 year .
duration of bloom of different crops differ widely as do persistence 
 of different pesticides , but we here chose a 30 day exposure period 
 as typical .
timing - dependent effects were investigated by running 
 scenarios with the 30 day exposure period beginning on the first day 
 of each month of the year .
imposed mortalities were applied as both 
 multiples of the control value in the model and as set percent daily 
 mortalities , while reduced egg - laying rate was only applied as a percent 
 reduction .
testing a multiple of the control reflects the typical 
 procedure of pesticide risk assessments .
we also ran simulations with set percent daily mortalities to determine 
 the actual percentage of increased mortality that the colony could 
 withstand .
the daily egg - laying rate varies seasonally 
 depending on the day of the year ( for distribution , see becher et 
 al . ) , and eggs are lost at a rate of 
 3% per day by default . for the 
 simulations ,
the egg laying rate ( number of eggs produced on a particular 
 day ) was reduced by 25 , 50 , 75 , and 90% for a period of 30 days with 
 zero reduction applied as a control .
the daily mortalities 
 of the larvae , in - hive workers , and foragers were altered in two ways : 
 ( 1 ) control daily background mortality was multiplied by a factor 
 of 1 , 1.5 , 2 , or 3 .
( 2 ) daily background mortality was set to a set 
 percentage during the treatment period : one of 1 , 5 , 10 , 25 , and 50% 
 each day .
the control daily background mortality is typically 
 low : 0.4% for the in - hive workers and foragers and 1% for the larvae . for the larvae
, this mortality does not include the chance of dying 
 from lack of food or brood care .
increased 
 foraging trip mortality was simulated in two ways , similar to the 
 stage - specific daily mortality simulations : ( 1 ) control value was 
 multiplied by 1 ( control ) , 1.5 , 2 or 3 ; and ( 2 ) set values of 1 , 2.5 , 
 5 , 7.5 , and 10% mortality per trip .
lower values than for the daily 
 mortalities were used because foragers take multiple trips on a single 
 day , so the majority of foragers may die if a forager had a 25 or 
 50% chance of dying on each trip , reducing the impact of higher mortalities 
 as each bee can only die once .
these settings were used to simulate 
 pesticide exposure at levels high enough to cause death in the foragers 
 through either immediate acute mortality , gradual weakening during 
 the return flight , or through behavioral changes leading to impaired 
 orientation and consequent homing failure .
foraging mortality in the model depends on the duration of a foraging 
 trip and is applied before an individual forager returns to the colony . 

for the single food patch present in the simulations , the mortality 
 is 1.5% for nectar foragers and 0.9% for pollen foragers 
 under control conditions ( values taken from beehave model during control 
 simulations ) .
although these values can vary during a day ( as handling 
 time of a food patch is increased when the patch is depleted ) , enough 
 nectar and pollen are provided at the patch that this variation is 
 negligible . to simulate an event in which several life stages 
 are affected ,
the mortality of each of the larvae , in - hive workers , 
 and foragers were all modified simultaneously in two ways : ( 1 ) control 
 daily background mortalities of larvae , in - hive bees and foragers 
 were multiplied by a factor of 1 , 1.5 , 2 , or 3 .
( 2 ) daily background 
 mortalities of larvae , in - hive bees , and foragers were set to a set 
 percentage during the treatment period : one of 1 , 5 , 10 , 25 , and 50% 
 each day . while it is unrealistic that different life stages 
 are affected with identical effect levels , this scenario demonstrated 
 the colony s sensitivity to multiple effect types .
each 
 scenario was run for 30 replicates , with the mean number of 
 live bees at the end of three years as output . for each combination 
 of mortality type and 30 day exposure period ,
a linear regression 
 was carried out between either the factor increase of the control 
 or the percentage imposed mortality per bee and the mean number of 
 bees alive per colony at the end of the 3 year simulation .
the slopes 
 of these regressions were plotted ( figure 1 ) , showing how sensitive the colony is to 
 increased mortality of each life stage . calculated sensitivity 
 of colonies to each stage mortality imposed 
 for 30 days , calculated as the slope of the linear regression for 
 the simulation data shown in figures s1s3 .
for each combination of imposed stress and treatment month , a linear 
 regression was performed with the colony population at the end of 
 the third year against the magnitude of the imposed stress .
the graphs 
 show the reduction in colony size ( a ) per percent decrease in egg - laying 
 rate ( elr ) ; ( b ) per multiple of the control background daily mortality 
 for larvae , in - hive bees , and foragers ; ( c ) per multiple of control 
 background per - trip mortality ; ( d ) per percent daily mortality of 
 larvae , in - hive bees , and foragers ; and ( e ) per percent daily per - trip 
 mortality .
(  ) in these months , all levels of the combined 
 mortality except 1% mortality lead to all colonies being lost ; therefore , 
 it was not possible to fit a linear regression .
(  ) in these 
 months , all levels of both the forager and the combined mortalities 
 except 1% mortality lead to all colonies being lost ; therefore , it 
 was not possible to fit a linear regression . to compare between the effects of
these imposed 
 stresses at colony level , we calculated a new index analogous to the 
 ld50 : the lis50 was calculated as the level 
 of imposed stress at the individual level that led , statistically , 
 to 50% of the colonies dying in the beehave simulations within 3 years 
 ( using a threshold for survival of at least 4000 bees alive on the 
 last day of each year ) . in these simulations , 

the level of imposed stress was the percentage stage - specific daily 
 mortality or percentage chance of dying during a foraging trip .
 dose.p  function 
 in r s mass library on a generalized linear model ( glm ) built 
 using data on the number of colonies alive after increased mortalities 
 were imposed .
for each of the imposed stresses in question , the mortality 
 was applied from 0 to 100% ( in 5% increments ) for each month of the 
 year ( separately ) with 50 replicates . for foraging mortality per trip , 
 preliminary runs showed that colony death occurred when foraging mortality 
 was 40% for all tested months , so higher mortalities were not tested .
the lis50 was chosen for its theoretical parallel to 
 the ld50 , but a lisx could 
 be calculated for any percentage of colony failure ( x ) that is of interest , for example , lis10 figures are 
 also presented , predicting the level of stress resulting in 10% colony 
 deaths .
reducing the elr for 
 30 days had only a moderate impact with none of the colonies dying 
 in any of the simulations ( figure s1 ) . 
 a reduction of the daily egg laying rate by 90% ( i.e. , to 10% of the 
 control ) in june led to the average colony size at the end of three 
 years being reduced by 35% of the initial population ( figure s1 )
. between april and august , each percent 
 reduction in elr led to only 50 fewer bees per colony after three 
 years ( figure 1a ) . 

nevertheless , colony dynamics were affected to varying degrees depending 
 on the season and the reduction in the egg laying rate ( figure s1 ) .
the colony was not highly sensitive 
 to an increase in daily mortality 
 of the larvae or the in - hive workers within the tested range ( figure 1b ; figure s2a , b ) .
for the larvae , the control background mortality 
 was already low ( 1% ) and the majority of larvae that died 
 in the control simulations did so from a lack of resources ( food or 
 brood care ) .
therefore , small larval losses from increased background 
 mortality could be compensated in the model by allowing resources 
 to be spread among remaining larvae , reducing mortality from a lack 
 of these resources . as with background larval mortality ,
the control 
 value of daily in - hive worker mortality in the model is small ( 0.4% ) , 
 such that trebling it equates to 1.2% daily mortality and does not 
 result in large losses over the course of the month .
the impact of 
 increasing the control daily forager mortality was low when imposed 
 in january to august , but the colony was sensitive to increased mortality 
 imposed in september to december ( figure 1b ; figure s2c ) . 

the critical threshold for colony survival in the beehave model was 
 applied on the last day of december ; therefore the colony had the 
 whole year to recover from increased individual mortality applied 
 in january , before winter survival was calculated .
when the increased 
 foraging mortality was applied to foragers at the food patch on each 
 successful foraging trip , the impact on the colony was much larger 
 ( colony reduced down to almost 4,000 bees in june ) ( figure 1c ; figure s2 d ) , as the mortality was applied many times per day and 
 background mortality is higher than for in - hive life stages .
this 
 impact on the colony was likely due to the decreased food stores in 
 the colony .
these effects were particularly strong if the stress was 
 imposed during the summer months when foragers were making the most 
 foraging trips . for simulations multiplying the stage specific control 
 mortalities ,
per - trip foraging mortality was the only single imposed 
 stress to lead to colony failure with 3x mortality in june leading 
 to 77% colony survival .
when the mortality of larvae , in - hive workers 
 and foragers were applied simultaneously as a multiple of the control 
 mortalities , the impact on the colony was similar to the worst case 
 equivalent single mortality ( figure 1b , figure s4 ) , the single 
 life - stage daily mortality to which the colony is most sensitive when 
 applied as a multiple of default .
the 
 largest impact on the colony from larval mortality came when the effect 
 was applied in one of the months between april and august ( figure 1d , e ; figure s3a ) . during this period
, the colony has 
 a lot of larvae as it is building to peak numbers , and increased mortality 
 reduced or delayed this peak ( figure s5 ) .
very high larval mortality in may and june led to the colony population 
 being reduced to between 2000 and 3000 individuals , and winter mortality 
 was high ( figure s3a ) . when larval mortality 
 was increased ( illustrated in figure s5 for a level of 25% daily mortality ) , the resulting loss of larval 
 numbers had the effect of reducing deaths due to lack of food or care 
 during the treatment period , as these became more readily available 
 for the surviving larvae .
however , high larval mortalities 
 during summer led to a reduction in the worker population , which in 
 turn led to a further peak in larval mortality 1 week after the end 
 of the treatment period ( figure s5 ) .
the modeled colony was sensitive to losses of adult bees in most 
 months ( figure 1d , e ; figures s3b  d , s6 , and s7 ) .
with respect 
 to daily mortalities , the colony was more sensitive to losses of the 
 younger in - hive workers than to the older foragers . during the period 
 of april  september , the same period in which brood mortalities 
 had a noticeable impact ( figure 1d ; figure s3 ) , a daily in - hive 
 worker mortality of over 25% led to all colonies being lost between 
 may and july ( table s2 ) and a 5% daily 
 mortality led to up to 40  000 more in - hive worker deaths over 
 the course of the month ( figure s7 ) .
loss 
 of in - hive bees led to a large increase in brood loss from lack of 
 care or food over the rest of the year ( figure s6c ) and reduced the honey stores in the hive ( figure s6e ) .
outside spring and summer , high daily forager mortality 
 was devastating to the colony ( figure 1d ; figure s3c ) .
this is 
 because during the autumn and winter only few eggs are laid , so , the 
 colony consists primarily of older bees still termed  foragers  
 ( even though they rarely exited the colony ) .
the results of 
 these simulations also highlighted the potential 
 sensitivity of the colony to patch - specific forager mortalities , experienced 
 on each foraging trip ( figure 1e ) .
there was little effect at the very beginning or end of 
 the year due to the lack of foraging activity at these times . between 
 may and october
, there was a large impact on the colony from increasing 
 this foraging mortality ( june was the most sensitive month , as there 
 was more time to forage in june than other months ) .
a 5% mortality 
 at the food patch applied in june led to an average colony size of 
 1000 bees at the end of the 3rd year ( figure s3d ) with only 5 of 30 replicate colonies surviving 
 ( 17% table s2 ) . when the mortalities 
 were applied as a set percent to several life 
 stages simultaneously , this had a consistently higher impact than 
 the worst case individual daily life stage mortality in each particular 
 month ( forager mortality in winter and in - hive mortality in summer ) 
 ( figure 1d ) .
when colonies 
 were subjected to combined daily mortalities of over 10% at any time 
 of the year , then no colonies survived ( table s2 ) .
the lis50 values represent 
 the statistical likelihood that a certain imposed stress will lead 
 to 50% colony failure for the specific control conditions used in 
 the model ( in this case calculated after 3 years ) . with agreement 
 on appropriate control settings ,
the lis50 could be standardized 
 for use over any number of months or years , depending on the sensitivity 
 required .
table 1 contains lis50 values for four stressors imposed for 
 30 day exposures in 4 different months .
the months were chosen to 
 be those when foragers are active and crops flower and the colony 
 is therefore most likely to be exposed .
a low value indicates that 
 a low daily percentage mortality imposed on individuals led to high 
 colony failure and , therefore , identifies stressors to which the colonies 
 are most sensitive .
no values for the reduction in egg - laying rate 
 were given , as no 30 day reduction of egg - laying rate led to colonies 
 dying for any of the chosen months .
values of > 100% 
 imply that in 
 all of the simulations , 50% colony loss was not reached .
the colonies were most sensitive 
 to in - hive worker daily mortality 
 and to per - trip foraging mortality ( table 1 , figure 2 ) . the in - hive worker mortality started to become very 
 influential in the period between april and may , when the respective 
 lis50 went from over 100% in april to 11% , in may and 7% 
 in june ( table 1 , figure 2 ) as the brood nest 
 was growing exponentially , requiring a large workforce of nursing 
 bees , and the colony structure moved from mostly foragers ( the overwinter 
 bees ) to more younger in - hive workers .
the lis50 for the 
 forager mortality per trip has a relatively low value during the summer , 
 with a value of just 4% in june .
such mortality was applied many times 
 a day to foragers , especially those that were particularly active 
 within the treated patch so the cumulative daily mortality was higher . 

the colonies were also sensitive , but to a lesser extent , to daily 
 forager and larval mortality .
daily forager mortality had the largest 
 impact in june and july , larval mortality in may and june .
imposed stress 
 response curves for the four individual mortalities 
 investigated : ( a ) daily larval mortality , ( b ) daily in - hive worker 
 mortality , ( c ) daily forager mortality , and ( d ) forager mortality 
 per foraging trip .
these show the % survival of 30 colonies for each 
 of the varying mortalities , at the end of three years .
different colored 
 lines are shown for these mortalities applied for 30 days in ( yellow ) 
 april , ( orange ) may , ( red ) june , or ( black ) july .
the intercept between 
 a response curve and the solid horizontal line indicates its lis50 ( table 1 ) , 
 while the intercept with the dashed horizontal indicates its lis10 .
importantly , the different imposed 
 stresses had their greatest 
 impact ( smallest lis50 ) at different times of the year . 

specifically , larval mortality had the lowest lis50 in 
 may , whereas the two forager mortalities and the in - hive mortalities 
 were at their lowest in june .
the reason was that increased larval 
 mortality led to a reduction of the adult in - hive population later 
 in the year ( figure s5a ) therefore reducing 
 larval population in may could lead to reduced in - hive worker population 
 in june ( and all impacts which arise from that ) .
alternative 
 thresholds of colony failure may be explored with lisx : so lis10 values have also been 
 included in table 1 showing the level of stress causing 10% colony failure .
although 
 the lis10 is likely to be quite variable , it gives useful 
 information when used in conjunction with lis50 : for certain 
 life stages in certain months ( in - hive bees and foraging trip mortality ) , 
 lis10 and lis50 were remarkably similar ( figure 2b , d ) where the stress 
 response curve was so steep that there were effectively tipping points 
 when any increase in daily mortality rates ( imposed for this period 
 of 30 days ) led to all colonies failing .
using 
 a set of simplified scenarios , our results showed a large 
 variation in the impacts of imposed stress on the honeybee colony 
 depending on both the demographic stage targeted by the imposed stress 
 and the time of year in which the stress is applied .
imposed stress 
 on all stages , except for daily forager mortality , led to highest 
 colony losses from april to august . imposed stress to the adult workers 
 was , most often , more damaging to the colony than effects on the brood ; 
 and imposed stress applied to in - hive workers had a larger impact 
 in late summer than the rest of the year .
this was partly a consequence 
 of the large proportion of in - hive workers , and that individuals were 
 in - hive bees for a relatively long time such that cumulative stage 
 mortality was higher , even if daily mortality was the same as for 
 other life stages . in - hive
bees ( table s1 ) would have consumed a lot of resources in their development but 
 as yet not started generating them for the colony by foraging for 
 nectar and pollen . when the stress was imposed as a multiple 
 of the default
, there 
 was little impact on the colony , except in the case of mortality calculated 
 per foraging trip .
this suggests that similar fluctuations in daily 
 mortality are insufficient to cause colony loss in isolation , whereas 
 foraging mortality calculated on a per trip basis carries a higher 
 risk to the colony because a forager can perform many trips per day . 

when mortality of a life stage is a set percentage , > 10% daily 
 ( or 
 per - trip ) mortality for 30 days is very damaging in all cases .
the impact of decreased egg laying rate was sizable but not lethal 
 to the colony and other models show similar results .
( using the pc beepop model ) find 
 that eggs are the least damaging of the life stages to lose and adults 
 are the most .
similarly , schmickl and crailsheim ( using the hopomo model ) find that reducing the elr to 
 60% reduced the number of bees in the colony on day 360 down by 40% 
 from control . in real colonies ,
that may experience swarming events , 
 there may be periods of around 3 weeks with no egg laying .
even when 
 egg production is high , as during the summer , these require no food 
 and only a small amount of nursing , so the investment lost with an 
 egg is minimal . large increases of larval mortality at particular 
 times of year ( figure 1 ) can have a significant impact on the colony .
individuals only spend 
 6 days as larvae so , as the stress was applied daily , an individual s 
 chance of being affected during their larval period is lower for the 
 same daily mortality than for other life stages with longer developmental 
 periods ( table s1 ) .
however , the colony 
 invests honey and pollen in feeding larvae and has invested care from 
 in - hive workers , and so , losing larvae will represent a net loss of 
 effort to the colony .
figure s5 shows the 
 feedback effect of high larval mortalities , at a sensitive time of 
 year , leading to far fewer bees in the colony as a result of reduced 
 potential worker population .
for newly emerged workers , a large 
 amount of resources have been 
 used to raise them to adulthood and they have not yet contributed 
 to the colony . depending on the state of the colony and the time of 
 year , in - hive bees spend around 20 days before becoming a forager , 
 meaning there is a long period over which the imposed stress can have 
 an effect .
daily mortalities will build up quickly ; a 5% daily in - hive 
 worker mortality in august can lead to overall stage mortality of 
 65% and approximately 40  000 more in - hive workers dying ( figure s7 ) and further impacts from a 5% daily 
 in - hive worker mortality ( e.g. , increase in larval loss and reduced 
 food stores ) are shown in figure s6 .
figure 1 shows that 
 the colony was more sensitive to in - hive worker losses than forager 
 losses during summer , and the colony was more sensitive to forager 
 mortality toward the end of the year . at the beginning and end of 
 the year
, the modeled colony contains mostly foragers ; no new workers 
 were emerging , there was little or no foraging taking place , and in 
 beehave , existing workers are classified as foragers once reaching 
 a certain age .
therefore , at these times of year , impacts from forager 
 mortality should be seen as impacts from general adult mortality . 

hence , high daily adult mortalities can heavily reduce either the 
 colony s ability to survive over winter or the colony s 
 ability to build resources early the following year .
high foraging 
 mortality will also trigger in - hive workers to become foragers at 
 an earlier age , reducing the age of first foraging . in reality
, such 
 precocious foragers may not be as successful as older foragers , resulting 
 in further stress to the colony .
the colony is very sensitive to high percentages of this combined 
 mortality throughout the year ( figure 1d ) but , in many months , not much more sensitive than 
 the worst - case daily life - stage mortality at any one time period . 

an explanation could be that the loss of certain life stages can lead 
 to the loss of other life stages , and hence , removing , for example , 
 both in - hive bees and larvae will not necessarily cause more damage 
 than only removing in - hive bees , as the larvae would have died anyway 
 due to a lack of brood care . at many time points in the year , there 
 is one life stage in the model that the colony is highly sensitive 
 to losing , but at other times , the colony is more sensitive to losing 
 multiple life stages ( e.g. , april and september ) , and these dynamics 
 need further investigation .
the set of simulations described here use a precisely 
 defined exposure period , effects on single life stages , and a stylized 
 landscape . in reality , the heterogeneity of the cropped landscape 
 over time and space and the relative toxicity and persistence of different 
 pesticides in the landscape , and in the hive , may lead to a diverse 
 range of sublethal and lethal impacts on individual bees at different 
 life stages . the next steps in using beehave to examine more realistic 
 scenarios will involve using detailed empirical evidence to capture 
 those exposure routes and timeframes , for specific chemicals in precise 
 locations , and a specific module for this is in development .
there 
 are many empirical studies showing how stressors affect individuals 
 or , in some cases , the colony in the short term .
long - term , multiyear 
 studies are available , yet uncommon , so the impact of imposed stresses over multiple years is 
 not fully understood .
find that 1.5 month exposure to two neonicotinoid 
 insecticides through pollen patties starting in may leads to a 28% 
 reduction in worker population in the following april , along with 
 effects on brood size and food stores .
dively et al . also find effects on colony strength and overwintering 
 success after 12 weeks ( may  august ) exposure to diet patties 
 with high ( 20100 ppb ) levels of imidacloprid .
in contrast , 
 three studies of honeybee colony growth and survival in the field , 
 when exposed via natural foraging on flowering crops treated with 
 neonicotinoids , have shown no significant impact of the pesticide 
 exposure on the colonies ( for clothianidin and for thiamethoxam ) .
carreck and 
 ratnieks suggest that the levels of pesticide 
 encountered by foraging honeybees are lower in the field than used 
 in many lab experiments . in large - scale field studies ,
in which the 
 bees are placed near treated crops to forage the bees may have lower and more variable 
 pesticide exposure than in studies where bees are fed with an artificial 
 feed , with pesticide added at  field realistic  levels and this may explain why the 
 former studies often find less damaging effects .
in addition field 
 studies offering the colony a known amount of pesticide ( such as sandrock 
 et al . and dively et al . ) find that the impact upon the hive from the 
 pesticide can appear sometime after exposure .
the simulations presented 
 here show how this can occur within the model : figure s5b shows how the number of larvae in the colony is 
 affected by a 25% larval mortality in june .
it is clear that there 
 is an additional delayed impact likely due to a reduction in workers 
 providing brood care .
these contrasts also highlight the difficulties 
 of scaling from individual level effects to those at the colony level . 

the beehave model contains a large number of feedback loops , allowing 
 in - depth investigation into how multiple stressors can disturb the 
 colony dynamics in terms of mechanism , and which particular stresses 
 are more damaging to the homeostasis of the colony .
for example , with 
 high forager mortality , worker bees become foragers earlier to compensate ; 
 this in turn may reduce the nursing force , increasing larval mortality . a small increase in larval mortality
can reduce 
 the mortality of the surviving larvae from other causes such as lack 
 of food or brood care , and reduces further losses , i.e. show a compensatory 
 effect ( figure s6 ) .
the beehave model is a 
 useful tool in the risk assessment of stressors 
 to bees as many potential stressors can be assessed simultaneously , 
 and testable hypotheses can be developed .
indeed efsa have recently 
 published a review to suggest , with further development , beehave could 
 be the model of choice for regulatory pesticide risk assessment .
several models have been used to explore the impact of pesticides 
 on bee colonies . however , the models of khoury et al . and bryden et al . focus on 
 limited portions of colony dynamics , and lack key processes required 
 to accurately predict how a bee colony reacts to numerous stressors . 

we have 
 shown that the time at which a stress is applied greatly affects the 
 colonies response .
a stress imposed in april has little effect , 
 while the same stress imposed in june will devastate the colony .
pcbeepop is a model that includes colony dynamics similar 
 to beehave ; although , beehave also includes a number of factors , such 
 as the landscape and foraging dynamics ( including the flow of energy 
 in the form of honey stores ) integrated with the colony module , which 
 may be key to understanding how pesticides can impact the colony .
the beehave model is the only tool to date that 
 also includes a dynamic landscape module and weather providing the 
 potential for climate or location - specific simulations , as well as 
 integration with the foraging and varroa and virus modules , to apply 
 many stressors to the colony at any one time , as would be happening 
 to real colonies in the field .
further development of beehave , with 
 a  pesticide module  , to ensure correct implementation 
 of exposure routes from flower , via forager , into the colony is underway . to quantify the impact of a pesticide on a hive , the efsa guidance classifies the magnitude of an effect by the 
 % change in colony size .
efsa considers a change between 3.5 and 7% 
 negligible ; and a change larger than 35% to be large .
2011 model to estimate what forager loss would be permissible 
 for  negligible  change and find that forager losses 
 of 1.5  control for 6 days ; or 2  control for 3 days 
 or 3  control for 2 days would be permissible .
we have shown 
 that effects on fecundity or brood mortality are not as impactful 
 on the colony as adult loss , so worker loss is a conservative measure 
 of the damage possible from a pesticide to the colony .
the modeled 
 colony has a certain capacity for compensation , which varies with 
 the life stage affected and time of year and durations , but once the 
 compensation threshold is exceeded the colony is likely to fail .
levels 
 of  background  mortality in the absence of pesticide 
 exposure , depending on weather , forage quality and other stressors 
 present , are likely to influence compensation capacity . due to this 
 compensation capacity and
how it may vary with the health of the colony , 
 a percent reduction of bees in the colony could have highly variable 
 results on the health of the colony .
modeling , such as with beehave , 
 could , therefore , help supplement the risk assessment procedure by 
 teasing apart such dynamics . lis50 and
lis10 provide a tool to compare the effects of a variety of imposed stresses 
 on the colony using beehave , treating the colony as an individual 
  super  organism by using the percent chance of colony 
 mortality as a measure of sensitivity to imposed stress .
colony failure 
 as a result of an introduced chemical is not an acceptable end point , 
 but these indices ( calculated from simulations ) could be used to provide 
 theoretical comparisons of the effects of different stressors on the 
 colony , which may be informative in discussions of future regulatory 
 risk assessment procedures , and protection goals .
this study was designed 
 with impacts of pesticides in mind , but impacts on the colony driven 
 by varroa destructor , related diseases , nosema sp
also , comparing lis10 and lis50 provides hypothetical evidence of which 
 stressors , at which levels , may lead to colony tipping points , with 
 the caveat that the tipping point will depend on the control scenario 
 ( e.g. , forage availability and weather will all affect the colony s 
 capacity for compensation ) .
the beehave model , together with the use 
 of lis50 , allows consistent investigation into the impact 
 of multiple stressors on the honeybee colony , and could be key for 
 future risk evaluation .
 to simulate effects of pesticides 
 on different honeybee ( apis mellifera l. ) life stages , we used the beehave 
 model to explore how increased mortalities of larvae , in - hive workers , 
 and foragers , as well as reduced egg - laying rate , could impact colony 
 dynamics over multiple years . 
 stresses were applied for 30 days , both 
 as multiples of the modeled control mortality and as set percentage 
 daily mortalities to assess the sensitivity of the modeled colony 
 both to small fluctuations in mortality and periods of low to very 
 high daily mortality . 
 these stresses simulate stylized exposure of 
 the different life stages to nectar and pollen contaminated with pesticide 
 for 30 days . 
 increasing adult bee mortality had a much greater impact 
 on colony survival than mortality of bee larvae or reduction in egg 
 laying rate . 
 importantly , the seasonal timing of the imposed mortality 
 affected the magnitude of the impact at colony level . in line with 
 the ld50 
 , we propose a new index of  
 lethal 
 imposed stress  : the lis50 which indicates the level 
 of stress on individuals that results in 50% colony mortality . 
 this 
 ( or any lisx ) is a comparative index for 
 exploring the effects of different stressors at colony level in model 
 simulations . 
 while colony failure is not an acceptable protection 
 goal , this index could be used to inform the setting of future regulatory 
 protection goals . 
Introduction
Methods
Results
Discussion