CLIMATE RESPONSES
Predicting temperature mortality and selection in
naturalDrosophilapopulations
Enrico L. Rezende^1 *, Francisco Bozinovic^1 , András Szilágyi2,3, Mauro Santos3,4
Average and extreme temperatures will increase in the near future, but how such shifts will affect mortality in
natural populations is still unclear. We used a dynamic model to predict mortality under variable temperatures
on the basis of heat tolerance laboratory measurements. Theoretical lethal temperatures for 11Drosophila
species under different warming conditions were virtually indistinguishable from empirical results. For
Drosophilain the field, daily mortality predicted from ambient temperature records accumulate over weeks or
months, consistent with observed seasonal fluctuations and population collapse in nature. Our model quantifies
temperature-induced mortality in nature, which is crucial to study the effects of global warming on natural
populations, and analyses highlight that critical temperatures are unreliable predictors of mortality.
G
lobal warming is a major threat to bio-
diversity, with temperature averages
and extremes forecasted to change sub-
stantially in the next 50 years ( 1 ), and
predicting which lineages, commu-
nities, and geographical regions are more
vulnerable constitutes a major challenge ( 2 , 3 ).
Numerous research groups have used critical
limits, namely the lower or upper temper-
atures at which performance drops to zero
( 4 , 5 ), to unravel broad-scale macroecolog-
ical patterns such as a higher vulnerability to
rising temperatures in terrestrial organisms
from the tropics ( 6 , 7 ). However, the reliability
of these proxies is uncertain because different
experimental protocols elicit different estimates
( 8 , 9 ) and values are often unusually high when
compared with temperatures encountered in
nature [( 10 ), but see ( 11 )].
Here, we show that these inconsistencies
can be explained with a common theoretical
framework, whose main premise is that the
cumulative impact of any thermal stress varies
with temperature and time. Similar methods
are commonly used in the food processing and
pest control literature ( 12 , 13 ), and yet their
application in thermal ecology remains conten-
tious [but see ( 14 , 15 )]. We previously combined
survival probability functions with measure-
ments of elapsed time for thermal death to
obtain a continuous“tolerance landscape”at
different constant temperatures ( 16 ) and now
expand this framework to predict survival in a
variable environment. The logarithm of sur-
vival times varies linearly with temperature
(Fig. 1A), and results in parallel thermal death
time curves for different relative survivals (S) that
can be described with a simple relation between
exposure times (t)andtemperature(T):
t 2
t 1¼ 10 ðT 2 T 1 Þ
z ðÞðfor any givenS 1 Þwherez> 0 corresponds to the thermal sen-
sitivity describing theDTrequired to change
tone order of magnitude (Fig. 1A and sup-
plementary materials). Thus, ifz= 2°C, an
organism that tolerates 40°C for 1 min could
withstand 38°C for 10 min and 36°C for
100 min. For standardization purposes, hereafter
we refer to the temperature at which meant=
1minasTmax,whichcorrespondstothetem-
perature at which the linear regression touches
the abscissa with log 10 -transformedt(Fig. 1A).
Equation 1 implies that any survival proba-
bility functionST(t) shifts horizontally by
10 (^1) z
as a consequence of 1°C increase in tem-
perature, and therefore, we can transform
any survival probability function fromT 1 to
T 2 with the relationship (for notational sim-
plicity, we denote the temperature dependence
by lower index):
ST 1 ðt 1 Þ¼ST 210
ðT 2 T 1 Þ
z t 1 ð 2 Þ
(Fig. 1B). In a variable thermal environment,
changes in the survival probability function
are coupled to changes in temperature and
survival times as
DSTðtÞðtÞ≈
dSðtÞ
dt
TðtÞ
Dt ð 3 Þ
(Fig. 1C). The survival rate at any given time
t′canbecalculatedbysummingupthein-
finitesimal small changes in the time interval
[0,t′]. This can be accomplished analytically
or numerically (supplementary materials).
We validated the numerical method, which
has the advantage of not requiring the analyt-
ical form ofS(t)tobedefined,bysuccess-
fully predicting survival responses of several
Drosophilaspecies subjected to highly contrast-
ing warming regimes. The dataset ( 17 )comprises
11 species whose survival was measured at
constant temperatures between 32° and 43.5°C
(n= 1289 individuals) and that were also
RESEARCH
Rezendeet al.,Science 369 , 1242–1245 (2020) 4 September 2020 1of4
(^1) Departamento de Ecología, Center of Applied Ecology and
Sustainability (CAPES), Facultad de Ciencias Biológicas,
Pontificia Universidad Católica de Chile, Santiago 6513677,
Chile.^2 Department of Plant Systematics, Ecology and
Theoretical Biology, Eötvös Loránd University, 1117 Budapest,
Hungary.^3 Institute of Evolution, Centre for Ecological
Research, Tihany 8237, Hungary.^4 Departament de Genètica
i de Microbiologia, Grup de Genòmica, Bioinformàtica i
Biologia Evolutiva (GBBE), Universitat Autonòma de
Barcelona, Bellaterra, Barcelona 08193, Spain.
*Corresponding author. Email: [email protected]
Fig. 1. Predicting mortality in
thermally variable environ-
ments.(A) Time to death
under a constant thermal
regime varies predictably in a
log-linear fashion with body
temperature, giving rise to
typical thermal death time
curves whose slope quantifies
the thermal sensitivityz. Data
points represent simulated
individuals that collapsed dur-
ing a static assay. (B) In light
of this relationship, results
from different temperature
assays can be expressed using
a single survival probability curve that shifts in time by a factor determined byz, increasing or decreasing mortality rates. (C) Using this framework predicted how
temporal variation in temperature affects the survival probability curve and, therefore, mortality rates under variable temperature conditions.