Journal of Experimental Marine Biology and Ecology 400 (2011) 227–235

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Journal of Experimental Marine Biology and Ecology

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Exploring mechanisms linking temperature increase and larval phenology: Theimportance of variance effects

Luis GiménezSchool of Ocean Sciences, Bangor University, LL59 5HP, Anglesey, United Kingdom

E-mail address: l.gimenez@bangor.ac.uk.

0022-0981/$ – see front matter © 2011 Elsevier B.V. Aldoi:10.1016/j.jembe.2011.02.036

a b s t r a c t

a r t i c l e i n f o

Keywords:Climate changeMarine larvaeMatch/mismatchPhenologyRecruitment

In temperate environments, many animals and plants show seasonal peaks of abundance. Risingtemperatures due to climate change could affect the timing of these peaks with important consequencesfor populations of organisms positioned higher in the food web. If the peak of consumer species shifts withrespect to the resources a trophic mismatch occurs by which many individuals of a population of consumersmay not encounter the food source. I show that increased temperatures can lead to trophic mismatch throughan alteration of the variance of the abundance distributions of consumers or resources over time; such changewould reduce the overlap between the temporal distribution of consumers and resources. This occursthrough: (1) a non-linear effect of temperature on the developmental rates; and (2) variations in the shape ofthe temperature curve during the year. These effects should be widespread among different kinds oforganisms. Temperature increase may therefore have consequences for trophic mismatch through thecombined effect of differential shifts in the average timing of life history events and through the reduction inthe spread or variance of these events.

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© 2011 Elsevier B.V. All rights reserved.

1. Introduction

In recent years, important changes in biodiversity, structure anddynamics of marine populations, communities and ecosystems havebeen associated to climate variations (Southward et al., 1995;Ottersen et al., 2001; Beaugrand et al., 2008; Cury et al., 2008;Hawkins et al., 2009; Johnson et al., 2011-this issue; Menge et al.,2011-this issue; Philippart et al., 2011-this issue; Wernberg et al.,2011-this issue all in this volume). At the level of ecosystems, thesechanges consist of e.g. latitudinal shifts in species distributions, fromlow to high latitudes (Beaugrand et al., 2003), or “phase shifts”consisting of a sudden reorganisation of the elements (e.g. speciescomposition) of an ecosystem (Hare and Mantua, 2000; Reid et al.,2001; Beaugrand et al., 2008).

At the level of populations changes in phenological events inrelation to climate change have been detected (e.g. Sims et al., 2001;Sims et al., 2004; Genner et al., 2010). Phenology is the study ofperiodic biological events (e.g. reproductive period, larval season, birdnesting period, migrations) as influenced by the environment,especially temperature changes, driven by weather and climate(Schwarz, 2003). In recent years, the timing of events such as egglaying, bird nesting and seasonal peaks of planktonic populationsoccurs earlier in the year than some decades ago (Fitter and Fitter,2002; Parmesan and Yohe, 2003; Edwards and Richardson, 2004;Miller-Rushing and Primack, 2008). However, not all the species of an

ecosystem respond in the same way; the magnitude of the shift in thetiming of peaks of abundance of food resources (e.g. plants,phytoplankton) may differ from the population peak shift of theconsumers (grazers, zooplankton). Differential shifts in the timing ofevents in resources and consumers can lead to trophic mismatches(Greve et al., 2004; Edwards and Richardson, 2004), where the peak ofabundance of a species does not coincide with the peak of its food.This leads to negative consequences for the consumers: several yearsof mismatch may lead to population extinction.

The idea of trophic mismatch has been developed by Cushing asthe “match/mismatch hypothesis” (see Cushing, 1990; Durant et al.,2007): this hypothesis states that if predators and preys showseasonal patterns of abundance and if a predator's abundance iscontrolled by the one of the preys, then the inter-annual variability inrecruitment should be a function of the timing of the production offood in relation to the timing of production of larvae. When peaks oflarval production do not coincide with peaks of food availability(mismatch), high larval mortality and low recruitment is predicted;conversely when both peaks coincide (match) high recruitment isexpected (see e.g. Fortier et al., 1995; Brander et al., 2001; Beaugrandet al., 2003; Philippart et al., 2003 for evidence). In the marineenvironment, the problem of food limitation is particularly importantin crustacean larvae (Olson and Olson, 1989), and it may be alsoimportant in some bivalve larvae (Philippart et al., 2003).

The problem of phenology and trophic mismatch is not onlyrelated to a shift in the average timing of one or more events of the lifehistory of marine organisms. Peaks may vary in other characteristicssuch as the maximum abundance and its spread over time. Durant et

228 L. Giménez / Journal of Experimental Marine Biology and Ecology 400 (2011) 227–235

al. (2005) have confirmed predictionsmade by Cushing (see Durant etal., 2007) in that apart from peak shifts, mismatches involve changesin food availability that may exacerbate or reduce the effects of peakshifts on mismatch (Durant et al., 2005). I focus on the spread or theduration of the seasonal peaks of organisms. This spread can becharacterised as the variance of the temporal distribution ofabundance of the target organisms. We know very little aboutchanges in the spread of seasonal peaks of organisms. Cushing (1990)stated that a wide spread in the pulse of production of predatorsshould counteract variations in the timing of production peaks ofprey; this was supported by a study done by Mertz and Myers (1994).Recently, Batten and Mackas (2009) found that the duration of theannual peak of the copepod Neocalanus plumchrus has beenprogressively narrower since 1957–1965 to the period 2000–2007.Winkler et al. (2002) showed that variance in date of clutch initiationin a passerine bird decreased in warmer years. Stenseth andMysterud(2002) attributed this pattern to non-linear dependencies betweendemographic rates and climate, but they did not further elaborate onthat topic. The variance of ecological processes is central tounderstand the function of communities and ecosystems (Bene-detti-Cecchi, 2000, 2003). In particular for the case of match/mismatch, the variance in the temporal distribution of organisms isimportant because it can affect the overlap between production at onelevel and consumers at the next level of the food web. If changes invariance are not an adaptive response to changes in food (e.g. increasein the level of synchronisation to an environmental signal), then theymay result in negative effects at the level of populations.

Both, timing and spread of events in the life cycle of organismsmaybe based on different mechanisms where variations in temperature,light, salinity, food and other factors may play key roles. The objectiveof this paper is to explore two mechanisms by which temperaturemay affect the timing and spread of the peaks in larval production.Temperature strongly affects developmental rates of organisms at alllife stages, while the influence of other factors may be stage-dependent. In marine ectotherms, increases in temperature lead toreduced duration in the development of organisms (e.g. see Anger,2001; O'Connor et al., 2007 for review of examples) up to a certainoptimum. In the next two sections I address these two mechanisms:(1) the nonlinear relationship of temperature and duration ofdevelopment; and (2) temperature seasonality. In each section, themodelling approach and the results are explained and describedseparately. In the last section, I discuss the effect of temperature onthe timing and spread of life history events in the context ofenvironmental variability and genetic and plastic responses totemperature.

2. Methods and results

2.1. Non-linear relationships between temperature and development

2.1.1. Modelling approachThe variance in the timing of events in the life history is here

modelled from the relationship between temperature and duration ofdevelopment and from the distribution of temperatures experiencedby a population of developing individuals. The temperature condi-tions considered here are restricted to those that do not compromisesurvival through direct physiological stress and are below thetemperature optimum. In that range, developmental rates of marineinvertebrates and temperature are non-linearly related, so that theduration of development tends to approach an asymptotic value astemperature increases towards the optimum. Although the individualresponses may be affected by genetic variability or maternal effects,these should not blur the general non-linear relationship betweendevelopment and temperature. In the case of larval development ofmarine invertebrates some of these relationships are demonstrated inAnger (2001) and O'Connor et al. (2007). Such relationship has been

modelled by several functions such as the Belehradék's (1935, 1957)equation and the Arrhenius model used in the metabolic theory ofecology (Gillooly et al., 2002; Brown et al., 2004; O'Connor et al., 2007;Duarte, 2007).

If all individuals of a population were spatially distributed over ahomogeneous temperature field and exhibited the same response totemperature, different events of the complex life cycle (e.g. spawning,larval release, metamorphosis) would occur with high synchrony, withvariation depending on genetic variability or phenotypic plasticresponses. However, populations of manymarine and terrestrial speciesare distributedoverhundreds to thousands of kilometres andsometimesextend through several degrees of latitude. At that scale there should besome variation in many factors, but temperature probably plays adominant role. In addition habitat heterogeneity or aggregation oforganisms may lead to small-scale heterogeneity in temperature fields.The temperature conditions experienced by a population shouldtherefore be characterised by a frequency distribution.

The changes in the variance of duration of development of apopulation will be the consequence of the combination of thedistribution of temperatures and the relationship between tempera-ture and development. Below, the distribution of duration ofdevelopment is derived according to both the Arrhenius model andthe Belehradék's equation.

2.1.2. Arrhenius equationThe Arrhenius equation relates development, D, and temperature

as:

D = d × eE = T × kð Þ ð1Þ

where d is a constant, k is the Boltzmann constant (=8.62×10−5) andE is the activation energy (O'Connor et al., 2007; see also Fig. 1a). Inorder to describe and model the distribution of duration ofdevelopment a function may be derived as the inverse map of Eq. (1):

T = ln−1 D= dð Þ × E = kð Þ ð2Þ

Assuming that the distribution of temperatures experienced by theorganisms is Gaussian, characterised by a mean temperature, MT, andstandard deviation, ST, the distribution of duration of developmentcan be derived from the function:

f Dð Þ = C × eg Dð Þ ð3Þ

So that C=1/(2×π×ST)1/2 and g Dð Þ = − ln−1 D=dð Þ × E =kð Þ−MT Þ½ �22 × S2T

I used the above equation to estimate the variance in larvaldevelopment using parameters derived from O'Connor et al. (2007)for marine invertebrate larvae. The Arrhenius model predicted thatthe variance of the duration of larval development should decrease astemperature increases (Fig. 2a); linear regression between thecomputed variance and temperature showed that the variancedecreased exponentially (Fig. 2b).

2.1.3. Belehradék equationThe Belehradék equation relates development, D, and temperature

as D = AT−að Þb, so that themap is T =

ffiffiffiffiAD

b

r+ a, that gives the following

g(D) function in Eq. (3), assuming again a normal distribution oftemperatures:

g Dð Þ = −A=Dð Þ1=b + a−MT Þ

h i22 × S2T

ð4Þ

As an example, I used the parameters derived by Guerrero et al.(1994) for the duration of embryonic development of the marine

a

80

100

120

60

80

100

120

D = e-22.47 x e 0.64/(k(T+273)) D = 1656 x (T-3.48) -1.36

Arrhenius Belehradek

0

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60

0 5 10 15 20 25 30 35 40 10 15 20 25 30 350

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atio

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elop

men

t

Temperature °C

Consumer

Time of the year Time of the year

Resource

b

Abu

ndan

ce

Abu

ndan

ce

Increase in temperature

Fig. 1. The effect of temperature on duration of development: (a) calculations using the Arrhenius equation with parameters from O'Connor et al. (2007) and the Belehradékequation with parameters from Guerrero et al. (1994) for a marine copepod. (b) if the range of variation in duration of development decreases at higher temperatures, then increasesin temperature lead to a mismatch due to the decreases in the variance of the distribution of duration of development of predators and preys.

0.20

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)

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1500

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10 oC

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Var (D) = e8.718 x e-6.625 T

Var (D) = e21.241 x T-6.333

Var

(D

)

0

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Duration of development (days)

0 20 40 60 80

5 10 15 20 255 10 15 20 250

10

Temperature °C

Fig. 2. Predictions from Arrhenius and Belehradék equations on the effect of temperature on the variance of the duration of development. (a) Higher temperature leads to a decreasein themean and variance in the duration of development. (b) Decay in the variance as a function of temperature with adjusted functions after linear regression. The function f(D)wasstandardised to obtain stf(D) so that its indefinite integral equals 1. This was done as: stf Dð Þ = f Dð Þ= ∑900

1 f Dð Þ (see Appendix for Matlab code).

229L. Giménez / Journal of Experimental Marine Biology and Ecology 400 (2011) 227–235

121314151617

Cold: T= 3.522 sin(0.542 ·t -3)+10.266

6789

1011

121314151617

6789

1011

121314151617

6789

1011

121314151617

6789

1011

Mild: T= 3.541 sin(0.534 ·t -3)+10.742

Mild with cold winter

T= 4.2 sin(0.534 ·t -3)+10.2

Warm: T= 3.541 sin(0.534 ·t -3)+11.742

9 10 11 121 2 3 4 7 85 6

9 10 11 121 2 3 4 7 85 6

9 10 11 121 2 3 4 7 85 6

9 10 11 121 2 3 4 7 85 6

Time (month)

Tem

pera

ture

°C

Fig. 3. Seasonal temperature cycles used to simulate the timing of hatching, moulting toZoea II, III, IV, megalopa, and metamorphosis to the first juvenile stage in Carcinusmaenas. The four modelled scenarios (cold year, mild year, mild year with cold winter,and warm year) are represented by the respective seasonal cycles defined by theequations givenwithin each graph. The thick horizontal lines show the timing of events,starting with initiation of embryogenesis (lowest line) and ending with the timing ofmetamorphosis to the first juvenile stage (highest line). Vertical lines show the month

230 L. Giménez / Journal of Experimental Marine Biology and Ecology 400 (2011) 227–235

copepod Acartia grani (see Fig. 1 for details). Under the Belehradék'smodel, variance in the timing of embryo hatching decreased astemperature increased, but following a geometric function (Fig. 2).

In both models, increases in temperature led to a decrease in thevariance of the temporal distribution of abundances of a given stage ofthe life cycle. The decay in variance with increasing temperature is theconsequence of the negative non-linear relationship between tem-perature and duration of development, which is well documented(Anger, 2001; O'Connor et al., 2007).

2.2. Temperature seasonality

The life cycle of many marine temperate species include one ormore stages with long embryonic or larval developmental periods.During a season, the developmental rate of these stages should changeas a consequence of temperature change. In addition, due to geneticvariability and contingencies related to ecological factors or matingchances, not all eggs start maturation at the same time; there shouldbe some temporal variation that can be characterised by a frequencydistribution. In a population of eggs starting maturation at differentdates, the distribution of larval peaks will be the result of thedistribution of spawning eventsmodified by the seasonal temperaturecycle. This has been termed the “Doppler effect” of temperature (Bell,1997; Xiao, 2003). Obviously, in nature there will be a number offactors affecting the distribution of larval peaks (e.g. predation oneggs); in order to focus on the mechanism of seasonal temperaturechanges these are not considered here.

2.2.1. Modelling approachAs an example I used the embryonic and larval development of the

shore crab Carcinus maenas, a key coastal invertebrate of the NorthernHemisphere. In this species, relationships between temperatureversus embryonic and larval development have been described byWear (1974) and Dawirs (1985) respectively. I developedmodels thatpredict the temporal distribution of the following events: (a) larvalhatching, (b) moulting to the different larval stages and (c)metamorphosis to the first juvenile crab. The model uses equationsrelating duration of development (in days) and temperature (in °C)for the embryogenesis, zoeal and megalopa stages (Table 1).

I modelled the temperature seasonal cycle as sine functions (Fig. 3,right panels) based on averaging monthly temperature valuesrecorded for the Isle of Man (source CEFAS, UK: Joyce, 2006). Theseshould represent temperatures of the Irish Sea and elsewhere. Iexplored the following scenarios (Fig. 3): (1) a “cold year” (averagesof period 1903–1930, temperature range 7 and 14 °C); (2) “mild year”(averages of period 1981–2004; range 7.5–14.5 °C), (3) “mild year”with a cold winter, (range 6–14.5 °C) and (4) a warm year (averagesof period 1981–2004+1 °C, range 8–15 °C). In the “mild” and “warm”

years the maximum temperatures are reached in September. In the“cold” year temperature increases up to a maximum in August andremains constant until September.

These scenarios have been chosen as they represent usual year-to-year changes in the seasonality patterns as well as long-term

Table 1Equations relating duration of development, D in days, and temperature, T in °C, for theembryos, zoeal and megalopa stages of the shore crab Carcinus maenas.

Stage Equation

Embryo DE=6.053×1010×(T+28.71)−5.6

Zoea I DZ− I=314.2×T−1.45

Zoea II DZ− II=292.9×T−1.47

Zoea III DZ− III=595.9×T−1.70

Zoea IV DZ− IV=593.4×T−1.79

Megalopa DM=757.5×T−1.44

of the predicted maximum temperature.

increases in the average temperature. For instance, in the North Seamost warming has occurred during winter (Franke et al., 1999). Long-term trends in benthic communities and the timing of recruitment ofmussels and shore crabs appear to respond to years with cold winters(Strasser, 2002; Beukema et al., 2009).

I assumed that embryonic development starts when temperatureis 11° or higher: although embryogenesis may occur at lowertemperatures, this is the lowest value for which there are data

2.4

2.6 Cold

2.0

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Mild

1.8

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Mild with cold winter

Var

ianc

e (d

ays2 )

Warm

Life history stageZI Z-II ZIII ZIV M J

Fig. 4. Predicted variance in the timing of events of the early life cycle of Carcinusmaenas, from the hatching of the Zoea I stage (Z-I) to the metamorphosis to the firstjuvenile stage (J), under four different scenarios of seasonal variations in temperature(see Fig. 3). Variance was calculated from discrete distributions of timing of eventsconstructed by binning data from day 1 to day 31 into ten day categories starting withdays 1–3 for category 1, days 4–6 for category 2 and following through to days 28 to 31for category 10. Selected distributions are given in Fig. 5.

231L. Giménez / Journal of Experimental Marine Biology and Ecology 400 (2011) 227–235

available on the duration of embryonic development; the expectedduration of embryonic development at 11° is 66 days. In principle,model results are therefore valid for species for which the initiation ofkey life history events (e.g. maturation, embryogenesis) is timed bytemperature.

The starting conditions of the model consisted of a population ofindividuals initiating embryonic development along an arbitraryperiod of 31 days with the first group of individuals starting on theday when the estimated temperature reaches 11°. The population ofindividuals initiating the embryonic development was characterisedby a normal distribution of average=15 days and standard devia-tion=5 days. These parameter values ensured that the peak ofinitiation of embryonic development was in the centre of the 31dperiod and that there was enough spread over that period. Previousmodel trials showed that small values of standard deviation result in avery low proportion of individuals starting the embryogenesis early orlate. This led consistently to trivially small spreads in the timing ofevents (e.g. metamorphosis).

The model calculations followed the same method described byDawirs (1985), which were used to predict the timing of metamor-phosis of C. maenas and by Anger (1983) for the spider crab Hyasaraneus in the German Bight. Predictions of the timing of hatching,moulting and metamorphosis were done by computing fraction, f(T(t)), of total duration of development completed by an individual ateach day, t, characterised by a temperature T and accumulating thedaily fractions until they reached a value of 1. For instance, if for thefirst day T=15 °C and the predicted duration of development was5 days, then f(day 1)=1/5. The fraction corresponding to the secondday was computed, and both were used to calculate F=Σf. Thisprocedure was repeated until F=1; the number of steps (=days)required to reach F=1 gave the duration of development. Once F=1the procedure was re-started using the equations of the nextdevelopmental stage.

2.2.2. Average timing of eventsModel results showed effects of temperature on the average

timing and spread of events of the life cycle. If the day of initiation ofthe embryonic development in the warm year is set as the day 1(middle May in Fig. 3), then the initiation of embryogenesis in the“cold”, “mild”, and “mild with cold winter” years were respectively inthe days 22, 17 and 22 (early to middle June: Fig. 3). In consequencean increase in 1 °C to 1.5 °C resulted in a shift of 2–3 weeks betweenthe warm and the mild or cold years. The hatching period started, inall years, 53–55 days after the start of embryonic development (July–August in warm year, August in mild and cold years: Fig. 3), whentemperatures were between 11 and 14 °C. Differences in the timing ofhatchingweremainly affected by the timing of initiation of embryonicdevelopment, with a small contribution of the effect of temperatureon embryogenesis. Metamorphosis to the juvenile stage started96 days after the initiation of embryonic development in the warmyear (August–September); in the cold year it started after 103 days(day 125, September), while in both mild years metamorphosisoccurred after100 days (on days 117 and 122 for cold winter,September: Fig. 3). Again, the timing of metamorphosis wasdetermined mainly by the timing of the initiation of embryogenesiswith a small contribution of the effect of temperature on embryonicand larval development: differences among years in embryonic andlarval developmental rates led only to a shift of 4–7 days. Therefore, ifthe timing of initiation of embryogenesis was set by temperature,global warming should operate on the average timing of eventsthrough a forward shift in the timing of initiation of embryogenesis.

2.2.3. Spread of eventsSeasonality reduced the spread of events to 23–27 days as

compared to a situation with constant temperature where eventsshould spread over 31 days; this meant a reduction in variance from

2.67d2 for the timing of initiation of embryogenesis to 1.93–2.62d2 forthe timing of hatching, moulting and metamorphosis, depending onthe scenario and developmental stage (Fig. 4). The main change in thetemporal distribution of events consisted of a reduction in the lengthof the right tail (Fig. 5). This occurred because individuals developinglater in the season did so under higher temperatures and showedhigher developmental rates than individuals starting earlier. Highertemperature led to a reduction in the variance and spread of the

0.2

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port

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Hatching Megalopa Metamorphosis

1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10

Day categories (each category = 3 days except category 10 = 4 days)

232 L. Giménez / Journal of Experimental Marine Biology and Ecology 400 (2011) 227–235

233L. Giménez / Journal of Experimental Marine Biology and Ecology 400 (2011) 227–235

temporal distribution of events. In a cold year, the metamorphosistook place for 27 days; by contrast in the mild and warm years thisoccurred along a period of 24 and 21 days respectively and resulted ina smaller variance (Fig. 4). Differences in 1.5 °C of average temper-ature between the cold andwarm year led to a reduction in the spreadby 6 days. In a cold year the variances in the distribution of moultingto the zoeal stages was reduced progressively, but the variance atmetamorphosis increased (Figs. 4 and 5). This occurred because, inthis scenario, some of the development of Zoea IV and megalopastages took place after the summer peak of temperature was reached(Fig. 3); after that period the duration of development increased astemperature decreased through time. In addition, in the cold year, thedistribution of metamorphosis showed two maxima (Fig. 5). In themild and the warm years the variance in the time of hatching to Zoea Iand moulting to Zoea II was lower than that of moulting to megalopaand metamorphosis (Figs. 4 and 5); distributions of time ofmetamorphosis showed only one maximum. In these scenariosmost or all larval development took place before the maximumtemperature was reached (Fig. 3). In the mild year with cold winter,the variances of the timing of hatching and moulting to zoeal stageswere lower than those of the megalopa. In this scenario, thedevelopment of the megalopa took place after the maximum seasonaltemperature was reached.

3. Discussion

My results emphasise the potential mechanisms underlyingchanges in the spread or variance of phenological events ofinvertebrates. Spread in the temporal distribution of abundance oforganisms may be related to temperature but also to other factorssuch as variations in food availability, selective predation, or transportprocesses. Spread may change as the consequence of an adaptiveresponse to an environmental signal or as a consequence of non-adaptive mechanisms. Here, I evaluated two non-adaptive mecha-nisms by which temperature may affect the spread (=variance) inthe timing of life history events. The spread can change as aconsequence of: (1) the non-linear relationship between temperatureand developmental rates in a population of organisms distributedalong a spatial gradient of temperature; and (2) the averagetemperature, steepness and location of summer maxima characteringseasonal patterns of temperature. In nature, manymarine populationsextend over wide areas characterised by a thermal gradient, and at thesame time, individuals start gonad maturation or embryogenesis overan extended time period. These spatial and temporal differencesgenerate a spread in the timing of events that leads to the varianceeffect. In real populations, the timing of events should result from thecombined effect of both processes described here. Therefore, ifconditions modelled here are held, increases in temperature shouldresult in the synergistic effects on the spread of life history events.

Predictions may not hold if species show compensatory responsesto temperature arising from selection of particular genotypes orthrough phenotypic plasticity. Full compensation should result in lackof response of organisms to temperature both in terms of variance andin the average timing of events. Although these responses may bepresent, long-term time series do show forward shifts in the timing ofpulses associated with recent temperature increase (e.g. marineorganisms: Greve et al., 2004; Edwards and Richardson, 2004) thatmay be based on developmental responses to temperature. Therefore,adaptive responses, if present, may not be strong enough to fullycompensate the effects of increasing temperature on developmental

Fig. 5. Predicted distribution of the timing of hatching of Zoea I, moulting tomegalopa andmof seasonal variations in temperature. The distribution of the timing of initiation of embryogewere constructed by binning the timing of events from day 1 to day 31 into ten day categoriedays 28 to 31 for category 10.

rates; however they may reduce these effects. According to Parmesan(2006) there have been some evolutionary changes in response towarmer conditions, but there is little evidence that they will mitigatenegative effects. A second possibility is that individuals acclimate toincreasing temperatures experienced during early development sothat the effects of temperature on late development are minimal. Thisshould reduce the effects of temperature on developmental rates;however, the observed curves should already reflect any plasticresponse occurring during the experiment.

A third possibility is that species extend the periods of breeding oregg production, thereby increasing the spread of events. This is notunlikely at least for some species: for instance, the larval period of theshore crab C. maenas is restricted to spring–summer in Scotland(Crothers, 1967), it extends mainly between January and Septemberin the southern UK coast (Crothers, 1967), and between February toJuly in Portugal (Queiroga, 1996). These ranges might be determinedby temperatures extending beyond the upper and lower thermallimits of tolerance at the southern and northern distribution of thespecies; these effects were not considered in the models above. Apotential consequence of temperature increase is therefore anincrease in the spread of the breeding season at higher latitudes,and a decrease in the North and Irish Seas as well as on the Portuguesecoast, again assuming that local adaptation cannot fully compensatefor changes in temperature increase. It is therefore at the middle andat the southern end of the distribution where the variance effect mayinfluence the level of mismatch. In these areas, if higher temperaturesthan those considered here surpass some physiological optimum(Pörtner, 2001; Weiss et al., 2009), development during summer maybe compromised.

Provided that the assumptions are met, the predictions are thatincreases in temperature lead to a reduction in variance, according tothe species-specific temperature-development function. The rele-vance of this change may depend on the relationships between pulsesof a species and its prey, predators or competitors. Mismatch may beavoided if predators switch diet (e.g. see Ito et al., 2009); otherwise,mismatch may occur if relationships between developmental ratesand temperature of predators and preys are different. In the absenceof seasonality, global warming should result in a decrease in thevariance of abundance peaks as a consequence of the non-linearrelationship between temperature and developmental rates. If peaksof species shift with respect to each other, the reduction in varianceleads to a further increase of mismatch; this effect is added to the oneproduced by changes in the average timing of life history events. Ifpeaks of species do not shift with respect to each other, then varianceeffects still lead to mismatch. This is shown in Fig. 6 depicting themismatch between predators and preys at different temperatures butwithout shifts in the abundance pulses as a consequence oftemperature increase. Adding a time lag, τ, between population ofpreys and predators responding to temperature through the UTDleads to:

D = d × eE = T × kð Þ + τ and g Dð Þ = −ln−1 D + τð Þ=dð Þ × E=kð Þ−MT

h �i22 × S2T

ð5Þ

Under this condition the area of overlap between the distributionsof both species is reduced at higher temperatures, indicating anincrease in the degree of mismatch (Fig. 6b).

etamorphosis to the first juvenile state of Carcinus maenas under four different scenariosnesis is shown in the first panel and was defined frommodel parameters. Distributionss starting with days 1–3 for category 1, days 4–6 for category 2 and following through to

120a

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atio

n of

dev

elop

men

t

b

20°C 10°C

0.3

0.4

0.5

Pro

port

ion

of in

divi

dual

s

0.0

0.1

0.2

Time (days)

0 20 40 60

Fig. 6. Match/mismatch under different temperature scenarios (10 and 20 °C) for ahypothetical consumer–resource system. (a) Predicted duration of development; and(b) predicted abundance distributions. The duration of development and thedistribution were computed from Eq. (5) (see text) using the parameters given inFig. 1 for the Arrhenius equation with a time lag τ=6 days. The areas in grey show theoverlap between distributions, indicating the level of mismatch.

234 L. Giménez / Journal of Experimental Marine Biology and Ecology 400 (2011) 227–235

Under seasonal temperature conditions, global warming should alsoreduce the spread of the timing of life history events. Models includingseasonality showed that the key points in the spread of timing of eventswere: (1) the temperature, (2)whether development still occurred afterthe maximum summer temperature and (3) the steepness of thetemperature curve. In the scenario of “cold winter”, low temperaturesresulted in development extending beyond the maximum summertemperature and in a widespread timing of metamorphosis character-ised by two maxima. However, if temperature increases, most eventswould take place before the summer temperature maximum (e.g. the“warmyear” scenario) anda considerable reduction in the spread shouldoccur. These three factors can be also seen in the scenario representing amild year with a cold winter: this is characterised by a steep change inspring temperature that leads to a reduction in spread of events, asshown for the timing of hatching and moulting to early zoeal stages.However, low early temperaturesmay lead to some development takingplace after the summer temperature maximum (megalopa stage in themodel), and result in an increment in the spread of the timing of events.

In addition, the effect of global warming on physiological rates maylead to more complex responses than those evaluated here. Early stagesmay experience extremely lowor high temperatures, leading to increasesin mortality. For instance, predictions on the timing of events in theEuropean lobster under warming conditions suggest that larvae mayexperience high mortalities as a consequence of hatching occurring atextremely low spring temperatures (Schmalenbach and Franke, 2010).This is counterintuitive, but also logical: as stated by Schmalenbach andFranke (2010) such possibility may occur since embryonic developmentof lobster larvae, takingplace inwinter,maybe completed sooner under awarming scenario, resulting in larvae hatching under extremely low

temperatures. In addition there are some complex long-term effects thatremain to be explored. High temperatures experienced by larvae mayresult in reduced settlement success or juvenile survival mediated byreduced amount of nutritional resources or small size at metamorphosis(see Giménez, 2004, 2010 for discussion on these trait-mediated effects).These types of effects have been found inmanymarine invertebrates as aresponse to a diverse number of environmental factors: they may be theresult of environmentally induced phenotypic variation that is carriedover to advanced stages or that remain latent until they aremanifested atvulnerable stages (Pechenik et al., 1998; Qiu and Qian, 1999; Giménez,2006; Pechenik, 2006; Podolsky and Moran, 2006; Thiyagarajan, 2010).

In conclusion, increases in temperature should result in changes inthe spread in the distribution of life history events. Reductions maycontribute to trophic mismatches that may lead to the failure ofrecruitment in predator species. This “variance effect” of temperatureshould add up to the forward shifts expected from temperatureincrease, contributing to further change in marine ecosystems.

Acknowledgements

This paper benefited from fruitful afternoon discussions with K.Anger and G. Torres, around some mugs of coffee, at the MarineStation of Helgoland. I would like to acknowledge an invitation toCEFAS by Melanie Sapp and discussions about temperature data withD. Sivyer also at CEFAS. I would also like to thank funding from theResearch and Enterprise Partnership CCCR and the Climate ChangeConsortium of Wales C3W. [SS]

Appendix

Matlab code for calculations of variance of duration of develop-ment as the consequence of temperature increase.

This example is given for a cohort of larvae developing at anaverage temperature of 10° with standard deviation=1, using theArrhenius equation and the parameters derived by O'Connor et al.(2007) (see Figs. 1 and 2).

1) Definition of parameters:

NNclearNNu=exp(−22.47);NNE=0.64;NNk=0.0000862;NNz=E/kNNS=1;NNM=10;NNA=1/((2⁎3.141592)^0.5⁎S)NNC=2⁎S^2;

2) Defining the function through Eq. (3) and calculation of area underthe function within the range 1, 900.

NNF=@(x)A⁎exp(−(z./log(x/u)−M−273).^2./C);NNQ=quad(F,1,900);

3) Standardising the function so that the area under it equals 1:

NNG=@(x)A⁎exp(−(z./log(x/u)−M−273).^2./C)/Q;NNH=quad(G,1,900)

4) Calculating mean duration of development:

NNG=@(x)A.⁎x.⁎exp(−(z./log(x/u)−M−273).^2./C)/Q;NNJ=quad(G,1,900)J=43.7815

5) Calculating variance of duration of development

NNI=@(x)A.⁎x.⁎x.⁎exp(−(z./log(x/u)−M−273).^2./C)/Q;NNL=quad(I,1,900)

6) This procedure can be repeated for each average temperaturemaintaining the standard deviation constant.

235L. Giménez / Journal of Experimental Marine Biology and Ecology 400 (2011) 227–235

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