DEBBIES to compare life history strategies across ectotherms

Demographic models are used to explore how life history traits structure life history strategies across species. This study presents the DEBBIES dataset that contains estimates of eight life history traits (length at birth, puberty and maximum length, maximum reproduction rate, fraction energy allocated to respiration versus reproduction, von Bertalanffy growth rate, mortality rates) for 185 ectotherm species. The dataset can be used to parameterise dynamic energy budget integral projection models (DEB-IPMs) to calculate key demographic quantities like population growth rate and demographic resilience, but also link to conservation status or biogeographical characteristics. Our technical validation shows a satisfactory agreement between observed and predicted longevity, generation time, age at maturity across all species. Compared to existing datasets, DEBBIES accommodates (i) easy cross-taxonomical comparisons, (ii) many data-deficient species, and (iii) population forecasts to novel conditions because DEB-IPMs include a mechanistic description of the trade-off between growth and reproduction. This dataset has the potential for biologists to unlock general predictions on ectotherm population responses from only a few key life history traits.


Background & Summary
Matrix population models (MPMs) and integral projection models (IPMs) provide the basis for exploring how variation in the demographic rates of survival, growth and reproduction fuels variation across species in life history traits (like the timing, intensity, frequency and duration of key demographic processes, such as longevity, generation time or degree of iteroparity) and in combinations of life history traits that form life history strategies (including pace of life and reproductive strategy) [1][2][3] .Life history traits and strategies calculated from these structured population models predict not only key demographic properties such as population growth rate and demographic resilience, but also have important connections to other disciplines like biogeography, evolutionary biology and conservation biology [4][5][6] .
Important datasets exist that collate MPMs (COMPADRE 7 ; COMADRE 8 ) and IPMs (PADRINO 9 ) for plants and animals, and even algae, fungi, bacteria, and viruses.Recent efforts have furthermore linked the latter datasets in a centralised meta-database of trait data (MOSAIC 10 ) so they can be interrogated at the same time.While these datasets are valuable in improving both data access and data usability 11 and are used globally in networks like the Open Trait Network (https://opentraits.org/), the parameterisation of the structured population models that are within these datasets requires long-term individual-level data that are scored from birth till death.Yet, there are many organisms for which such data are not available, for example, because it is difficult to track individuals over their lifetime (e.g.micro-organisms, small (soil-dwelling) animals).Because such MPM and IPM datasets can form part of pipelines to develop, for example, essential biodiversity variables to observe and report global biodiversity change 12 , it is pertinent to avoid any unwilling species bias.We thus critically need to include datasets of structured population models that can also accommodate more data-deficient species to have a taxonomically most balanced representation as possible.
One type of structured population model that does not require many long-term individual-level life history data is the dynamic energy budget (DEB) IPM 13 .To parameterise a DEB-IPM for a species, one requires eight life history traits to be estimated (traits include length measures, rates of growth, reproduction and mortality [Fig.1]) to be able to predict survival, growth and reproduction for a simple life cycle (more complex life cycles would require more parameters) 13 .These traits are assumed to be fixed for a life cycle (Fig. 1); that is, length at birth and at puberty represent specific moments in the life cycle and are timeinvariant; maximum length and maximum reproduction rate, in turn, are maximum values that are achieved under the most favourable circumstances a life cycle is in, and thus are also time-invariant.We assume that kappa remains constant over a life cycle because empirical evidence suggests so 14 .To estimate the von Bertalanffy growth rate and mortality parameters (Fig. 1) one does require repeated observations on individual growth or survival of individuals within a population.So far, only two small datasets of DEB-IPM parameters have been generated, comprising estimates of the eight life history traits for 13 species of marine megafauna 3 and 13 microorganisms 15 .Here, we introduce a much larger and taxonomically diverse dataset that we refer to as DEBBIES in which we compiled estimates of the eight life history traits for 185 ectotherm species.Ectotherms are taxonomically diverse and their growth and reproduction can be captured in simple energy budget models, like the one incorporated into the DEB-IPM.Also, more than 99% of species are ectotherms 16 ; consequently, no biological prediction can be considered universal if it is does not include these organisms.We find in our technical validation that our model outputs exhibit good agreement with observations on key life history traits (age at maturity, longevity, generation time).The dataset can be used for a variety of different applications of eco-evolutionary studies (e.g. 15,17) (Fig. 1).Because DEB-IPMs (unlike MPMs and other IPMs) across species are built from the same life history traits, they can readily be used for comparative studies of life histories and population dynamics across a wide range of species, for which DEBBIES provides all the necessary input data.Finally, because DEB-IPMs include a mechanistic description of the trade-off between growth and reproduction, they are particularly suited to create population forecasts to novel conditions (like those created by climate change) 13 for the species currently listed in the dataset.

Methods
Because the main purpose of DEBBIES is to parameterise DEB-IPMs for further analysis (Fig. 1), we first give a brief description of what a DEB-IPM is, and how a species' eight life history traits feed into a DEB-IPM, before explaining how we collated the life history data presented in DEBBIES.

Brief description of a DEB-IPM
The three demographic rates of survival, growth, reproduction and the relationship between parent and offspring size are captured in the DEB-IPM by four fundamental functions, which describe the dynamics of a population comprising cohorts of females of different sizes 3,13 : (1) the survival function, (()), describing the probability of surviving from time t to time t+1; (2) the growth function, ( ′ , ()), describing the probability that an individual of body length L at time t grows to length L' at t + 1, conditional on survival; (3) the reproduction function, (()), giving the number of offspring produced between time t and t + 1 by an individual of length L at time t; and (4) the parent-offspring function, ( ′ , ()), the latter which describes the association between the body length of the parent L and offspring length L' (i.e. to what extent does offspring size depend on parental size).Denoting the number of females at time t by (, ) means that the dynamics of the body length number distribution from time t to t+1 can be written as: ( ′ ,  + 1) = ∫ [( ′ , ())(()) + ( ′ , ())(())](, ) Ω (1)    where the closed interval Ω denotes the length domain.
The survival function (()) in equation ( 1) is the probability that an individual of length L survives from time t to t + 1: where E(Y) can range from zero (empty gut) to one (full gut).Individuals die from starvation at a body length at which maintenance requirements exceed the total amount of assimilated energy, which occurs when  >   • ()/ and hence, then, (()) = 0 (e.g., an individual of size L m will die of starvation if E(Y) < ).Juveniles and adults often have different mortality rates, and, thus, juveniles (  ≤  <   ) that do not die of starvation (i.e. ≤   • ()/) have a mortality rate of  j , and adults (  ≤  ≤   ) that do not die of starvation (i.e. ≤   • ()/) have a mortality rate of  a .
The demographic functions that describe growth and reproduction in the DEB-IPM are derived from the Kooijman-Metz model 3,13,18 .This is is a simple version of the standard model of Kooijman's DEB theory, but one that still fulfils the criteria for general explanatory models for the energetics of individuals 19 .The Kooijman-Metz model assumes that individual organisms are isomorphic (which means that body surface area and volume are proportional to squared and cubed length, respectively).The rate at which an individual ingests food, I, is assumed to be proportional to the maximum ingestion rate I max , the current feeding level Y and body surface area, and hence to the squared length of an organism:  =    2 .
Ingested food is assimilated with a constant efficiency .A constant fraction  of assimilated energy is allocated to respiration; this respiration energy equals    2 and is used to first cover maintenance costs, which are proportional to body volume following  3 ( is the proportionality constant relating maintenance energy requirements to cubed length), while the remainder is allocated to somatic growth.The remaining fraction 1 - of assimilated energy, the reproduction energy, is allocated to reproduction in case of adults and to the development of reproductive organs in case of juveniles, and equals (1 − )   2 .This means that, if an individual survives from time t to time t+1, it grows from length L to length L' following a von Bertalanffy growth curve,   = ̇(  •  − ), where ̇ is the von Bertalanffy growth rate (here assumed to be constant across feeding levels, but can be adjusted if necessary 13 ) and   =   / is the maximum length under conditions of unlimited resource.Both  and I max are assumed to be constant across experienced feeding levels, and therefore L m is also assumed constant.
Implicitly underlying the population-level model of equation (1), like in any IPM, is a stochastic, individual-based model, in which individuals follow Markovian growth trajectories that depend on an individual's current state 20 .This individual variability is in standard IPMs modelled in the functions describing growth, ( ′ , ()), and the parent-offspring association, ( ′ , ()) (see below), using a probability density distribution, typically Gaussian 21 .In the DEB-IPM, this individual variability arises from how individuals experience the environment; specifically, the experienced feeding level Y follows a Gaussian distribution with mean E(Y) and standard deviation (Y).It means that individuals within a cohort of length L do not necessarily experience the same feeding level due to demographic stochasticity (e.g.individuals, independently of each other, have good or bad luck in their feeding experience).Taken together, this means that the function ( ′ , ()) is the probability that an individual of body length L at time t grows to length L' at t + 1, conditional on survival, and, following common practice [20][21][22] , follows a Gaussian distribution: (3) with the growth realized by a cohort of individuals with length L(t) equalling and the variance in length at time t + 1 for a cohort of individuals of length L as where (Y) is the standard deviation of the expected feeding level.
If a surviving female is an adult, she also produces offspring.According to the Kooijman-Metz model 18 , reproduction, i.e. the number of offspring produced by an individual of length L between time t and t + 1, equals  •   •  2 /  2 .The parameter R m is the maximum reproduction rate of an individual of maximum length L m .Note that R m is proportional to (1 -) 18 , whereas L m is proportional to ;  thus controls the trade-off between energy allocation to reproduction versus growth.However, the role of  in the DEB-IPM is mostly implicit, as  is used as input parameter only in the starvation condition (see below), whereas R m and L m are measured directly from data.Like L m , R m is also proportional to I max ; since both  and I max are assumed to be constant across experienced feeding levels, R m is also assumed constant.The reproduction function (()) gives the number of offspring produced between time t and t + 1 by an individual of length L at time t: Individuals are mature when they reach puberty at body length L p and only surviving adults reproduce (equation ( 1)); thus, only individuals within a cohort of length   ≤  ≤   / reproduce.
The probability density function ( ′ , ()) gives the probability that the offspring of an individual of body length L are of length L' at time t + 1, and hence describes the association between parent and offspring character values: where    (()) is the expected size of offspring produced by a cohort of individuals with length L(t), and    2 (()) the associated variance.For simplicity, we set    (()) constant and assumed its associated variance,    2 (()), to be very small.Finally, note that the DEB-IPM assumes no effect of temperature on fundamental functions.Temperature effects on fundamental functions, however, can be approximated by varying experienced feeding level.Alternatively, one could resort to a more detailed and more parameter-rich DEB-IPM that links individuals' size-and temperature-dependent consumption and maintenance via somatic growth, reproduction, and size-dependent energy allocation to emergent population responses 23 , but this is not linked to DEBBIES.

Collection of life history trait data required to parameterise a DEB-IPM
Running a DEB-IPM for a species requires estimates for eight life history traits: the fraction respiration energy , length at birth L b , length at puberty L p , maximum length L m , juvenile mortality rate  j , adult mortality rate  a , von Bertalanffy growth rate   ̇ and maximum reproduction rate R m (Fig. 1).
For the elasmobranchs, we obtained von Bertalanffy growth rate values using the following search, in order of priority: (i) primary literature, using female growth curve, measured empirically using data from animals, (ii) from Froese 24 supplementary material, or (iii) using the equation ̇ = − log(1 − 0.95)   ⁄ , where t max is a species' longevity (years), sourced from Fishbase 25 .If multiple values were available, only those in the highest priority group were kept.If there were still multiple values, their median value was used.Any values listed as 'Questionable' on Fishbase 25 were not used.Body lengths for 152 species were sourced from Sharks of the World 26 or Rays of the World 27 .Total lengths were converted to fork lengths using scalar values on Fishbase 26 .Length at birth was sourced from the IUCN red list 28 for five species (M.ambigua, M. birostris, A. parmifera, D. trachyderma and R. australiae).Length at puberty for Maculabatis ambigua was sourced from primary literature 29 .We calculated maximum reproduction rate R m as   = ( × )  ⁄ , where c is the mean clutch size, n is the mean number of litters produced per year, and i is the remigration interval, which is the minimal number of years between reproductive seasons.
Minimum and maximum pup numbers were sourced from Sharks of the World 26 , Rays of the World 27 , IUCN red list 28 , Fishbase 25 , or Barrowclift et al. 30 .The sources for maximum and minimum pup numbers were not prioritised, and therefore some maximums and minimums were obtained from different sources.Breeding intervals were found in the same way, except for C. granulosus, S. californica, F. macki and R. porosus, which data we sourced from primary literature [31][32][33][34] .If the number of pups or breeding interval were not found, we took those data from the next closest species within the same genus.Mode of reproduction was sourced from the Sharks of the World 26 and Rays of the World 27 .Adult mortality rate was calculated 35 by taking the inverse of the mean of longevity and age at maturity (a) (  = 1 [(  + )/2] ⁄ .Juvenile mortality rate 36 was calculated as   = −log (  1  ), where survival to maturity 37 ,   , equals   =  −  (  −) .
Values for all other species were taken directly from the primary literature.Finally, for most species, we were able to take values for  from the Add My Pet database 38 .If no values for  were available for a species, we assumed  = 0.8 as is common practice 39 .The parameter kappa is explicit in the starvation condition 13 , which states that individuals of length L die of starvation when they can no longer cover their maintenance costs, which occurs when  =   () =  starvation .At any feeding level, the ultimate length that individuals can grow to equals  ∞ =   ().Substituting  ∞ into the starvation condition returns:  starvation =  ∞ /.In our case,  = 0.8 so that  starvation = 1.25 ∞ .This means that at any constant feeding level, individuals will never reach the length at which they starve because that is 25% larger than the ultimate length they can achieve at that feeding level.
Only when feeding level varies over time, like in a stochastic time series, can  affect population responses if, for example, individuals that were large in a good feeding environment suddenly find themselves in a poor feeding environment.

Data Records
The DEBBIES dataset (Version 5) includes eight life history trait records for 185 ectotherm species that were sourced from the scientific literature and are stored in one csv file with accompanying metadata text file on FigShare 40 .Each row in the file represents one species record.For most species, we sourced life history traits from different studies as rarely only one single study provided estimates for all traits for one species.Each data record therefore describes a species' general life history and is not specific to a particular population.On the one hand, this approach is in line with the assumption of DEB theory that individual-level differences are sufficiently small to take mean values to represent species-specific parameters 41 .On the other hand, recent work on different populations of Trinidadian guppies cautions against combining life history data from different studies, because systematic bias during parameter estimation can generate substantial variation, and similar patterns of growth and reproduction can be produced with very different parameter sets 42 .In contrast, focusing only on parameter sets specific to a particular population of Trinidadian guppies returns life history variation predictions that are in line with observations 42 .Users should thus carefully interpret their results, especially when predictions are not in line with expectations.One could, for example, explore the robustness of a DEB-IPM to uncertainty or perturbation of the input data to assess how much the data can be changed before any desired property of the model, like predicted population growth rate, is lost 43,44 .The columns of the data file are described in Table 1.

Technical Validation
Two model performance tests on a subset of DEBBIES that have validated the reliability of the dataset are presented elsewhere 3,13 .Here, we conducted a similar model performance test on the full dataset by exploring the distribution of predicted population growth rates, and by comparing predicted and observed generation time (years), age at maturity (years), and longevity (the sum of age at maturity and mature life expectancy; years) for three different feeding levels.Because not all species were represented at all feeding levels (less than half of all species in the dataset can persist at low feeding levels), any effect of feeding level cannot be estimated independently.Therefore, we ran the model performance tests separately for each feeding level.Predicted values of the latter quantities are calculated as explained below in the usage notes (see also Fig. 1: derived life history traits).For ray-finned fish, observed values were obtained from Fishbase 25 and, if unavailable, we obtained generation times from the IUCN Red List 28 and age at maturity values from the Animal Diversity Web 45 .For the cartilaginous fish, we obtained generation times (for all species) and longevities (18 species) from the IUCN Red List 28 , and longevity and age at maturity values from the Sharks of the World book 26 , the Rays of the World book 27 or from Barrowclift et al. 30 .For one cartilaginous fish, we obtained the longevity value directly from the scientific literature (silvertip shark Carcharhinus albimarginatus) 47 and for the Galapagos shark Carcharhinus galapagensis from Fishbase 25 .For all other species, we first consulted the Animal Diversity Web 45 , then the IUCN Red List 28 for observations on generation time and AnAge 47 for observations on age at maturity and/or longevity if these were unavailable in the Animal Diversity Web 45 .If, for a particular quantity, a value range was given, we took the median; if a series of observations was given, we took the mean.
Our validation shows that the predicted population growth rate  (calculated as the dominant eigenvalue of the matrix approximation of equation ( 1), see also Table 3) most species are slightly higher than  = 1 (denoting population increase) at high experienced feeding level (E(Y) = 0.9), centred around  = 1 (denoting stability) at an intermediate feeding level (E(Y) = 0.7), and mostly lower than  = 1 (denoting population decline) at low feeding level (E(Y) = 0.5) (Fig. 2a).This is in line with the general expectation in ecology that populations increase under favourable conditions but decline when conditions deteriorate.Predicted generation times were higher than observed generation times at the lower experienced feeding levels but not significantly different from observed generation times at the highest experienced feeding level (Table 2; Fig. 2b).Using the root mean square error (RMSE) (Table 2), we can quantify the overall deviation.Specifically, we estimate that 95% of the observed generation time values fall within a range that extends 19 -23 years from the predicted generation times across feeding levels (assuming the residuals follow a Normal distribution, 95% of observed values fall within 2  RMSE from the predicted values, and we took the lowest and highest RMSE value from across the range of feeding levels to estimate this 95% confidence interval).The average RMSE value for generation time across the three feeding levels equals 10 years (Table 2).Given the fact that the highest observed generation time is 53 years (Carcharodon carcharias), the average RMSE of 10 years indicates that the model predictions have an average error rate of 19% (10  53 = 0.19).We surmise that one reason for this relatively large error rate is that predicted generation time is, following convention [1], calculated as  = log( 0 ) /log(), where R 0 is the net reproductive rate and  the population growth rate.Calculated this way, generation time represents the time it takes a population to increase by a factor R 0 , which might not always be a good approximation of how generation time is measured in the field.
Predicted longevity was lower than observed longevity at the lower experienced feeding levels but not significantly different from observed values at the highest experienced feeding level (Table 2; Fig. 2c).Using the root mean square error (RMSE) (Table 2), we estimate that 95% of the observed longevity values fall within a range that extends 12 -43 years from the predicted longevities across feeding levels.The average RMSE value for longevity across the three feeding levels equals 13 years (Table 2).Given the fact that the highest observed longevity is 100 years (Squalus suckleyi), the average RMSE of 13 years indicates that the model predictions have an average error rate of 13% (13  100 = 0.13).
Finally, predicted age at maturity was higher than observed age at maturity and the best fit with observed values was at the lowest experienced feeding level (Table 2; Fig. 2d).We are unsure why this is the case, but it most likely indicates a mismatch between the functional biology of maturation, and the assumptions underlying the calculations of age at maturity 48 .Using the root mean square error (RMSE) (Table 2), we estimate that 95% of the observed age at maturity values fall within a range that extends 11 -13 years from the predicted ages at maturity across feeding levels.The average RMSE value for longevity across the three feeding levels equals 6 years (Table 2).Given the fact that the highest observed longevity is 39 years (Chelonia mydas), the average RMSE of 13 years indicates that the model predictions have an average error rate of 15% (6  39 = 0.15).
In summary, the model predicts generation times and longevity values accurately at high experienced feeding levels, but predicted generation times showed the highest average error rate.Predicted age at maturity values were significantly higher than observed values.However, their error rate was overall lower than the error rate of predicted generation times and only slightly higher than the error rate of predicted longevity values.Depending on the specific question a user is interested in, these error rates can be acceptable or not.What gives us confidence in the technical quality of the dataset and its potential applications, is the fact that predicted population growth rates are within the range that we would expect biologically (Fig. 1a).

Usage Notes
This data descriptor was peer reviewed in 2023 based on version 5 of the DEBBIES dataset 40 .All versions are available online 40 as described as in Table 1.Version 1 contains data on 47 species; some of these entries were incorrect and removed in version 2. In version 3, 157 species of elasmobranchs were added, with three more elasmobranchs added in version 4. In the current version 5, we changed the symbols in the dataset that denote  and   ̇ to match the symbols used in this data descriptor.We anticipate future versions to include more species.
The main purpose of the DEBBIES dataset is to be able to parameterise a DEB-IPM for each of the species in the dataset, but the dataset on its own can also feed into other databases (Fig. 1).Once parameterised, running a DEB-IPM requires setting a value for the experienced feeding level E(Y), which value can range from zero (empty gut) to one (full gut).We find that for many species, E(Y) should be higher than about 0.7 for the model to run, although it can run for some species at much lower values, down to 0.4 13 .A feeding level of around 0.7 can be considered to represent a gut that is 'just filled', on a scale between empty and bursting 49 .In that sense, we should perhaps not be surprised DEB-IPMs require a minimum experienced feeding level of around 0.7.
Many different quantities can be calculated from a parameterised DEB-IPM.For example, like current MPM and IPM datasets [7][8][9] , DEB-IPMs can be used to calculate key demographic quantities such as population growth rate and demographic resilience, but also nine key derived life history traits that inform on a species' turnover rate, longevity, growth and reproduction (Fig. 1) (Table 3) 1 .Additionally, because all DEB-IPMs have the same structure, one can run perturbation analyses to estimate for each species the proportional change in the population growth rate for a proportional change in each of the input life history traits (, L b , L p , L m ,  j ,  a ,   ̇, R m ).These results can be used to pinpoint those parts of an organism's life history that should be the focus of monitoring or research to inform conservation management, or those life history traits that contribute most to fitness.We provide MatLab code to calculate the aforementioned quantities (see Code Availability below).Some users, however, might be more interested in exploring the dynamics of single species, rather than performing cross-taxonomical analyses.For those, we have included code to explore how the aforementioned quantities vary with experienced feeding level E(Y) for a particular species (see Code Availability below).
The nine derived life history traits 1 (Fig. 1, Table 3) can be used for more in-depth cross-taxonomical analyses (Fig. 1).For example, statistical analyses (e.g., a phylogenetically corrected principal component analysis 50 can be used to explore how life history variation can be structured and summarised into a few life history strategies 51 .Previous studies using MPM databases have revealed that plant and animal life history variation is predominantly structured along a fast-slow life history speed axis (rapid growth, high reproduction and short lifespan versus slow growth, low reproduction but long lifespan) and a reproductive strategy axis (concentrated versus more dispersed reproduction events across the adult lifespan) [1][2] .An interesting exercise would be to see if the same structuring holds when individual growth and reproduction rates are described mechanistically using an energy budget model (like in DEB-IPMs) instead of being estimated from observational data (like in MPMs).What is more, because a DEB-IPM is run for a specific feeding level set by the user, one could also investigate if the same structuring applies across a range of feeding levels (but note that our validation only covers feeding levels between 0.5-0.9).Finally, if species can be ranked along one or two life history strategy axes, their position along these axes can be linked to quantities from other disciplines (Fig. 1).This opens op possibilities for users to explore the potential for life history strategies to, for example, predict the likelihood of extinction or invasion (e.g. 4 ) investigate to what extent such strategies map onto phylogenetic trees (traitgrams) to answer questions about their evolution (e.g. 6 ).
Finally, users should be aware that, for the species currently included in DEBBIES, the projection interval between time t and time t + 1 is set at 1 year; all rates are therefore expressed per year and all durations are expressed in years.Likewise, all length measurements in DEBBIES are currently expressed in centimetres.Future versions, however, could include species which demographic rates are better projected over shorter time intervals and which lengths are better expressed in millimetres or even micrometres (e.g., microorganisms 6 ).  3) that can in turn be summarised into life history strategies 1 .The resulting 'fast-slow continuum and reproductive strategy framework' can be linked to quantities from other disciplines 4 .2. Technical validation that fitted linear regression models without an intercept (y ~ x) on observed (x) and predicted (y) values of generation time (G), longevity (L) and age at maturity (A) for three experienced feeding levels E(Y) = 0.5, E(Y) = 0.7, and E(Y) = 0.9.The 95% confidence intervals (CIs) of the regression coefficient are approximated as the regression coefficient  twice its standard error.If a 95% CI overlaps with 1, predicted values do not significantly differ from observed values.Also given is the root mean square error (RMSE) and the coefficient of determination (R 2 ) of each model.See also Fig. 2 40 .To calculate life history traits, one needs to discretise the IPM (equation ( 1)) by dividing the length domain Ω into very small-width discrete bins (we chose 200 bins), resulting in a matrix A of size p  q, where p = q = 200, and which dominant eigenvalue equals λ, the population growth rate.Mean lifetime reproductive success R 0 is the dominant eigenvalue of the matrix  = ( − ) −1 , where I is the identity matrix and V = DR, with D as the parent-offspring association, R the reproduction, G the growth and S the survival matrix 52 ; this gives generation time 52 T = log(R 0 )/log(λ).The mean life expectancy, η e , is calculated as η e = 1 T N, where 1 is a vector of ones of length m and N is the fundamental matrix  = ( − ) −1 .The longevity of an individual of length L is η L , which means we can calculate age at sexual maturity   =    and mature life expectancy   =    so that   =   +

48
. l x is the probability of surviving to age at least x, and m x is the average fertility of age class x (cf. 53). ̅ is the mean of G,  ̅ is the mean of V, and i and j are the row and column entries of the matrix, respectively.The vital rates included in progressive growth γ, retrogressive growth ρ, and sexual reproduction φ, were averaged across the columns j (the length bins), weighted by the relative contributions of each stage at stationary equilibrium.For example, to calculate mean sexual reproduction φ, we summed the values in the columns j of the V matrix and multiplied each φ ij by the corresponding jth element w j of the stable stage distribution w, calculated as the right eigenvector of A. Finally, the degree of iteroparity  = √  /

Figure 1 .
Figure 1.Workflow of parameterising a DEB-IPM and example applications, including what databases DEBBIES can feed into (Essential Biodiversity Variables 12 ; MOSAIC 10 ).DEBBIES currently contains 185 ectotherms of 18 different orders.Eight life history trait values are required to parameterise a DEB-IPM (top-right box).Once parameterised, it can be used to calculate a further nine derived life history traits (Table3) that can in turn be summarised into life history strategies 1 .The resulting 'fast-slow continuum and reproductive strategy framework' can be linked to quantities from other disciplines 4 .

Figure 2 .
Figure 2. Technical validation.Shown are for three levels of experienced feeding level (blue: E(Y) = 0.9; red: E(Y) = 0.7; yellow: E(Y) = 0.5) the frequency distributions of the population growth rate  (a), observed versus predicted generation time (years) (b); observed versus predicted longevity (years) (c); and observed versus predicted age at maturity (years) (d).The black lines in (B-D) denote the x = y line of equal values.

Table 1 .
Description of the columns in the data records file; each row in the file is a species.

Table 3 .
Nine key derived life history traits that inform on a species' turnover rate, longevity, growth and reproduction, for which we provide MatLab code to calculate them (see Code Availability) ̅  , with   =    T = (1 2 ••• ) 48 .Number of days from the mean age at maturity (L α ) until the mean life expectancy (η e ) of an individual in the population.