DEBBIES Dataset to study Life Histories across Ectotherms

Abstract

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 (COMPADRE⁷ COMADRE⁸) and IPMs (PADRINO⁹) 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 (MOSAIC¹⁰) so they can be interrogated at the same time. While these datasets are valuable in improving both data access and data usability¹¹ 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 change¹², 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) IPM¹³. 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 time-invariant; 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 so¹⁴. 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 megafauna³ and 13 microorganisms⁶. 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 ectotherms¹⁵ 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.^6,16) (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.

Fig. 1

Workflow of parameterising a DEB-IPM and example applications, including what databases DEBBIES can feed into (Essential Biodiversity Variables¹² MOSAIC¹⁰). 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 (Table 1) that can in turn be summarised into life history strategies¹. The resulting ‘fast–slow continuum and reproductive strategy framework’ can be linked to quantities from other disciplines⁴.

Table 1 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)³⁹.

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. Please note that this information is already presented elsewhere^3,13, but we include it here for convenience. Lastly, we explain 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, S(L(t)), describing the probability of surviving from time t to time t + 1; (2) the growth function, G(L′, L(t)), 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, R(L(t)), 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, D(L′,L(t)), 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 N(L, t) means that the dynamics of the body length number distribution from time t to t + 1 can be written as:

$$N\left(L{\prime} ,t+1\right)={\int }_{\Omega }\left[D\left(L{\prime} ,L\left(t\right)\right)R\left(L\left(t\right)\right)+G\left(L{\prime} ,L\left(t\right)\right)S\left(L\left(t\right)\right)\right]N\left(L,t\right)dL$$

(1)

where the closed interval Ω denotes the length domain.

The survival function S(L(t)) in Eq. (1) is the probability that an individual of length L survives from time t to t + 1:

$$S\left(L\left(t\right)\right)=\left\{\begin{array}{cc}{e}^{-{\mu }_{{\rm{j}}}} & {\rm{for}}\;{L}_{b}\le L < {L}_{p}\& L\le {L}_{m}E\left(Y\right)/\kappa ,\\ {e}^{-{\mu }_{{\rm{a}}}} & {\rm{for}}\;{L}_{p}\le L\le {L}_{m}\& L\le {L}_{m}E\left(Y\right)/\kappa ,\\ 0 & {\rm{otherwise}}\end{array}\right.$$

(2)

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 $L > {L}_{m}\cdot E\left(Y\right)/\kappa$ and hence, then, $S\left(L\left(t\right)\right)=0$ (e.g., an individual of size L_m will die of starvation if E(Y) <κ). Juveniles and adults often have different mortality rates, and, thus, juveniles (${L}_{b}\le L < {L}_{p}$) that do not die of starvation (i.e. $L\le {L}_{m}\cdot E\left(Y\right)/\kappa$) have a mortality rate of μ_j, and adults (${L}_{p}\le L\le {L}_{m}$) that do not die of starvation (i.e. $L\le {L}_{m}\cdot E\left(Y\right)/\kappa$) have a mortality rate of μ_a.

The demographic functions that describe growth and reproduction in the DEB-IPM are derived from the Kooijman-Metz model^3,13,17. This 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 individuals¹⁸. 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: $I={I}_{max}Y{L}^{2}$. Ingested food is assimilated with a constant efficiency ε. A constant fraction κ of assimilated energy is allocated to respiration; this respiration energy equals $\kappa \varepsilon {I}_{max}Y{L}^{2}$ and is used to first cover maintenance costs, which are proportional to body volume following ξL³ (ξ is the proportionality constant relating maintenance energy requirements to cubed length), while the remainder is allocated to somatic growth. The remaining fraction 1 – κ 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 $\left(1-\kappa \right)\varepsilon {I}_{max}Y{L}^{2}$. 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, $\frac{dL}{dt}={\mathop{r}\limits^{.}}_{B}({L}_{m}\cdot Y-L)$, where ${\mathop{r}\limits^{.}}_{B}$ is the von Bertalanffy growth rate (here assumed to be constant across feeding levels, but can be adjusted if necessary¹³) and ${L}_{m}=\kappa \varepsilon {I}_{max}/\xi$ is the maximum length under conditions of unlimited resource. Both κ 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 Eq. (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 state¹⁹. This individual variability is in standard IPMs modelled in the functions describing growth, G(L′, L(t)), and the parent-offspring association, D(L′, L(t)) (see below), using a probability density distribution, typically Gaussian²⁰. 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 σ(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 G(L′, L(t)) 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^19,20,21, follows a Gaussian distribution:

$$G\left(L{\prime} ,L\left(t\right)\right)=\frac{1}{\sqrt{2\pi {\sigma }_{L}^{2}\left(L\left(t+1\right)\right)}}{e}^{\frac{-\left(L{\prime} -E{\left(L\left(t+1\right)\right)}^{2}\right.}{2{\sigma }_{L}^{2}\left(L\left(t+1\right)\right)}}$$

(3)

with the growth realized by a cohort of individuals with length L(t) equalling

$$E(L(t+1))=\left\{\begin{array}{ll}L(t){e}^{-{\mathop{r}\limits^{.}}_{B}}+(1-{e}^{-{\mathop{r}\limits^{.}}_{B}}){L}_{m}E(Y) & {\rm{for}}\;L\le {L}_{m}E(Y)\\ L(t) & {\rm{otherwise}}\end{array}\right.,$$

(4)

and the variance in length at time t + 1 for a cohort of individuals of length L as

$${\sigma }^{2}(L(t+1))=\{\begin{array}{cc}{(1-{e}^{-{\mathop{r}\limits^{.}}_{B}})}^{2}{L}_{m}^{2}{\sigma }^{2}(Y) & {\rm{f}}{\rm{o}}{\rm{r}}\,L\le {L}_{m}E(Y)\\ 0 & {\rm{o}}{\rm{t}}{\rm{h}}{\rm{e}}{\rm{r}}{\rm{w}}{\rm{i}}{\rm{s}}{\rm{e}}\end{array},$$

(5)

where σ(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 model¹⁷, reproduction, i.e. the number of offspring produced by an individual of length L between time t and t + 1, equals $Y\cdot {R}_{m}\cdot {L}^{2}/{L}_{m}^{2}$. 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 – κ)¹⁷, whereas L_m is proportional to κ; κ thus controls the trade-off between energy allocation to reproduction versus growth. However, the role of κ in the DEB-IPM is mostly implicit, as κ 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 κ and I_max are assumed to be constant across experienced feeding levels, R_m is also assumed constant. The reproduction function R(L(t)) gives the number of offspring produced between time t and t + 1 by an individual of length L at time t:

$$R\left(L\left(t\right)\right)=\left\{\begin{array}{ll}0 & {\rm{for}}\;{L}_{b}\le L < {L}_{p}\\ E\left(Y\right){R}_{m}L{\left(t\right)}^{2}/{L}_{m}^{2} & {\rm{for}}\;{L}_{p}\le L\le {L}_{m}E\left(Y\right)\\ \frac{{R}_{m}}{1-\kappa }\left[E\left(Y\right)L{\left(t\right)}^{2}-\frac{\kappa L{(t)}^{3}}{{L}_{m}}\right] & {\rm{for}}\;{L}_{m}E\left(Y\right) < L\le {L}_{m}E\left(Y\right)/\kappa \end{array}\right.$$

(6)

Individuals are mature when they reach puberty at body length L_p and only surviving adults reproduce (Eq. (1)); thus, only individuals within a cohort of length ${L}_{p}\le L\le {L}_{m}Y/\kappa$ reproduce.

The probability density function D(L′, L(t)) 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:

$$D(L{\prime} ,L(t))=\left\{\begin{array}{ll}0 & {\rm{for}}\,L < {L}_{p}\\ \frac{1}{\sqrt{2\pi {\sigma }_{{L}_{b}}^{2}(L(t))}}{e}^{\frac{-{(L{\prime} -{E}_{{L}_{b}}(L)(t))}^{2}}{2{\sigma }_{{L}_{b}}^{2}(L(t))}} & {\rm{otherwise}}\end{array}\right.$$

(7)

where ${E}_{{L}_{b}}\left(L\left(t\right)\right)$ is the expected size of offspring produced by a cohort of individuals with length L(t), and ${\sigma }_{{L}_{b}}^{2}\left(L\left(t\right)\right)$ the associated variance. For simplicity, we set ${E}_{{L}_{b}}\left(L\left(t\right)\right)$ constant and assumed its associated variance, ${\sigma }_{{L}_{b}}^{2}\left(L\left(t\right)\right)$, 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 responses²², 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 κ, length at birth L_b, length at puberty L_p, maximum length L_m, juvenile mortality rate μ_j, adult mortality rate μ_a, von Bertalanffy growth rate ${\mathop{r}\limits^{.}}_{B}$ 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 Froese²³ supplementary material, or (iii) using the equation ${\mathop{r}\limits^{.}}_{B}=-\log (1-0.95)/{t}_{max}$, where t_max is a species’ longevity (years), sourced from Fishbase²⁴. 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 Fishbase²⁴ were not used. Body lengths for 152 species were sourced from Sharks of the World²⁵ or Rays of the World²⁶. Total lengths were converted to fork lengths using scalar values on Fishbase²⁵. Length at birth was sourced from the IUCN red list²⁷ for five species (M. ambigua, M. birostris, A. parmifera, D. trachyderma and R. australiae). Length at puberty for Maculabatis ambigua was sourced from primary literature²⁸. We calculated maximum reproduction rate R_m as ${R}_{m}=\left(c\times n\right)/i$, 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 World²⁵, Rays of the World²⁶, IUCN red list²⁷, Fishbase²⁴, or Barrowclift et al.²⁹. 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^30,31,32,33. 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 World²⁵ and Rays of the World²⁶. Adult mortality rate was calculated³⁴ by taking the inverse of the mean of longevity and age at maturity (a) (${\mu }_{a}=1/\left[\left({t}_{max}+a\right)/2\right]$. Juvenile mortality rate³⁵ was calculated as ${\mu }_{j}=-\log ({l}_{\alpha }^{\frac{1}{a}})$, where survival to maturity³⁶, l_α, equals ${l}_{\alpha }={e}^{-{\mu }_{a}\left({t}_{max}-a\right)}$.

Values for all other species were taken directly from the primary literature. Finally, for most species, we were able to take values for κ from the Add My Pet database³⁷. If no values for κ were available for a species, we assumed κ = 0.8 as is common practice³⁸. The parameter kappa is explicit in the starvation condition¹³, which states that individuals of length L die of starvation when they can no longer cover their maintenance costs, which occurs when $L={L}_{m}E\left(Y\right)\kappa ={L}_{{\rm{starvation}}}$. At any feeding level, the ultimate length that individuals can grow to equals ${L}_{\infty }={L}_{m}E\left(Y\right).$ Substituting L_∞ into the starvation condition returns: ${L}_{{\rm{starvation}}}={L}_{\infty }/\kappa$. In our case, κ = 0.8 so that ${L}_{{\rm{starvation}}}=1.25{L}_{\infty }$. 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 κ 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 (version 18 contains DEBBIES V5)³⁹. 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 parameters⁴⁰. 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 sets⁴¹. 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 observations⁴¹. So far, our approach of sourcing life history data from different populations has been satisfactory in the study of general patterns in life history strategies in various species of elasmobranchs³, reptiles³, and ray-finned fish¹⁶. However, users should always carefully interpret their results because life history traits for a given species can vary over time and across ecosystems, environmental conditions and populations. 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^42,43. The columns of the data file are described in Table 2.

Table 2 Description of the columns in the data records file; each row in the file is a species.

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 Fishbase²⁴ and, if unavailable, we obtained generation times from the IUCN Red List²⁷ and age at maturity values from the Animal Diversity Web⁴⁴. For the cartilaginous fish, we obtained generation times (for all species) and longevities (18 species) from the IUCN Red List²⁷, and longevity and age at maturity values from the Sharks of the World book²⁵, the Rays of the World book²⁶ or from Barrowclift et al.²⁹. For one cartilaginous fish, we obtained the longevity value directly from the scientific literature (silvertip shark Carcharhinus albimarginatus)^45,46 and for the Galapagos shark Carcharhinus galapagensis from Fishbase²⁴. For all other species, we first consulted the Animal Diversity Web⁴⁴, then the IUCN Red List²⁹ for observations on generation time and AnAge⁴⁶ for observations on age at maturity and/or longevity if these were unavailable in the Animal Diversity Web⁴⁴. 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 λ (calculated as the dominant eigenvalue of the matrix approximation of Eq. (1), see also Table 3) most species are slightly higher than λ = 1 (denoting population increase) at high experienced feeding level (E(Y) = 0.9), centred around λ = 1 (denoting stability) at an intermediate feeding level (E(Y) = 0.7), and mostly lower than λ = 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 3; Fig. 2b). Using the root mean square error (RMSE) (Table 3), 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 3). 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 $T=\log ({R}_{0})/\log (\lambda )$, where R₀ is the net reproductive rate and λ the population growth rate. Calculated this way, generation time represents the time it takes a population to increase by a factor R₀, which might not always be a good approximation of how generation time is measured in the field.

Fig. 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 λ (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 3 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.

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 3; Fig. 2c). Using the root mean square error (RMSE) (Table 3), 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 3). 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 3; 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 maturity⁴⁷. Using the root mean square error (RMSE) (Table 3), 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 3). 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 dataset³⁹. All versions are available online³⁹ as described as in Table 2. Version 1 contained 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 κ and ${\mathop{r}\limits^{.}}_{B}$ 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 0.4¹³. A feeding level of around 0.7 can be considered to represent a gut that is ‘just filled’, on a scale between empty and bursting⁴⁷. 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 1)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 (κ, L_b, L_p, L_m, μ_j, μ_a, ${\mathop{r}\limits^{.}}_{B}$, 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 traits¹ (Fig. 1, Table 1) can be used for more in-depth cross-taxonomical analyses (Fig. 1). For example, statistical analyses (e.g., a phylogenetically corrected principal component analysis⁴⁸ can be used to explore how life history variation can be structured and summarised into a few life history strategies⁴⁹. 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., microorganisms⁶).