Global patterns in mortality, growth, and offspring size

Natural mortality (M) (expressed as a size-independent mortality rate that is not a product of fishing) is highest at the tropics and decreases by 80% closer to the poles (from 0.85 y⁻¹ at 0° to 0.17 y⁻¹ at 60°), which constitutes nearly a 2-fold increase in yearly survival probabilities (from 0.43 at 0° to 0.84 at 60°, 95% CI 1.33- to 3.69-fold) (R² = 0.16) (S1A Fig). The effect of latitude on mass-specific growth rate (k) could not be differentiated from zero (the slope of ln(k) with latitude had an estimate of −0.01, 95% CI: −0.03 to 0.01; S1 Table), although the tendency was for k to decrease with increasing latitude (from 4.36 g^1/4 y⁻¹ at 0° to 2.11 g^1/4 y⁻¹ at 60°) (R² = 0.13) (S1B Fig). We did not detect an effect of latitude on the theoretical initial offspring weight (w₀) (similar to t₀ in the von Bertalanffy equation) (the slope of ln(w₀) with latitude had an estimate of 0.00, 95% CI: −0.5 to 0.2), with the median expectation for w₀ ranging between 12.9 and 14.4g (R² = 0.14) (S1C Fig). Using these estimated relationships (with their attendant uncertainty), we calibrated the life history model to predict optimal reproductive schedules (see Methods).

Model predictions: Patterns in reproductive schedules and scaling

Age at maturity was predicted to increase from the tropics to the poles (reproduce in the first year at 0° and 12.1 y at 60°; Fig 1A). Reproductive scaling was predicted to triple across the same latitudes (2.8 at 0° to 8.7 at 60°; Fig 2A). Consequently, reproductive scaling and age at maturity were predicted to positively covary with each other. Similar predictions arise under the assumption of size-dependent mortality (S2 Fig).

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Fig 1. Predicted and observed maturity schedules across latitudes.

(a) Optimal age at maturity predicted across latitudes. (b) Observed age at 50% maturity (A₅₀) (years) across latitudes. The solid line shows the statistical fit to the compiled data (Ln(A₅₀) = a + b * latitude (absolute value), where a is −0.28 (95% CI: −2.10 to 1.57), and b is 0.03 (95% CI: −0.03 to −0.02); S1 Table). The grey points show the compiled data for age at 50% maturity (found in S1 Data). Note that the scale is arithmetic in (a), and logarithmic in (b).

https://doi.org/10.1371/journal.pbio.3002114.g001

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Fig 2. Predicted and observed fecundity–mass relationships across latitudes.

(a) Reproductive scaling resulting from the predicted optimal age at maturity across latitudes. The black line shows the median of the predictions, and the grey ribbon shows the 95% credible intervals. (b) Observed mass scaling exponent of the number of eggs per female (RS) across latitudes (RS = a + b * latitude (absolute value), where a is 1.00 (95% CI: 0.94 to 1.07) and b is 0.004 (95% CI: 0.003 to 0.005); S1 Table). The black line shows the model estimates, and the dashed lines show the 95% credible intervals; the dotted red line shows an isometric scaling (i.e., when the reproductive scaling is 1). (c) The observed relationship of female mass and number of eggs (F) for different latitudes (F = c + d * latitude + RS * mass, where c is 5.39 (95% CI: 4.95 to 5.85, d is −0.02 (95% CI: −0.03 to −0.02), and RS is calculated as for (b); S1 Table). The points show the data corrected for phylogeny, and the lines show the fitted model. The colours indicate absolute latitude from 0° (yellow) to 75° (purple). The underlying data for (b) and (c) can be found in S2 Data.

https://doi.org/10.1371/journal.pbio.3002114.g002

Testing the predictions: Global patterns in reproductive schedules and scaling

We found qualitative support for the predictions of our model when we compiled the available data from the literature. Age at maturity is difficult to measure, but a proxy for maturity, age at which 50% of individuals become mature (A₅₀), increased 7.7-fold across the same range of latitudes (0.76 y at 0° to 5.87 at 60°; R² = 0.84, 95% CI: 0.78 to 0.88) (Fig 1B).

When we examined the available batch fecundity data for 1,000s of individuals in over 100 species, we find support for the model predictions. Intraspecific reproductive scaling—the slope of the relationship between fecundity and mass (in log–log scale) for individuals of the same species differing in size—is always greater than 1 and increases with latitude (13% increase from 0° to 60°; Fig 2B). For example, a 10-kg fish is predicted to produce approximately 2.2 million eggs at 0° latitude (0.5 to 9.2 million, 95% CI) and approximately 3.5 million at 60° latitude (0.9 to 14.4 million, 95% CI), a 20-kg fish is predicted to produce approximately 4.7 million eggs at 0° latitude (1.2 to 19.1 million, 95% CI) and approximately 8.1 million at 60° latitude (2.2 to 14.4 million, 95% CI). The number of eggs per female is higher for high-latitude species relative to low-latitude species across all female sizes except for the smallest females, where fecundities are essentially equivalent (Fig 2C). Because only a few species had data across a range of latitudes, different species were analysed at different latitudes, and, therefore, the dependence of within-species reproductive scaling on latitude must be treated as interspecific in Fig 2. For those species where mass and fecundity data were available across at least 20 degrees latitude, reproductive scaling also increased with latitude within species (S3 Fig). In contrast, when the relationship between mass and fecundity is estimated by taking a snapshot of the within-species relationship (e.g., only mass and fecundity at maturity instead of fecundity across all mature sizes within a population) and comparing this snapshot across species, such interspecific relationship is typically hypoallometric [6,17].

Although the direction of the relationship between reproductive scaling and latitude is successfully predicted by life history optimisation, the values of reproductive scaling estimated from the data are markedly lower than those predicted by the life history model. We suspect this discrepancy arises for 2 reasons: (i) how reproductive output is estimated; and (ii) how reproductive costs are modelled. First, our model makes predictions about the scaling of total reproductive output while we test these predictions based on the available data, which includes only 1 component of reproduction (batch fecundity). As well as having higher fecundity, larger females also tend to spawn more frequently and produce larger, heavier eggs than smaller females [18], so the scaling of total reproductive output (which incorporates the effects of spawning frequency, egg size, and batch fecundity) will be steeper than estimates based on batch fecundity alone. For example, Sardiops sagax shows a batch fecundity scaling of only approximately 1, but the scaling of total reproductive output in this species is approximately 3.5 because larger females spawn much more frequently than smaller females [18]. Hence, more comprehensive estimates of the scaling of total reproductive output are likely to be closer to those predicted by our model. Second, our model assumes all of the energy that goes into reproduction manifests as reproductive output, but in reality, a nontrivial proportion of reproductive allocation is likely to be expended as “overhead.” While the overheads costs of reproduction are poorly resolved empirically, initial theoretical explorations show that including such costs would lower our predicted estimates of reproductive scaling and bring them closer to those observed in nature (S4 Fig). Empirically estimating how energy allocated into reproduction translates to reproductive output across different body sizes is necessary for better quantitative predictions of size–fecundity relationships.

While we acknowledge that our predictions differed quantitatively from the observed patterns, it is striking that a simple life history optimisation model [9], parameterised only with data on mortality, somatic growth, and offspring size across latitudes, can successfully predict qualitative global patterns in maturation and reproductive scaling for marine fish. Indeed, even when the effect of offspring size is neglected, the model still recovers the direction of change in age at maturity and reproductive scaling across latitudes. Broadly, and in relative terms, tropical fish suffer high mortality and maximise their fitness by diverting energy into reproduction earlier in life, reaching smaller sizes, having only shallow reproductive scaling exponents (though they are still greater than 1), and producing fewer eggs per unit mass. In contrast, polar fish experience lower mortality, and, therefore, their optimal strategy is to continue growing until later in life, reaching a larger size, and having steep reproductive scaling. In other words, in a fast–slow continuum, low-latitude fish tend to have fast life histories, whereas high-latitude fish tend towards the slow-paced end of the spectrum. These results contradict the expectation that highly seasonal environments should select for faster life history strategies, while in stable environments—such as the tropics—it would be beneficial to tend towards a slow-paced demography [19]. For example, low-latitude birds tend to show higher parental care and delayed maturation than temperate birds [20,21]. This discrepancy with our findings may be explained by patterns in mortality: in birds, mortality increases with latitude, as many die when temperatures drop in winter [22]. Our findings, in conjunction with others [11], imply that many of the life history patterns we observe in nature are driven, not only by mechanistic constraints, but also by the evolutionary optimisation of life histories. At the very least, life history optimisation approaches may be a useful tool for explaining patterns in life history based only on a few key parameters.

Hyperallometric scaling occurs because, as an increasing proportion of energy is diverted from growth to reproduction with time, the increments of female size decrease with age while the increments of reproductive output increase. Our model makes the novel prediction that fishes delaying reproduction because of low mortality produces a higher reproductive scaling. This pattern arises because the delay in the onset of reproduction yields larger sizes at maturity, and a shallower rate of increase in the size–production relationship whenever the scaling of production is <1 (Fig 3A and 3B). Hence, when a fish that has delayed reproduction finally starts allocating resources into reproduction, proportional changes in size between time-steps are small. If energy allocation from growth to reproduction changes with age rather than size, the amount of production allocated to reproduction increases more rapidly with size than for a fish that matures early. For example, for a fish in the tropics, the total amount of production allocated into reproduction increases slowly across sizes (Fig 3A). In contrast, for a fish at high latitudes, while the postmaturity change in energy allocation with time is the same, the change with respect to size occurs much more abruptly (Fig 3B). Hence, the rate of increase in reproduction is much greater in a relative sense than the rate of growth compared to fish that mature early (Fig 3C). This means that reproductive scaling should be steeper in organisms that delay reproduction for longer—the compiled data support this prediction: higher-latitude species have later reproduction and higher reproductive scaling. Importantly, our model makes no predictions about how reproductive allocation should be divided in terms of offspring size and number though other models make such predictions [23]. Given that higher-latitude species tend to produce larger offspring, it would be interesting to see whether both fecundity and offspring size show steeper scaling at higher latitudes.

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Fig 3. Schematic demonstrating how reproductive hyperallometry increases with delayed maturity.

(a and b) Change in production and resource allocation as a function of size. Orange and blue areas show production allocated to growth and reproduction, respectively, and the opacity of the colours reflect early (solid) or late (translucid) maturity. The dotted vertical lines show the respective age at maturity (α). Panel (a) shows predictions for early maturity (20° latitude), and panel (b) shows predictions for late maturity (40° latitude). For both latitudes, the scaling of the exponential decline in energy allocation for growth is the same, but the production curve is lower in panel (b) to reflect lower estimates of k at high latitudes. (c) The predicted relationship between weight and fecundity (log–log scale) for fish maturing earlier (black line) and later (grey line). The red and pink squares show yearly-steps for early and late maturating fish, respectively. A steeper slope indicates higher reproductive scaling. These predictions were generated using Eqs 1–4 (α = 1.99, k = 3.41, w₀ = 13.87 at 20°; α = 5.02, k = 2.68 w₀ = 13.35 at 40° latitude).

https://doi.org/10.1371/journal.pbio.3002114.g003

A steeper fecundity scaling in cold temperatures also occurs in taxa other than fish (e.g., flies [24], water fleas [25], and water snails [26]), but with exceptions (e.g., mosquitoes [27] and water striders [28]). A previous life history optimisation model from Arendt [29] argues that the size–temperature relationship, where organisms living in colder environments reach larger sizes than organisms in warm areas, can be explained by a steeper size–fecundity relationship in cold environments. If large organisms have a greater advantage in terms of fecundity, it may be optimal to delay maturation and reach a larger size. Here, we make the inverse argument: that delaying maturity is optimal when mortality is low, and the steeper reproductive scaling is the product of delaying reproduction. It is important to note that, although the changes in mortality and growth with latitude are certainly affected by a temperature gradient, other factors, such as light and predation [30], are likely influencing these patterns too. Experimental evolution studies seem ideally suited to teasing apart these 2 hypotheses: for example, multigenerational, orthogonal manipulations of mortality rate and temperature, and measuring life history changes (e.g., maturation schedules, size, and fecundity scaling) should provide a test for whether mortality drives life history evolution or temperature effects drive fecundity and size evolution. Interestingly, these data may already exist for some species but have not been analysed in this context [31].

In terms of fecundity, the average tropical fish produces fewer offspring than the average polar fish, and this disparity increases with female size such that larger, colder fish produce far more offspring for a given female mass than smaller, warmer fish. These results are also consistent with life history patterns of freshwater species [32,33] as well as other marine studies [34]. This is not to say that higher-latitude fish necessarily have higher fitness, as contrasting life history strategies may yield similar population growth in different environments [35]. The congruence between the model predictions and the compiled reproductive data suggests that reproductive schedules might well be a product of life history optimisation given local demographic or environmental constraints, particularly those affecting mortality. It is worth noting that in our model, we consider mortality as the driver of resource allocation, yet it is equally likely that different life histories will result in different levels of mortality-determining causality is difficult. A useful illustration of this point comes from a recent synthesis whereby mortality rates are the product of life history strategies [23]. Certainly, there is evidence that mortality can shape life history evolution [36] and that life history strategies affect mortality (e.g., in semelparous species). We suspect that causality is bidirectional—there is an interplay between mortality and life history, but reconciling these effects into the same modelling framework represents a formidable challenge.

Hyperallometric reproduction has important consequences for the replenishment of fish populations and how they are managed [37]. Fishing practices tend to disproportionally remove older, larger fish (i.e., “age-truncation”; [38,39]), shifting population size structure towards smaller sizes. Therefore, reductions in spawning biomass through harvesting can have disproportionate consequences on reproductive output [40,41]. Our model predicts that accelerated mortality schedules associated with harvesting should lead to the evolution of lower mass-specific reproductive outputs—with concomitant losses in replenishment. Similarly, reproductive scaling is likely to strongly affect the spillover benefits of marine protected areas (MPAs) [8]. Both our model and data compilations show that high-latitude fisheries are likely to show steep reproductive scaling relative to the tropics. The degree to which reproductive hyperallometry matters for both fisheries models and MPAs is likely to systematically vary with latitude—while hyperallometry is ubiquitous, it is particularly pronounced near the poles. We would therefore predict that MPAs in polar regions, in particular, are likely to yield the greatest benefit for exploited populations.

If the latitudinal patterns observed here are mostly driven by temperature, global warming will reshape fish life histories and their demography. The general expectation is that fish will shrink in response to warming oceans [42–45] and that the productivity of most fisheries will decline with rising temperatures [46]. However, patterns in fish sizes associated to climate change are variable in nature [47]; tropical species have shrunk with increasing temperature, while temperate species show much more variable responses [48]. Assuming that temperature drives latitudinal changes in mortality, growth, and offspring size, our results suggest that regardless of how fish sizes change with increasing temperatures, mass-specific reproductive outputs are still likely to decline. We find that fish in warmer waters have lower mass-specific reproductive output than fish in cooler waters, and this discrepancy is particularly pronounced in larger fish. If future populations show the same temperature relationships as we observe here, a given standing spawner biomass of fish in the future will have much lower reproductive outputs than that same biomass today. For example, if CO₂ emissions remain high (i.e., an increase of 2.58°C in sea surface temperature; [49]), our model predicts that a 25-kg fish at 60° latitude will produce about 300,000 fewer eggs by the end of the century, a difference of 5% of its mass-specific fecundity (Figs 4, S5 and S6). Such changes would have worrying consequences for replenishment and, thus, the productivity of global fisheries and may impact the food web in ways that are difficult to anticipate [50]. However, these predictions critically depend on all the inputs (offspring size, growth, and mortality) changing with temperature in the same ways as seen in a latitude gradient—an untested, yet critical assumption. Certainly, temperature is not the only factor that affects fecundity and changes across latitudes, and the effects of climate change on fish reproduction will depend on the joint effects of climate change on all drivers.

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Fig 4. Expected changes in mean fecundity with climate change (for a predicted 2.58°C increase in SST at the end of the century under a high emissions scenario; [49]).

(a) Expected changes in the mean number of eggs across latitudes for different female sizes. The colours show the reduction in the expected number of eggs (in millions), with the smallest reduction in yellow and the largest in black. The white contour lines show reductions of 200,000 eggs. (b) Expected change in the mass-specific fecundity (in percentage) across latitudes for different female sizes. The colours show the reduction in the percentage change in mass-specific fecundity, with the largest increase in yellow and the largest decrease in black. The white contour lines show 2% changes in mass-specific fecundity. Current sea surface water temperature (SST) was assumed to be the historical mean (1981–2010) from the COBE-SST2 data provided by the NOAA/OAR/ESRL PSL (Boulder, Colorado, USA) (https://psl.noaa.gov/).

https://doi.org/10.1371/journal.pbio.3002114.g004

Predictions of marine fish reproductive schedules using life history optimisation prove similar to patterns observed in the compiled data. A valuable extension of the approach taken here would be to resolve the other parameters that likely change with latitude. For example, processes affecting resource acquisition and transformation to biomass and how they change with temperature were not considered here. Particularly, we expect the scaling of production to be temperature dependent, hence affecting the optimal life history strategy at each latitude. As an essential next step, we need a better understanding of how production scales with size, and how this relationship is affected by temperature.

Data compilation

To test whether the optimal reproductive schedules change across latitudes, we compiled data on location-specific mortality, growth, and initial size to calibrate the life history model (S7 Fig). For mortality, we compiled data on the rate of natural mortality (M) from literature, including datasets in [52–54]. We used only estimates of M estimated from age-based catch curves or tag and release data (i.e., direct estimates) where the reference specified that the population was unfished or that fishing was insignificant, giving us a total of 131 observations for 74 species from 59 references. However, some references had multiple estimates of M for the same species across a small range of latitudes. For those references, we grouped estimates of the same species and used the mean M and the mean latitude instead, giving a total of 82 observations across latitudes 0° to 72.5°.

To estimate the growth parameter k and initial weight w₀, we compiled length at age data before maturity for 44 species from 32 references (n = 49), with latitudes ranging from 7.5° to 63°. Length was converted into mass using length–weight relationships in FishBase that were either species specific or based on closely related species with similar body shape [55,56]. For each species at each location, we fitted Eq 4 (with t<0) to the data. Similarly, to restrict the range of the possible values of h when optimising R₀ using Day and Taylor’s model, we used the subset of these references where species approached their asymptotic mass to estimate h. In these instances, all mass at age data was used, and both Eq 2 and Eq 3 were fitted to the data. The subset of references for which h was estimated included 28 species across latitudes ranging from 15.4° to 61°. When optimizing maturity schedules in Day and Taylor’s model, h was fixed at its median value (h = 0.26; S8 Fig), but α was allowed to vary. Results are robust to fixing h at its median observed value because variation in R₀ is consistently higher across values of α than across values of h (S9 and S10 Figs).

Data on age at 50% maturity (A₅₀) were also compiled from published literature. Age at 50% maturity is the age at which half of the individuals are expected to be mature. Although often estimates of A₅₀ could be obtained indirectly when both length at 50% maturity (L₅₀) and the von Bertalanffy growth equation were known, we only used estimates of A₅₀ that were directly reported in the literature. The R² decreased by 42% if indirect estimates of A₅₀ were included (R²: 0.33, CI: 0.21 to 0.43 if indirect estimates of A₅₀ were excluded versus R²: 0.14, CI: 0.07 to 0.20 if indirect estimates of A₅₀ were included). We compiled a total of 127 observations of A₅₀ from 34 references and 59 species, with latitudes ranging from 9° to 73°.

We used data on batch fecundity–female size relationships for marine fish from the published literature. Most of the data had been previously compiled by Barneche and colleagues [1], but we searched for additional studies, particularly at high latitudes and in underrepresented areas to have a broader geographical scope. Only marine species were considered for the analysis; species that migrate to or from freshwater were not included. Sharks and rays were also excluded since their fecundity was much lower than for the rest of the species because of their viviparity or large egg envelops, and tuna were excluded because their sizes were much larger than for the rest of the species. We used the number of eggs per reproductive pulse (i.e., batch fecundity) as the measurement for fecundity. While the literature also includes other measurements of fecundity, such as annual fecundity, such data are much less common and therefore were excluded from the analysis. Importantly, when the model included changes in seasonality across latitudes (i.e., longer periods favourable for reproduction at low versus high latitudes), age at maturity and reproductive scaling were still predicted to increase with latitude (S13 Fig). If a species had fecundity–female size data at one location for more than 1 year, only the year with the highest number of data points was included. To accurately estimate mass–fecundity relationships for each species, we excluded species for which less than 10 data points per location were available. We compiled a total of 13,739 observations from 157 references and 153 species, with latitudes ranging from 0.9° to 74.5°.

Data analysis

All of the analyses were performed in R version 3.5.2 [57]. We used linear mixed effects models to estimate M, k, w₀, fecundity (i.e., number of eggs per batch), and A₅₀ using the package “brms” version 2.7.0 [58] assuming a Gaussian distribution.

We fitted a linear model to predict M (in log-scale) as a function of absolute latitude (fixed effect) using only direct measurements of M. To predict k and w₀ (both in log-scale), we fitted linear models with absolute latitude as a fixed effect. To estimate k and w₀, we corrected for phylogenetic relatedness between species by including a random intercept of phylogeny with a covariance matrix reflecting the phylogenetic tree using the R package “rotl” [59]. For M, we chose not to correct for phylogenetic relatedness because our goal here was to understand the spatial distribution of different mortality rates or, in other words, what is the likely mortality rate of the “average fish” for a given latitude. We use predictions from these 3 models (S1 Table) to calibrate the life history model across latitudes. Life history models calibrated using the phylogenetically controlled estimates of M yielded qualitatively similar predictions (i.e., an increase in age at maturity and reproductive scaling with increasing latitude).

The model estimating fecundity (number of eggs or offspring per batch, in log-scale) included female weight (g, in log-scale), latitude (absolute value), and their interactions as fixed effects, assuming a Gaussian distribution. Here, the reproductive scaling is the slope of the regression between natural logarithm of fecundity and the natural logarithm of female weight. Since each species had multiple observations at each location, species was included as a random effect that could modify the intercept and the slope of relationship between fecundity and female weight. In addition, a random intercept was included for phylogeny, associated to a variance–covariance that corrected for phylogenetic relatedness.

The model estimating A₅₀ (years, in log-scale) included latitude as a fixed effect and the random intercept correcting for phylogenetic relatedness. The model was fitted assuming a Gaussian distribution.

Predicted size-specific changes in reproductive output with climate change

To estimate the expected change in fecundity for a given female mass with climate change, we used predicted increases in water temperature under different climate change scenarios: a low emissions scenario (RCP2.6) and a high emissions scenario (RCP8.5) [49]. We estimated mean sea surface water temperature (SST) (1981 to 2010) across the globe from the COBE-SST2 data provided by the NOAA/OAR/ESRL PSL (Boulder, Colorado, USA), from their website at https://psl.noaa.gov/. Using these data, we fitted a general additive model (GAM) to predict SST as a function of absolute latitude (S14 Fig).

At each latitude, we calculated the predicted SST mid-century (2031 to 2050) and late-century (2081 to 2100) for the low and high emissions scenarios predicted by the IPCC (an increase of 0.64°C and 0.73°C for the mid- and late-century for the low emissions scenario, and a 0.95°C and a 2.58°C for the high emissions scenario). The IPCC predictions were relative to temperature in 1986 to 2005, which is within the time interval when most of the fish reproductive data were collected (S15 Fig). For each scenario at each latitude, we calculated the predicted mid- and late-century SST, and we found the latitude that currently experienced that mean temperature. Then, assuming fish reproductive scaling responds to changes in temperature, we estimated future reproduction by using the fitted mass–fecundity relationship for the latitude that matched the predicted SST. At low latitudes, an increase in SST was unmatched (e.g., for any future temperature >27°C, there were no latitudes that were currently experiencing that mean temperature), and, therefore, changes in reproduction could not be predicted.