## Abstract

Probability of species recovery is thought to be correlated with specific aspects of organismal life history, such as age at maturity and longevity, and how these affect rates of natural mortality (*M*) and maximum *per capita* population growth (*r*_{max}). Despite strong theoretical underpinnings, these correlates have been based on predicted rather than realized population trajectories following threat mitigation. Here, we examine the level of empirical support for postulated links between a suite of life-history traits (related to maturity, age, size and growth) and recovery in marine fishes. Following threat mitigation (medium time since cessation of overfishing = 20 years), 71% of 55 temperate populations had fully recovered, the remainder exhibiting, on average, negligible change (impaired recovery). Singly, life-history traits did not influence recovery status. In combination, however, those that jointly reflect length-based mortality at maturity, *M _{α}*, revealed that recovered populations have higher

*M*, which we hypothesize to reflect local adaptations associated with greater

_{α}*r*

_{max}. But, within populations, the smaller sizes at maturity generated by overfishing are predicted to increase

*M*, slowing recovery and increasing its uncertainty. We conclude that recovery potential is greater for populations adapted to high

_{α}*M*but that temporal increases in

*M*concomitant with smaller size at maturity will have the opposite effect. The recovery metric documented here (

*M*) has a sound theoretical basis, is significantly correlated with direct estimates of

_{α}*M*that directly reflect

*r*

_{max}, is not reliant on data-intensive time series, can be readily estimated, and offers an empirically defensible correlate of recovery, given its clear links to the positive and impaired responses to threat mitigation that have been observed in fish populations over the past three decades.

## 1. Introduction

One of the central tenets of population biology is that *per capita* population growth rate increases with declining abundance, obtaining a maximum value (*r*_{max}) at the minimum viable population size [1]. This key assumption of classical single-species, population dynamical models underlies a fundamental premise of conservation biology, sustainable harvesting strategies and recovery planning: following amelioration of the anthropogenic threat(s) responsible for their decline, the recovery of small populations is facilitated by their comparatively greater *per capita* productivity.

While threat mitigation is clearly a necessary condition for recovery, it is not always sufficient. In addition to some birds and mammals [2], several marine fishes have exhibited little or no substantive recovery (some have declined further) decades after the threat responsible for their depletion—overfishing—was mitigated [3,4]. There is compelling evidence that magnitude of depletion affects recovery potential [5,6], population reductions exceeding 90% of abundance maxima plausibly representing a threshold below which recovery is impaired (manifest by negligible changes in population size), an observation consistent with the presence of Allee effects [4,7].

There is also reason to believe that rate and uncertainty of recovery is influenced by life history [2,8–10]. Being a product of age- (stage-)specific survival and fecundity (fertility) [11], life histories are directly linked to natural mortality, *M*, a parameter hypothesized to be associated with recovery potential [5,12,13]. In addition, traits such as age and size at maturity, individual growth rate and maximum size are correlated with *r*_{max} [10,14], a parameter positively linked to rate of recovery in fishes [5] and quite probably most species.

Despite strong theoretical underpinnings, the literature on life-history correlates of recovery is based on projected or inferred, rather than observed, population trajectories following threat mitigation [2,5,10,12,15]. Another potential limitation of previous work is the tendency to postulate links between recovery potential and individual life-history traits [8,15,16]—in isolation from others—rather than combinations of traits, an approach that might better reflect the ubiquitous trade-offs that exist between traits and that constrain their evolution [11,17,18]. Despite acknowledgement that suites of life-history traits are likely to provide more reliable predictors of recovery than traits considered singly, it has proven challenging to identify a single metric that meets this objective.

Here, we examine the level of empirical support for several hypothesized links between widely studied life-history traits and realized, rather than projected, recovery trajectories. Extending a previous compilation of recovered and non-recovered fish populations [4], our analyses focus first among populations and second within populations. At the among-population level, our objective is to determine the relative importance of life-history traits considered singly, or in combination, to population-recovery status; the trait combination we examine is directly linked to natural mortality, *M* (year^{−1}), in fishes [19]. As a corollary of this objective, we examine whether *M* is empirically associated with *r*_{max}. Our second objective explores the magnitude of change in natural mortality within populations associated with the reductions in size at maturity commonly observed to occur in fished populations [20–22]. Based on empirically documented declines in body size [21], we estimate the magnitude of increase in *M* associated with proportional reductions in size at maturity for two species having divergent life histories: Atlantic cod (*Gadus morhua*) and Atlantic herring (*Clupea harengus*).

## 2. Material and methods

### (a) Population data

We compiled a dataset on ‘recovered’ and ‘non-recovered’ temperate marine fish populations. The former is based on two sources. The first source comprises stock assessments undertaken by the National Marine Fisheries Service for previously overfished populations in US waters officially deemed to have been rebuilt as of September 2016 (www.nmfs.noaa.gov/sfa/fisheries_eco/status_of_fisheries/archive/2016/third/q3-final-rebuilt-map.png). The second comprises assessments undertaken by ICES (International Council for the Exploration of the Sea) for stocks inhabiting waters in northern and western Europe. Based on population trend data available as of January 2017 (ices.dk/community/advisory-process/Pages/Latest-Advice.aspx), we identified recovered populations as being those that (i) had once been in an overfished state (stock biomass was below a limit reference point, *B*_{lim}), (ii) currently exceed their biomass target reference point and (iii) are not currently experiencing overfishing. This yielded 29 recovered stocks from US waters and 10 from European waters (table 1).

Populations considered to have not recovered are defined as those for which little or no increase had been documented since fishing on the overfished populations had ceased or had been greatly reduced for at least a decade (a time frame based on [5]). For the non-recovered populations analysed here (table 1), 14 were previously identified as having experienced impaired recovery [4]. For this study, we added two additional stocks in the non-recovered category: whiting (*Merlangius merlangus*) in the west of Scotland; and yellowtail flounder (*Limanda ferruginea*) in southern New England–mid-Atlantic (biomass remained essentially unchanged between 2002 and 2011 despite massive reductions in fishing mortality; www.nefsc.noaa.gov/publications/crd/crd1524/Individual%20Stocks/SNEMA_yellowtail_flounder.pdf). For the 16 non-recovered populations, the median number of years that had passed since threat mitigation was 20; during that period, the median size of the non-recovered populations did not change (0.08 of maximum abundance, *N*_{max}) [4].

### (b) Life-history data and natural mortality

We collated data on five traits (figure 1; electronic supplementary material, table S1): age at (50%) maturity (*α*), length at (50%) maturity (*L _{α}*), maximum age, individual growth rate (

*k,*the von Bertalanffy growth coefficient) and maximum body size (based on

*L*, the von Bertalanffy asymptotic length). When data had been partitioned by sex, we included those for females only.

_{∞}To estimate natural mortality (*M*) for each population, we used a previously published metric of *M* that is based on a combination of the parameters collated here: *L _{α}*,

*k*and

*L*, [19]. Mortality at the age of maturity,

_{∞}*α*, is calculated as 2.1a metric of

*M*positively and highly significantly correlated with 168 direct estimates of natural mortality in fishes [19,23,24]. In addition to its strong association with direct estimates of

*M*across a broad taxonomic swathe of species, this metric of

*M*is theoretically well grounded from an evolutionary perspective and empirically well supported by the literature on life-history invariants [19,23].

To assess the degree to which natural mortality is related to maximum *per capita* population growth rate (*r*_{max}), we collated data on *M* from a recent compilation of direct measurements [23] for those species (or populations) for which we also had estimates of *r*_{max} [14,25] (electronic supplementary material, table S2).

Within populations, fishing—particularly overfishing—is associated with reductions in length at maturity [20–22]. Given a negative association between *L _{α}* and

*M*, equation (2.1) predicts that natural mortality will increase as size at maturity declines. However, equation (2.1) assumes constancy in

_{α}*k*and

*L*. Given the costs to future growth associated with maturity at a smaller size [13,26], it seems likely that reductions in

_{∞}*L*will also reduce

_{α}*L*which should result in an increased

_{∞}*k*[27] all else being equal. Thus, to increase the dynamical nature of equation (2.1), we allowed

*k*and

*L*to vary with

_{∞}*L*, based on empirical relationships between these parameters (see below).

_{α}### (c) Statistical analyses

Among populations, recovery status (0 = not recovered, 1 = recovered) was modelled, using a generalized linear mixed model for which the data were assumed to be binomially distributed and a logit link-function. The fixed effects were *L _{α}*, log-transformed

*k, L*, maximum age,

_{∞}*α*and

*M*while species was modelled as a random effect. However, because there was typically only 1 datum per species, the mixed-effects model did not converge. Thus, the fixed effects alone were modelled by a generalized linear model (GLM). A linear model (LM) was used to examine whether

_{α}*r*

_{max}is associated with

*M*. To achieve normality,

*M*was log-transformed and normality of the residuals was inspected, based on Q-Q plots.

To estimate changes in natural mortality with changes in length at maturity, we first modelled the associations between *L _{α}* and

*L*, and then between

_{∞}*L*and

_{∞}*k*, separately for two species with considerably different life histories. Atlantic cod is a comparatively long-lived, high-trophic-level fish that matures at a relatively large size (and somewhat older age) when compared with Atlantic herring. Species-specific parameters were those reported by FishBase [28], excluding data considered questionable (FishBase excludes parameter estimates from studies in which

*L*is 33% higher or lower than the reported maximum length).

_{∞}Our intent was to apply an LM to the *L _{α}* and

*L*data for each species. However, the resultant relationship for cod was highly suspect, yielding a nearly horizontal relationship between the two parameters (only 12 data points were available). As a consequence, for cod, we let

_{∞}*L*equal the ratio of the means of

_{∞}*L*to

_{∞}*L*, calculated from FishBase (i.e. 1.945). We did apply an LM to the data on herring, for which considerably more estimates were available. The equations used to relate

_{α}*L*to

_{∞}*L*were 2.2and 2.3

_{α}We applied a GLM to parametrize the associations between *k* and *L _{∞}* for each of the two species, using a Gaussian distribution to model the residual variability and the identity link to model the mean. The resulting equations were
2.4and
2.5

To estimate changes in natural mortality associated with proportional reductions in length at maturity, we substituted into equation (2.1) the values of *L _{∞}* calculated from equations (2.2) and (2.4), and the values of

*k*from equations (2.3) and (2.5), for cod and herring, respectively.

## 3. Results

### (a) Among-population correlates of recovery status

The initial GLM included all 55 populations in the dataset. Based on stepwise model reduction, the following fixed effects were reduced: maximum age (*χ*^{2} = 0.238, d.f. = 1, *p* = 0.625), log-transformed *k* (*χ*^{2} = 1.133, d.f. = 1, *p* = 0.287), *α* (*χ*^{2} = 0.252, d.f. = 1, *p* = 0.615), *L _{∞}* (

*χ*

^{2}= 0.726, d.f. = 1,

*p*= 0.394) and

*L*(

_{α}*χ*

^{2}= 0.541, d.f. = 1,

*p*= 0.462). Natural mortality at maturity,

*M*, could not be excluded from the best-fitting model (

_{α}*χ*

^{2}= 6.3858, d.f. = 1,

*p*= 0.011) and was positively correlated with recovery status (slope = 2.77, s.e. = 1.28; table 2). We examined the robustness of the results with respect to length at maturity by proportionately changing

*L*.

_{α}*M*remained the only significant fixed effect when

_{α}*L*was either reduced (slope = 3.48, s.e. = 1.31) or increased by 20% (slope = 6.39, s.e. = 2.41).

_{α}When the analysis was run on two subsets of the data (table 2), *M _{α}* was also the only remaining fixed effect. In the first, we excluded fishes from the class Chondrichthyes (sharks, skates and rays); their life histories can differ substantively from teleosts or ‘bony fishes’. In the second, in addition to excluding chondrichthyans, we restricted the populations in the recovered category to those in US waters, given an argument could be made that the determination of recovery in the USA is based on a more consistent set of criteria and rebuilding targets than those applied in Europe.

One potential concern is that *M _{α}* is derived from other covariates against which it is compared. That is,

*L*,

_{α}*L*and

_{∞}*k*may have been dropped from the model not because they are unrelated to recovery potential but because they appear in the model as components of

*M*and again as separate covariates. To examine this possibility, we re-ran the GLM, including only

_{α}*L*,

_{α}*L*and

_{∞}*k*as fixed effects, either together or singly, and compared the outputs with the GLM that included only

*M*as a fixed effect (table 3). None of the alternative model formulations (i.e. those excluding

_{α}*M*) was significant and the Akaike information criterion (AIC) was lowest for the model that included only

_{α}*M*

_{α}.Estimates of natural mortality and maximum *per capita* population growth were available for 14 species/populations (electronic supplementary material, table S2). *M* was positively associated with *r*_{max} (*p* = 0.0283) in accordance with the following equation:
3.1

### (b) Effect of declining length at maturity on natural mortality within populations

According to equation (2.1), natural mortality at maturity (*M _{α}*) will increase with reductions in length at maturity (

*L*). Fixing

_{α}*k*and

*L*at values corresponding to species averages [28],

_{∞}*M*increases curvilinearly with declining

_{α}*L*for both cod and herring across ranges of length at maturity typical for each species (figure 2).

_{α}Rendering the models more dynamic, by allowing *k* and *L _{∞}* to vary with

*L*(equations (2.2)–(2.5)), reveals differences in how natural mortality is perceived to change with body size. Compared with the fixed model for cod (dashed line in figure 2

_{α}*a*), the dynamic model formulation (black line in figure 2

*a*) produces lower values of

*M*and a slower rate of increase in

_{α}*M*with declining

_{α}*L*. By contrast, the dynamic model for herring results in higher values of

_{α}*M*with declining

_{α}*L*when compared with the results of the fixed model (figure 2

_{α}*b*).

The dynamic formulations of the natural mortality model were used to calculate changes in *M _{α}* with empirical estimates of reductions in mean length at maturity concomitant with fishing [21]. In a reference population of cod for which age at maturity is 60 cm and the proportional reduction in

*L*matches the average reported for the species (19%), natural mortality is predicted to increase 24% from 0.416 to 0.516 (table 4). If such a population were to experience the maximum reported proportional reduction in

_{α}*L*(26%),

_{α}*M*would be expected to increase 34% (0.416 to 0.559). By comparison, in a herring population for which

_{α}*L*= 25 cm,

_{α}*M*would be predicted to increase with declining length at maturity by only 3% on average (0.470 to 0.485) and by a maximum of 7.9% (table 4).

_{α}## 4. Discussion

The present study provides what is perhaps the strongest empirical link to date between life history and recovery in fishes. A combination of traits that reliably estimates natural mortality distinguishes marine fishes that have and have not recovered in response to threat mitigation. Among populations, those that have recovered are characterized by a significantly higher rate of natural mortality at maturity than those that exhibit impaired recovery (i.e. populations that have increased marginally, remained stable or declined further following meaningful reductions in fishing mortality). Considered singly, life-history traits appear not to be informative metrics of recovery. This is perhaps not surprising given that such an approach does not account for the ubiquitous trade-offs that exist between traits [11,17,29]. Metrics that incorporate a combination of fitness-related traits are more likely to be informative reflections of individual fitness, the primary determinant of genotypic and population rate of increase.

The positive association between probability of recovery and rate of natural mortality among populations can probably be attributed to local adaptation and to links between *M* and *r*_{max}. Adaptation is a result of selection acting on phenotypic traits. Different combinations of life-history traits result in different rates of natural mortality. Individuals that mature at relatively young ages and small body sizes tend to have comparatively short lifespans and small maximum body sizes, a combination associated with high *M* [9,12,27]. Theory predicts that the higher the rate of *M*, the greater the value of *r*_{max} and the faster the rate of recovery [5,14,26,30]. The prediction that *M* is positively associated with *r*_{max} is empirically supported by the present study.

Thus, populations for which local adaptation has resulted in high rates of *M* would be expected to respond more effectively to threat mitigation and to recover more rapidly than those with lower *M*. Our results confirm this prediction. But they are also consistent with the hypothesis that the lower the rate of natural mortality, the higher the uncertainty in recovery, given the observation that non-recovered populations have, on average, not changed in abundance two decades after threat mitigation [4]. This is supported by empirically based simulations that find that uncertainty in recovery increases as *r*_{max} declines [5].

A variety of metrics have been used to estimate recovery potential, particularly in fishes (recently summarized by Kindsvater *et al*. [9]). All of these sensibly focus on metrics of *r*_{max} [4,10]. But a challenge with their practical application is that they are data-intensive, requiring at least a decade (preferably more) of temporal estimates of the abundance of mature and immature individuals. Another limitation is that their utility has not been evaluated against empirical data (but see [31]), relying instead on predicted, albeit theoretically defensible, responses to threat mitigation. The metric of recovery identified here has the advantage of being based on simply estimated parameters and being significantly correlated with direct estimates of natural mortality across a taxonomic breadth of species [19,23].

In contrast to the positive association between *M* and recovery potential among populations, increases in natural mortality within populations will almost certainly prove detrimental to recovery [32–34]. Notwithstanding recent evidence to the contrary [32,34], a widely held assumption in fisheries science is that *M* does not change with changes in population size [35]. This assumption would seem to be inconsistent with the observations that size at maturity commonly decreases in fished populations [20–22,36] and that reductions in body size are likely to be associated with increased natural mortality [13,26,36,37].

The metric of recovery potential identified here (*M _{α}*) suggests that the increase in mortality attributable to declining size at maturity can be substantive in some species but less so in others. In cod, the model predicts an average 24% increase in

*M*associated with the average proportional reduction in length at maturity of 19% [21]. But in species for which length at maturity has declined relatively little, such as herring, the additional mortality caused by declining body size would seem to be small.

All metrics of recovery potential have their limitations. Notwithstanding measurement error, one drawback to *M _{α}* is that

*k*and

*L*

_{∞}would ideally be estimated prior to changes in length at maturity generated by fishing. In reality, such estimates are often not available; most of the von Bertalanffy parameters used in the present analysis were not made on unfished or lightly fished populations. However, we do not anticipate that this biases our primary findings. If anything, given that prolonged overfishing would be expected to lead to higher increases in

*M*, one could argue that our estimates of

_{α}*M*for non-recovered populations have been over-estimated relative to what they would be in the unfished state. Thus, the difference in

_{α}*M*between recovered and non-recovered marine fish populations documented here might have been underestimated.

_{α}In summary, the recovery metric documented here to quantify length-specific natural mortality at maturity (*M _{α}*) has a sound theoretical basis, is significantly correlated with direct estimates of

*M*that directly reflect

*r*

_{max}, does not depend upon data-intensive time series, and can be estimated on the basis of readily measured variables: length at maturity and two fundamental parameters of the von Bertalanffy growth equation (

*k*,

*L*

_{∞}). Our approach is not dissimilar to attempts to use information on body size coupled with life-history relationships to determine conservation limit reference points for fishes [38]. Compared with other metrics of recovery potential and

*per capita*population growth,

*M*offers an empirically strong metric, given its clear links to the positive and impaired responses to threat mitigation that have been observed in fish populations over the past three decades.

_{α}## Data accessibility

Data used in this manuscript are included as electronic supplementary material.

## Authors' contributions

The manuscript was jointly written by J.A.H. and A.K. Data collation and statistical analyses were carried out by J.A.H.

## Competing interests

We have no competing interests.

## Funding

The research was funded by the Natural Sciences and Engineering Research Council of Canada (J.A.H. and A.K.) and by the Academy of Finland (A.K.).

## Acknowledgements

We are grateful to Ole Shelton, Martin Krkosek and an anonymous referee for their helpful and constructive comments on the original version of the manuscript.

## Footnotes

Electronic supplementary material is available online at https://dx.doi.org/10.6084/m9.figshare.c.3789952.

- Received April 3, 2017.
- Accepted May 15, 2017.

- © 2017 The Author(s)

Published by the Royal Society. All rights reserved.