Ethics statement

Laboratory experiments on post-hatch H. amarus were conducted under permit TE065394-2 (U.S. Fish and Wildlife Service) and with authorization of the New Mexico State University Institutional Animal Care and Use Committee (IACUC, # 2005-006boeing). Field collections of H. amarus were conducted under permit TE045-235-3 (U.S. Fish and Wildlife Service) and permit 3143 (New Mexico Department of Game and Fish) by the senior author in association with SWCA Environmental Consultants, Albuquerque, New Mexico.

Implementation of a matrix population model

We use a single matrix population model that accommodates life spans of age 4+ and age 5+. We assume the last age class is composed of age 5 and older individuals, of which there is a non-zero probability of occurrence even with adult survival for an age 2 longevity. An age class model is preferred to a juvenile-adult stage-based model because many fish species have a strongly allometric increase in fecundity with body length (and age) that exceeds the slope of the relationship between fecundity and body mass [29,30]; a stage-based model may not accurately represent the contribution of fecundity from older females with disproportionately higher fecundity.

The vital rate parameters (Eq 1) in the simulated post-breeding birth-pulse female transition matrix include age-specific survival probability (S_i) and fecundity (number of eggs) (F_i). We assumed density independence because other species with similar life histories have conformed poorly to models of density dependence [31]. Note that the age-specific number of individuals (n_i) in the population vector are additional model parameters in transient LTREs [16]. We assume that S₁ = … = S₅ in the starting transition matrix for each simulation scenario; for simulations of delayed maturity F₁ = 0.

(1)

To facilitate simulating age truncation, we develop a hypothetical "natural equilibrium" view of a species in its natural environment wherein adult survival probability determines approximate natural lifespan. We assume for a natural equilibrium that a species’ fecundity at size and age is a result of selection in the natural environment. If juvenile mortality is a stochastic determination of the environment, then a species that persists in the natural environment must have fecundity at-age high enough to compensate for juvenile mortality.

In this hypothetical context, a species would have population growth rate close to equilibrium (λ ≌ 1) and the population would have an equilibrium age-class structure after some generations in the natural environment. A natural equilibrium perspective is helpful for simulations because there is inevitable uncertainty about true values of vital rates in contemporary, perturbed environments, and secondly, it provides a convenient frame of reference that can be developed for any species. With limited data it is possible to approximate aspects of life history sufficiently to define a natural equilibrium baseline for each example species. We simulate age truncation for age 1 and age 2 maturities because some fish species delay reproduction and attain larger body size and reproductive potential. We next describe how we derived values for survival probabilities and fecundity of our study species.

Adult survival. We used a theoretical context to derive the adult survival probability. Prior meta-analysis [32] and application [33] establish that natural mortality (M) in fishes is best approximated as M = 4.3/T_max, where T_max is the species’ life span (years) in an unperturbed natural environment (S2 Fig). The adult survival probability necessary for this longevity is S₁ = … = S₅ = e^-M. For exploited fish populations adult survival probability is commonly estimated as S₁ = … = S₅ = e^-(E+M), where natural mortality (M) is augmented by E, which represents mortality from environmental sources.

We begin our simulations at an adult survival necessary for the assumed life span for each species. The estimated values of adult survival using the equation given by [32] for natural mortality are 0.34 and 0.42 for life spans of four and five years, respectively. In our simulations we use adult survival values of 0.35 and 0.45 to represent life spans of ages 4+ and 5+, respectively. From this hypothetical baseline, we simulated systematically at values of adult survival of 0.15, 0.25, 0.35 and 0.45, while holding S₀ at its equilibrium value. Note that adult survival values of 0.25 and 0.15 in our simulations are equivalent to age-truncated life histories of age 3+ and 2+, respectively. We calculate a value of E, environmental mortality, at each reduced level of adult survival. Notice that e^-(E+M) = e^-E x e^-M where e^-E represents survivorship to environmental mortality and e^-M is survivorship to natural mortality.

Simulation details

Our approach to study age-truncation involved retrospective analysis of simulated transient variation in vital rates and population structure using transient LTREs [16]. For each simulation we generated random values of vital rates for 25 time steps [16]. At each time step, survival probabilities were drawn from a beta distribution with expected value equal to the starting value in the transition matrix and shape parameters a and b chosen for a coefficient of variation (CV) of 0.2. The effect of different levels of CV were evaluated at CV = 0.05, 0.1, 0.2 and 0.3. Random deviates for fecundity were drawn from a lognormal distribution with expected value equal to the logarithm of predicted fecundity and standard deviation (estimated from Bayesian analysis) equal to the standard deviation of the species-specific intercept divided by the square root of the sample size, an approximate standard error for mean fecundity at-age. Notice that a random transition matrix is generated each simulation time step using the starting transition matrix as the expected values for vital rates.

The stochastic realisation of the transition matrix at each time step (t) was used to calculate the realised population growth rate (λ_t = N_t/N_t-1), where population structure (n_i) is normalized at time t-1 [16]. The variance of realised population growth rate () was decomposed into a proportional contribution for each parameter in the matrix population model using the example of Koons et al. [16]. The estimation of parameter contributions involved calculation of sensitivities to changes in vital rates and population structure, and temporal covariances among these parameters [16]. Each simulation scenario was replicated 100 times and mean contributions were obtained for each vital rate and component of population structure. Transient LTRE results were summarized for each species by plotting the mean proportional contribution for each vital rate contributing at least 10% of at each level of adult survival. All simulations were conducted in R [38] following the example of Koons et al. [16].

Caveats and alternate models

With their high biodiversity globally, the rich evolutionary elaboration of fish life histories precludes any single model from accurately representing all species. Details of life history are important for a matrix population model to accurately represent a species’ population growth under specific environmental conditions. We focused narrowly on a systematic exploration of the process of age truncation and comparing simulations within and between species. Our population model mimics an iteroparous life history with reproduction in multiple years after reaching maturity, which is typical for a majority, but not all, freshwater and marine fishes.

There are many possible variations and extensions of our model. For example, fishes with a semelparous life history such as off-shore spawning capelin (Mallotus villosus) cannot retain older repeat spawners as represented in our transition matrix, whereas nearshore spawning iteroparous individuals can [44]. As a second example, the effects of reduced adult survival on short-lived marine fish species under commercial exploitation, such as Peruvian anchoveta (Engraulis ringens), will require model refinements to simulate its life history. This migratory, pelagic species can spawn throughout the year but exhibits two spawning peaks annually and age classes can be comprised of 2 cohorts a year of different sizes and ages (http://www.fao.org/fishery/species/2917/en, accessed 20 February 2020).

Additional model refinements ought to be examined for individual species in a particular environment. For example, only a fraction of individuals may be reproductively mature at younger adult ages in some species [45–47]. A maturation parameter for the first or several adult age classes could be included in the transition matrix, or, a model of density dependence could be informative with larger body size freshwater fishes. We predict that with partial maturation at age 1, reduced adult survival would yield a population response intermediate to our simulations of age 1 and age 2 maturities. Although we simulate a model of density independence, additional work is needed to clarify how density dependence might affect a population’s response to age truncation.

Environmental perturbations such as river intermittency associated with water extractions or drought, as occurs with four of our five simulated example species, can be included in the population model as a stochastic environmental source of reduced survival. Simulations of alternate models of transient mortality caused by river drying, for example, could be compared to discern the relative importance of juvenile versus adult mortality associated with river intermittency.

Detecting age truncation

We began our modelling work with H. amarus, a local species in our region. Initially, we attempted to estimate age-specific adult survival rates (results not shown) with a large sample dataset (S1 Data) but not all were estimable and temporal variation in survival was indicated. This further implied a likely nonequilibrium population structure and conveyed uncertainty about values of survival rates in the contemporary environment. The important question for us became "how might one develop a frame of reference to evaluate contemporary disturbances to a species?". This led to our hypothetical equilibrium baseline for a species in an unperturbed natural environment.

How might a manager detect age truncation in a population? Although manifestation of age truncation may be noticeable through increased fluctuations in population size over time [22], it may be difficult to identify if age truncation is the cause when we only have data on fluctuations in population size. We suggest that a simple binomial proportion (eq. 3) can be calculated on a sufficiently large, unbiased sample and compared with an equilibrium expectation to test for age truncation: (3) where θ_A represents the fraction of adults older than the first reproductive age divided by the total number across all k adult ages. The binomial proportion θ_A is the converse of Heinke’s method [48]. At the natural equilibrium adult survival rate, and at stable population structure, θ_A = 0.349 for an age 4+ lifespan, and θ_A = 0.427 for an age 5+ lifespan. The sample data for H. amarus (S1 Data) yields an estimate of θ_A = 0.258 (95% confidence limit: 0.24 ≤ θ_A ≤ 0.28), which can be calculated from (S5 Table). In R, the probability of the observed sample given the expected equilibrium value of θ_A [pbinom(573,2215,0.349)] is 4.1 x 10⁻²⁰, evidence of significant age truncation. We caution that analysis of a single sample should not be construed as proof of age truncation, but rather that the proposed metric θ_A should be examined in additional sufficiently large samples over time and space because, for example, an event of strong recruitment to the first reproductive age class will also result in a lower value of θ_A. Likewise, if strong recruitment events are associated with augmentation of the population from captive production or translocation [6,7], then inference of significant age truncation could be incorrect. Clearly it is important to consider the life span of a species and the contemporary historical (temporal) context for a sample to use θ_A as a test of age truncation. For our example species, a simple application of θ_A could be to use mean size at age of the second reproductive age class to assign individuals in a sample to first or later adult age classes.

Identifying causes of age truncation

Although one can test for age truncation, identifying the causes of adult mortality in contemporary environments may be difficult. There are many possible causes of reduced adult survival in fish populations, which may vary across species or across populations of the same species in different environments. As opposed to fishing being a primary cause of age truncation in the marine environment, there are multiple possible contributors to increased adult mortality of freshwater fishes. Direct exploitation of wild populations can drive age truncation for short-lived freshwater fish species in the ornamental fish trade [49]. However, for many fish species, especially those in rivers, causes of reduced adult survival may be indirect, arising from multiple factors and hence more difficult to quantify. The wide-spread introduction of exotic predatory fish species for sport fishing has led to homogenization of freshwater fish communities over large spatial extents [50]. In four of our simulated examples seasonal low river flows are thought to facilitate increased predation mortality by introduced exotic fishes [51–54]. Additionally, over-utilization of freshwater resources and river flow regulation for hydropower or irrigation are important global drivers of population declines in freshwater fish populations [3,55]. For example, water diversions for irrigation can cause seasonal occurrences of river intermittence that dries habitat and kills fish [56]. As a second example, a primary emphasis of conservation for H. amarus has sought to manage water resources to encourage spawning [43,57] and thereafter habitats can be depleted or dried through irrigation withdrawals. The emphasis on successful spawning involves early season water releases from upstream reservoirs, an irreversible commitment of water resources during drought. This management choice can reduce the water available to promote survival after spawning and it can maintain or increase age truncation if adult mortality occurs with river intermittence. Our results point directly to the importance of adult survival, not fecundity, for population growth of short-lived, iteroparous species like H. amarus. This implies that during dry years managers should consider reserving water to supplement flows later in the summer when demand is highest for water diversions.

Other human activities may reduce adult survival with indirect and subtle effects because freshwater ecosystems are imbedded in discrete watersheds of the terrestrial landscape. Each watershed is a spatial mosaic of influences from geology, climate and landform coupled with human-mediated ecosystem perturbations through uses of terrestrial and aquatic resources. Landscape impacts to river networks can be cumulative because of the directional topology of rivers. These effects can be subtle but important determinants of species’ distribution and abundance. For example, the spatial extent of agricultural and urban areas in a watershed can be important influences on freshwater invertebrates and fish when analysed with a spatial stream network model [58]. Spatial stream network models [59] offer an important analytic advancement that may facilitate identifying drivers of age truncation in contemporary freshwater environments. One approach, of perhaps several, would be to use θ_A as a response variable in a spatial stream network model, where θ_A has been estimated at many times and places.

Implications for biodiversity conservation

Reductions in adult survival are important potential concerns for thousands of fish species that share a common age-structured life history of iteroparity and an indeterminate lifespan dependent on adult survival. Extinction risk increases under age truncation because population persistence becomes more dependent on the first reproductive age class. As a result, population growth becomes highly sensitive to random fluctuations in juvenile survival [22]. For example, an age-truncated population is vulnerable to rapid declines in population size with successive years of lower juvenile survival such as might occur with drought. Managing habitats for increased adult survival would buffer temporal variation in juvenile survival [27] and generally improve reproductive resilience of fish populations. Although captive breeding or translocation [6,7] could be used to accomplish short-term increases in population size, the activity contributes nothing to alleviating the causes of age truncation. To achieve sustainable fisheries we must consider the sensitivity of fish populations to environmental changes that reduce adult survival.

Successful conservation programmes for freshwater biota may depend on accommodating local prevailing cultural and social values [60], which can present significant impediments to ecosystem restoration and biodiversity conservation [56]. A recently proposed emergency recovery plan [61] identified six global action priorities to stem the loss of freshwater biodiversity: (1) implement environmental flows, (2) improve water quality, (3) protect and restore critical habitats, (4) manage exploitation of species and habitats, (5) prevent and control non-native species and (6) safeguard and restore freshwater connectivity. All of these global action priorities are consistent with strategies to alleviate adult mortality in human-altered environments. Of these priorities, provision of environmental flows is fundamental to alleviating causes of age truncation. Although some countries have conferred rights to rivers [61] many others have not. In areas where water is allocated as a property right, such as our local region, there is no incentive to use water efficiently and water resources are insufficient to sustain aquatic systems during many irrigation seasons. Conservation of individual species or restoration of aquatic ecosystems is unlikely to be accomplished without provision of adequate environmental flows water. It has been argued recently that conferring rights to nature, such as rivers and their watersheds, might also directly benefit public health [62]. Alternatively, it has been argued that conferring rights to nature might violate some human rights [63]. Prospects are dim for many freshwater fish species where water has been overallocated to human uses because resolving these social matters will take time, which will likely cause extinction of some species. Conservation of social-ecological freshwater systems requires sustainability of people and ecosystem services that support aquatic biota. When the aquatic biota are endangered, one might logically ask if people and their livelihoods are also at elevated risk.

Sustainability management requires a holistic view of impacts to freshwater ecosystems caused by humans at local to watershed spatial extents and its aim should be managing human uses of land and water in ways that enable restoration of watershed-scale ecological systems [56]. Achieving higher species survival will require paradigm transformations at societal and governmental levels regarding water management priorities and legal accommodations that provide environmental flows of water needed to sustain aquatic ecosystems and their biota [4,61]. Alleviating human impacts to freshwaters is urgently needed for conservation of freshwater biodiversity.