Fig 1.
Three life history types expressed in terms of abundance and survival over time.
Type I populations (top panel) that are characterized by low fecundity, high survival, longer life span, with reproductive senescence. Type III (bottom panel) populations are characterized by high fecundity, low juvenile survival, with increasing survival of later age classes. Type II populations (middle panel) are an intermediary form with relatively constant survival throughout all age classes. Dotted lines represent juvenile stages; solid lines begin at the earliest onset of breeding. Lines from bordering panels are retained as faint grey lines for reference. Both abundance and lifespan proportion are normalized and used to find the metric A of life-history type (see Appendix B in S1 File). The average inverse survival to maturity is for the three types are 1.5, 6.3 and 84,000 respectively).
Fig 2.
(a) Simplified schematic of the life cycle of an organism described by Model 1. The environmental fluctuations in fecundity may be described by Eq (A7), a constant plus or minus an environmental perturbation. However, for survival the environment intrudes through the probability of a given individual dying within a given time-frame—the environment intrudes in a multiplicative way. (b) Dynamics of the total population of the organism. In general, the depth of oscillation will be greater for Type III organisms.
Table 1.
Mean conservation gain, G, observed in five different species and life history types for nine different conservation actions.
We define “conservation gain” as G = (r-r0)×200, where the model is set up so that growth rate is zero before applying either stochasticity or the conservation action. Then r0 is the growth rate with stochasticity but without the conservation action while r is the growth rate with both stochasticity and the conservation action. Na for Action-9 denotes the adult population. All results are based on simulations using Model 2. Organisms in age-class k = 0 are referred to as “recruits”; other pre-reproductive individuals are “juveniles”. Larger sensitivities shown are in bold for emphasis. Species are DE = Diomedea exulans (albatross), OO = Orchinus orca (orca), DC = Dermochelys coriacea (leatherback sea turtle), CP = Chrysemys picta (Striped bass) and LG = Lobatus gigas (Queen conch).
Fig 3.
Sensitivity of variance in population (lnNt) to variability of the mortality rate μ0 for the youngest sub-adult class.
We used simulations of Model 2 with noise (uncorrelated). (a) Total variance as a function of the value of mortality rate μ0 in the earliest stage. The distribution of strategy-types shows that Type III organisms have greater μ0 and this leads to a greater proportion of the overall variance in populations being dependent on the variability of this parameter. The distribution of the major strategy types shows that Type III organisms have greater μ0 and this leads to a greater overall variance in population growth rate. The curve corresponds to a best fit, after Eq (4), of the equation based on Eq (4). (b) Proportion of variability explained by variations in pre-reproductive survival for different organisms (see Fig 1) as a function of μ0.
Fig 4.
High mortality of early life stages and increased environmental autocorrelation have a combined effect that increases relative population variance.
In order to study the effect of autocorrelation we find the variance of the log-population as a function of first year survival (s0) and autocorrelation coefficient ρ of environmental variability. Here the variance of δt is chosen such that the variance of εt is exactly 0.1 for the duration of model time. For each set of parameters, in 500 replicate simulations we ran a Leslie matrix model for 250 years of model time. For each replicate we found the variance of log-population and plot the average of this over 500 replicate simulations. We run these simulations across 10 values of s0 (0.0001 to 0.5, exponential scale) and 9 values of ρ (0 to 0.8, linear scale). Onto the contour map of the simulation results, we place silhouettes of populations from Fig 1 based on their s0 value and the calculated ρ of their environment. The latter is determined from the dominant oceanographic index native to their population region (see Appendix F in S1 File). The greater sensitivity to environmental forcing seen for Type III populations is thus exacerbated by the environment itself, such that regions with more pronounced environmental memory will force even greater variability to these populations.