Habitat destruction is a critical factor that affects persistence in several taxa, including Paci... more Habitat destruction is a critical factor that affects persistence in several taxa, including Pacific salmon. Salmon are noted for their ability to home to their natal streams for reproduction. Since straying (i.e., spawners reproducing in nonnatal streams) is typically low in salmon, its effects have not been appreciated. In this article, we develop both a general analytical model and a simple simulation model describing structured metapopulations to study how weak connections between subpopulations affect the ability of a species to tolerate habitat destruction and/or declines in habitat quality. Our goals are to develop general principles and to relate these principles to salmon population dynamics. The analytical model describes the dynamics of two density-dependent subpopulations, connected by dispersal, whose growth rates fluctuate in response to environmental and demographic stochasticity. We find that, for moderate levels of environmental variability, small dispersal rates can significantly increase mean extinction times. This effect declines with increasing habitat quality, increasing temporal correlation, and increasing spatial correlation, but it is still significant for realistic parameter values. The simulation model shows there is a threshold rate of dispersal that minimizes extinction probabilities. These results cannot be seen in classical metapopulation models and provide new insights into the rescue effect.
We present a stochastic model for metapopulations in landscapes with a finite but arbitrary numbe... more We present a stochastic model for metapopulations in landscapes with a finite but arbitrary number of patches. The model, similar in form to the chain-binomial epidemic models, is an absorbing Markov chain that describes changes in the number of occupied patches as a sequence of binomial probabilities. It predicts the quasiequilibrium distribution of occupied patches, the expected extinction time (t), and the probability of persistence (l((x)) to time x as a function of the number N of patches in the landscape and the number S of those patches that are suitable for the population. For a given value of N, the model shows that: (1) t and l((x) are highly sensitive to changes in S and (2) there is a threshold value of S at which t declines abruptly from extremely large to very small values. We also describe a statistical method for estimating model parameters from time series data in order to evaluate metapopulation viability in real landscapes. An example is presented using published data on the Glanville fritillary butterfly, Meltiaea cinxia, and its specialist parasitoid Cotesia melitaearum. We calculate the expected extinction time of M. cinxia as a function of the frequency of parasite outbreaks, and are able to predict the minimum number of years between outbreaks required to ensure long-term persistence of M. cinxia. The chain-binomial model provides a simple but powerful method for assessing the effects of human and natural disturbances on extinction times and persistence probabilities in finite landscapes.
1. Understanding the role endogenous vs. exogenous forces play in determining the dynamics and ab... more 1. Understanding the role endogenous vs. exogenous forces play in determining the dynamics and abundance of natural populations has important implications for their conservation. 2. Changes in environmental conditions often have different effects on closely related species. For instance, recent studies show that a physical shift in ocean conditions in the mid-1970s in the California current have reduced coho salmon (Oncorhynchus kisutsch) populations, but not chinook salmon (O. tshawytscha). 3. An important question is whether this pattern is due to differences in the ability of coho and chinook salmon to respond to changing ocean conditions or to differences in their life-history traits. 4. We analysed a series of population models to test whether observed abundance patterns of coho and chinook salmon could be explained by one of the major differences in their life history, the spawning age distribution; in the California current, female coho salmon are considered to be obligate semelparous, spawning at age 3, while chinook salmon are considered indeterminate semelparous, with populations spawning over a range of ages. 5. Results from a deterministic model indicate that the sensitivity of the population growth rate to changes in ocean survival depends little on the spawning age structure, especially when the growth rate is small (λ ≈ 1). 6. Analysis of linear and non-linear stochastic models indicate that the probability of persistence increases with the width of the spawning age distribution, as the fraction of adults spawning at age 3 decreases from 100% to 95%. Further increases in the spawning age distribution have negligible affects on persistence. 7. Because coho salmon are not absolutely obligate semelparous (e.g. as many as 25% of males can spawn precociously at age 2 and their effect on annual reproduction is unknown), this range of sensitivity does not provide a firm basis for assuming that the observed abundance patterns of coho and chinook is due to differences in their spawning age distribution. 8. While other life-history differences could play a role, we recommend that ongoing field studies focus on the different effects changing ocean conditions have on the survival of individual salmon species.
In this paper we ask whether succession in a rocky subtidal community varies in space and time, a... more In this paper we ask whether succession in a rocky subtidal community varies in space and time, and if so how much affect that variation has on predictions of community dynamics and structure. We describe succession by Markov chain models based on observed frequencies of species replacements. We use loglinear analysis to detect and quantify spatio-temporal variation in the transition matrices describing succession. The analysis shows that space and time, but not their interaction, have highly significant effects on transition probabilities. To explore the ecological importance of the spatiotemporal variability detected in this analysis, we compare the equilibria and the transient dynamics among three Markov chain models: a time-averaged model that includes the effects of space on succession, a spatially averaged model that include the effects of time, and a constant matrix that averages over the effects of space and time. All three models predicted similar equilibrium composition and similar rates of convergence to equilibrium, as measured by the damping ratio or the subdominant Lyapunov exponent. The predicted equilibria from all three models were very similar to the observed community structure. Thus, although spatial and temporal variation is statistically significant, at least in this system this variation does not prevent homogeneous models from predicting community structure.
Deep Sea Research Part II: Topical Studies in Oceanography, 2005
While changes in the northeast Pacific Ocean in the mid-1970s apparently caused changes in salmon... more While changes in the northeast Pacific Ocean in the mid-1970s apparently caused changes in salmon population growth in the Gulf of Alaska and the California Current, the responses of California Current salmon species, coho salmon (Oncorhynchus kisutch) and chinook salmon (O. tshawytscha) differed. Coho salmon catches declined dramatically along the coasts of California, Oregon and Washington, while chinook salmon catches did not. This provides an opportunity for comparative analysis, a rarity in the study of long-term changes in the ocean. Here we test one possible explanation for that difference, that chinook salmon populations are inherently more persistent because chinook salmon populations spawn over a range of ages, while coho salmon spawn predominantly at age 3 yr. We extended a previous theoretical approach that had been used to assess the long-term response of salmon populations with various spawning age structures to different means and variances in environmental variability. New results indicate that populations with environmental variability at the age of return to freshwater have the same characteristic identified earlier for populations with variability in the age of entry: populations spawning at multiple ages are more persistent, but that increased persistence is gained in the first few percent of departure from all spawning at a single age. Thus, in both cases the results are too sensitive to values of uncertain parameters to depend on as an explanation of the differences in response. We also approached this question by subjecting model populations with coho and chinook salmon spawning age structures to an empirical estimate of actual marine survival of coho salmon over the years 1970-2002, asking the question, if chinook salmon had been subjected to the same ocean survivals would they have experienced the same decline. The differences in spawning age structure made little difference in population responses. The dominant factor influencing the response of these species to a decline in ocean survival was the behavior of the freshwater spawner/smolt relationship at low abundance, a factor that has recently been intensively studied for coho salmon, but is poorly known for chinook salmon. These results suggest that the GLOBEC NEP should focus attention on the ocean phase of salmon life, to explain the observed difference in population response to changes in physical conditions.
Habitat destruction is a critical factor that affects persistence in several taxa, including Paci... more Habitat destruction is a critical factor that affects persistence in several taxa, including Pacific salmon. Salmon are noted for their ability to home to their natal streams for reproduction. Since straying (i.e., spawners reproducing in nonnatal streams) is typically low in salmon, its effects have not been appreciated. In this article, we develop both a general analytical model and a simple simulation model describing structured metapopulations to study how weak connections between subpopulations affect the ability of a species to tolerate habitat destruction and/or declines in habitat quality. Our goals are to develop general principles and to relate these principles to salmon population dynamics. The analytical model describes the dynamics of two density-dependent subpopulations, connected by dispersal, whose growth rates fluctuate in response to environmental and demographic stochasticity. We find that, for moderate levels of environmental variability, small dispersal rates can significantly increase mean extinction times. This effect declines with increasing habitat quality, increasing temporal correlation, and increasing spatial correlation, but it is still significant for realistic parameter values. The simulation model shows there is a threshold rate of dispersal that minimizes extinction probabilities. These results cannot be seen in classical metapopulation models and provide new insights into the rescue effect.
We present a stochastic model for metapopulations in landscapes with a finite but arbitrary numbe... more We present a stochastic model for metapopulations in landscapes with a finite but arbitrary number of patches. The model, similar in form to the chain-binomial epidemic models, is an absorbing Markov chain that describes changes in the number of occupied patches as a sequence of binomial probabilities. It predicts the quasiequilibrium distribution of occupied patches, the expected extinction time (t), and the probability of persistence (l((x)) to time x as a function of the number N of patches in the landscape and the number S of those patches that are suitable for the population. For a given value of N, the model shows that: (1) t and l((x) are highly sensitive to changes in S and (2) there is a threshold value of S at which t declines abruptly from extremely large to very small values. We also describe a statistical method for estimating model parameters from time series data in order to evaluate metapopulation viability in real landscapes. An example is presented using published data on the Glanville fritillary butterfly, Meltiaea cinxia, and its specialist parasitoid Cotesia melitaearum. We calculate the expected extinction time of M. cinxia as a function of the frequency of parasite outbreaks, and are able to predict the minimum number of years between outbreaks required to ensure long-term persistence of M. cinxia. The chain-binomial model provides a simple but powerful method for assessing the effects of human and natural disturbances on extinction times and persistence probabilities in finite landscapes.
1. Understanding the role endogenous vs. exogenous forces play in determining the dynamics and ab... more 1. Understanding the role endogenous vs. exogenous forces play in determining the dynamics and abundance of natural populations has important implications for their conservation. 2. Changes in environmental conditions often have different effects on closely related species. For instance, recent studies show that a physical shift in ocean conditions in the mid-1970s in the California current have reduced coho salmon (Oncorhynchus kisutsch) populations, but not chinook salmon (O. tshawytscha). 3. An important question is whether this pattern is due to differences in the ability of coho and chinook salmon to respond to changing ocean conditions or to differences in their life-history traits. 4. We analysed a series of population models to test whether observed abundance patterns of coho and chinook salmon could be explained by one of the major differences in their life history, the spawning age distribution; in the California current, female coho salmon are considered to be obligate semelparous, spawning at age 3, while chinook salmon are considered indeterminate semelparous, with populations spawning over a range of ages. 5. Results from a deterministic model indicate that the sensitivity of the population growth rate to changes in ocean survival depends little on the spawning age structure, especially when the growth rate is small (λ ≈ 1). 6. Analysis of linear and non-linear stochastic models indicate that the probability of persistence increases with the width of the spawning age distribution, as the fraction of adults spawning at age 3 decreases from 100% to 95%. Further increases in the spawning age distribution have negligible affects on persistence. 7. Because coho salmon are not absolutely obligate semelparous (e.g. as many as 25% of males can spawn precociously at age 2 and their effect on annual reproduction is unknown), this range of sensitivity does not provide a firm basis for assuming that the observed abundance patterns of coho and chinook is due to differences in their spawning age distribution. 8. While other life-history differences could play a role, we recommend that ongoing field studies focus on the different effects changing ocean conditions have on the survival of individual salmon species.
In this paper we ask whether succession in a rocky subtidal community varies in space and time, a... more In this paper we ask whether succession in a rocky subtidal community varies in space and time, and if so how much affect that variation has on predictions of community dynamics and structure. We describe succession by Markov chain models based on observed frequencies of species replacements. We use loglinear analysis to detect and quantify spatio-temporal variation in the transition matrices describing succession. The analysis shows that space and time, but not their interaction, have highly significant effects on transition probabilities. To explore the ecological importance of the spatiotemporal variability detected in this analysis, we compare the equilibria and the transient dynamics among three Markov chain models: a time-averaged model that includes the effects of space on succession, a spatially averaged model that include the effects of time, and a constant matrix that averages over the effects of space and time. All three models predicted similar equilibrium composition and similar rates of convergence to equilibrium, as measured by the damping ratio or the subdominant Lyapunov exponent. The predicted equilibria from all three models were very similar to the observed community structure. Thus, although spatial and temporal variation is statistically significant, at least in this system this variation does not prevent homogeneous models from predicting community structure.
Deep Sea Research Part II: Topical Studies in Oceanography, 2005
While changes in the northeast Pacific Ocean in the mid-1970s apparently caused changes in salmon... more While changes in the northeast Pacific Ocean in the mid-1970s apparently caused changes in salmon population growth in the Gulf of Alaska and the California Current, the responses of California Current salmon species, coho salmon (Oncorhynchus kisutch) and chinook salmon (O. tshawytscha) differed. Coho salmon catches declined dramatically along the coasts of California, Oregon and Washington, while chinook salmon catches did not. This provides an opportunity for comparative analysis, a rarity in the study of long-term changes in the ocean. Here we test one possible explanation for that difference, that chinook salmon populations are inherently more persistent because chinook salmon populations spawn over a range of ages, while coho salmon spawn predominantly at age 3 yr. We extended a previous theoretical approach that had been used to assess the long-term response of salmon populations with various spawning age structures to different means and variances in environmental variability. New results indicate that populations with environmental variability at the age of return to freshwater have the same characteristic identified earlier for populations with variability in the age of entry: populations spawning at multiple ages are more persistent, but that increased persistence is gained in the first few percent of departure from all spawning at a single age. Thus, in both cases the results are too sensitive to values of uncertain parameters to depend on as an explanation of the differences in response. We also approached this question by subjecting model populations with coho and chinook salmon spawning age structures to an empirical estimate of actual marine survival of coho salmon over the years 1970-2002, asking the question, if chinook salmon had been subjected to the same ocean survivals would they have experienced the same decline. The differences in spawning age structure made little difference in population responses. The dominant factor influencing the response of these species to a decline in ocean survival was the behavior of the freshwater spawner/smolt relationship at low abundance, a factor that has recently been intensively studied for coho salmon, but is poorly known for chinook salmon. These results suggest that the GLOBEC NEP should focus attention on the ocean phase of salmon life, to explain the observed difference in population response to changes in physical conditions.
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Papers by Forrest Hill