Mortality of coho salmon (Oncorhynchus kisutch) associated with burdens of multiple parasite species.

Multiple analytical techniques were used to evaluate the impact of multiple parasite species on the mortality of threatened juvenile coho salmon (Oncorhynchus kisutch) from the West Fork Smith River, Oregon, USA. We also proposed a novel parsimonious mathematical representation of macroparasite distribution, congestion rate, which (i) is easier to use than traditional models, and (ii) is based on Malthusian parameters rather than probability theory. Heavy infections of Myxobolus insidiosus (Myxozoa) and metacercariae of Nanophyetus salmincola and Apophallus sp. occurred in parr (subyearlings) from the lower mainstem of this river collected in 2007 and 2008. Smolts (yearlings) collected in 2007-2010 always harboured fewer Apophallus sp. with host mortality recognised as a function of intensity for this parasite. Mean intensity of Apophallus sp. in lower mainstem parr was 753 per fish in 2007 and 856 per fish in 2008, while parr from the tributaries had a mean of only 37 or 13 parasites per fish, respectively. Mean intensity of this parasite in smolts ranged between 47 and 251 parasites per fish. Over-dispersion (variance to mean ratios) of Apophallus sp. was always lower in smolts compared with all parr combined or lower mainstem parr. Retrospective analysis based on smolt data using both the traditional negative binomial truncation technique and our proposed congestion rate model showed identical results. The estimated threshold level for mortality involving Apophallus sp. was at 400-500 parasites per fish using both analytical methods. Unique to this study, we documented the actual existence of these heavy infections prior to the predicted mortality. Most of the lower mainstem parr (approximately 75%) had infections above this level. Heavy infections of Apophallus sp. metacercariae may be an important contributing factor to the high over-wintering mortality previously reported for these fish that grow and develop in this section of the river. Analyses using the same methods for M.insidiosus and N. salmincola generally pointed to minimal parasite-associated mortality.

Mortality threshold for juvenile Chinook salmon Oncorhynchus tshawytscha in an epidemiological model of Ceratomyxa shasta.

The myxozoan parasite Ceratomyxa shasta is a significant pathogen of juvenile Chinook salmon Oncorhynchus tshawytscha in the Klamath River, California, USA. This parasite requires 2 hosts to complete its life cycle: a freshwater polychaete (Manayunkia speciosa) and a salmonid. The complex life cycle and large geographic area where infection occurs make it difficult to monitor and manage ceratomyxosis. We present a model for ceratomyxosis-induced mortality in O. tshawytscha, from which parameters important to the persistence of C. shasta are identified. We also experimentally quantify specific parameters from the model and identify a mortality threshold (a critical parameter), by naturally exposing native O. tshawytscha to C. shasta in the Klamath River. The average percent mortality that resulted from these experimental challenges ranged from 2.5 to 98.5% over an exposure dose of 4.4 to 612 x 10(6) parasites. This experiment identified a non-linear mortality threshold of 7.7 +/- 2.1 x 10(4) actinospores fish(-1) for Chinook salmon from the Iron Gate Hatchery on the Klamath River. Below this threshold no mortality occurred and above it mortality increased dramatically, thus providing a target by which to reduce parasitism in emigrating juvenile O. tshawytscha.

The control of vector-borne disease epidemics.

The theoretical underpinning of our struggle with vector-borne disease, and still our strongest tool, remains the basic reproduction number, R(0), the measure of long term endemicity. Despite its widespread application, R(0) does not address the dynamics of epidemics in a model that has an endemic equilibrium. We use the concept of reactivity to derive a threshold index for epidemicity, E(0), which gives the maximum number of new infections produced by an infective individual at a disease free equilibrium. This index describes the transitory behavior of disease following a temporary perturbation in prevalence. We demonstrate that if the threshold for epidemicity is surpassed, then an epidemic peak can occur, that is, prevalence can increase further, even when the disease is not endemic and so dies out. The relative influence of parameters on E(0) and R(0) may differ and lead to different strategies for control. We apply this new threshold index for epidemicity to models of vector-borne disease because these models have a long history of mathematical analysis and application. We find that both the transmission efficiency from hosts to vectors and the vector-host ratio may have a stronger effect on epidemicity than endemicity. The duration of the extrinsic incubation period required by the pathogen to transform an infected vector to an infectious vector, however, may have a stronger effect on endemicity than epidemicity. We use the index E(0) to examine how vector behavior affects epidemicity. We find that parasite modified behavior, feeding bias by vectors for infected hosts, and heterogeneous host attractiveness contribute significantly to transitory epidemics. We anticipate that the epidemicity index will lead to a reevaluation of control strategies for vector-borne disease and be applicable to other disease transmission models.

Discovering spatio-temporal models of the spread of West Nile virus.

Emerging infectious diseases are characterized by complex interactions among disease agents, vectors, wildlife, humans, and the environment. Since the appearance of West Nile virus (WNV) in New York City in 1999, it has infected over 8,000 people in the United States, resulting in several hundred deaths in 46 contiguous states. The virus is transmitted by mosquitoes and maintained in various bird reservoir hosts. Its unexpected introduction, high morbidity, and rapid spread have left public health agencies facing severe time constraints in a theory-poor environment, dependent largely on observational data collected by independent survey efforts and much uncertainty. Current knowledge may be expressed as a priori constraints on models learned from data. Accordingly, we applied a Bayesian probabilistic relational approach to generate spatially and temporally linked models from heterogeneous data sources. Using data collected from multiple independent sources in Maryland, we discovered the integrated context in which infected birds are plausible indicators for positive mosquito pools and human cases for 2001 and 2002.

Life expectancy change in perturbed communities: derivation and qualitative analysis.

Pollution, loss of habitat, and climate change are introducing dramatic perturbations to natural communities and affecting public health. Populations in perturbed communities can change dynamically, in both abundance and age structure. While analysis of the community matrix can predict changes in population abundance arising from a sustained or press perturbation, perturbations also have the potential to modify life expectancy, which adds yet another means to falsify experimental hypotheses and to monitor management interventions in natural systems. In some instances, an input to a community will produce no change in the abundance of a population but create a major shift in its mean age. We present an analysis of change in both abundance and life expectancy, leading to a formal quantitative assessment as well as qualitative predictions, and illustrate the usefulness of the technique through general examples relating to vector-borne disease and fisheries.

Community-level analysis of risk of vector-borne disease.

Ecological community structure is particularly important in vector-borne zoonotic diseases with complex life cycles. Qualitative community model analysis may provide a meaningful alternative to standard population-based models of vector-borne disease. We built on recent mathematical developments in qualitative community modeling coupled with conventional biomathematical models of vector-borne disease transmission, to provide a procedure to analyze risk. Using this procedure, we can hypothesize changes in risk of vector-borne disease from disturbances, such as control measures, habitat alteration, or global warming. We demonstrate the application of this procedure to an oak forest community to predict the risk of Lyme disease. Our predictions of Lyme disease risk in an oak forest community confirm reports of positive associations between deer abundance and risk of disease and are consistent with published observations.

Qualitative stability and ambiguity in model ecosystems.

Qualitative analysis of stability in model ecosystems has previously been limited to determining whether a community matrix is sign stable or not with little analytical means to assess the impact of complexity on system stability. Systems are seen as either unconditionally or conditionally stable with little distinction and therefore much ambiguity in the likelihood of stability. First, we reexamine Hurwitz's principal theorem for stability and propose two "Hurwitz criteria" that address different aspects of instability: positive feedback and insufficient lower-level feedback. Second, we derive two qualitative metrics based on these criteria: weighted feedback (wF(n)) and weighted determinants (wDelta(n)). Third, we test the utility of these qualitative metrics through quantitative simulations in a random and evenly distributed parameter space in models of various sizes and complexities. Taken together they provide a practical means to assess the relative degree to which ambiguity has entered into calculations of stability as a result of system structure and complexity. From these metrics we identify two classes of models that may have significant relevance to system research and management. This work helps to resolve some of the impasse between theoretical and empirical discussions on the complexity and stability of natural communities.