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The basic reproduction number, R0, determines the rate of spread of a communicable disease and therefore gives fundamental information needed to plan public health interventions. Using mortality records, we estimated the rate of spread of COVID-19 among 160 counties and county-aggregates in the USA at the start of the epidemic. We show that most of the high among-county variance is explained by four factors (R2 = 0.70): the timing of outbreak, population size, population density, and spatial location. For predictions of future spread, population density and spatial location are important, and for the latter we show that SARS-CoV-2 strains containing the G614 mutation to the spike gene are associated with higher rates of spread. Finally, the high predictability of R0 allows extending estimates to all 3109 counties in the conterminous 48 states. The high variation of R0 argues for public health policies enacted at the county level for controlling COVID-19.Ives and Bozzuto estimate the spread rate of COVID-19 in the USA at the start of the epidemic, extrapolating values of R0 for 3109 counties during the period before measures were taken to reduce the spread. Most of predictive variation in county-level values of R0 is explained by population density and spatial location, with differences among locations associated with differences among strains of SARS-CoV-2.

During the COVID-19 pandemic, many quantitative approaches were employed to predict the course of disease spread. However, forecasting faces the challenge of inherently unpredictable spread dynamics, setting a limit to the accuracy of all models. Here, we analyze COVID-19 data from the USA to explain variation among jurisdictions in disease spread predictability (that is, the extent to which predictions are possible), using a combination of statistical and simulation models. We show that for half the counties and states the spread rate of COVID-19, r ( t ), was predictable at most 9 weeks and 8 weeks ahead, respectively, corresponding to at most 40% and 35% of an average cycle length of 23 weeks and 26 weeks. High predictability was associated with high cyclicity of r ( t ) and negatively associated with R 0 values from the pandemic’s onset. Our statistical evidence suggests the following explanation: jurisdictions with a severe initial outbreak, and where individuals and authorities took strong and sustained protective measures against COVID-19, successfully curbed subsequent waves of disease spread, but at the same time unintentionally decreased its predictability. Decreased predictability of disease spread should be viewed as a by-product of positive and sustained steps that people take to protect themselves and others.

Many studies document negative inbreeding effects on individuals, and conservation efforts to preserve rare species routinely employ strategies to reduce inbreeding. Despite this, there are few clear examples in nature of inbreeding decreasing the growth rates of populations, and the extent of population-level effects of inbreeding in the wild remains controversial. Here, we take advantage of a long-term dataset of 26 reintroduced Alpine ibex ( Capra ibex ibex ) populations spanning nearly 100 years to show that inbreeding substantially reduced per capita population growth rates, particularly for populations in harsher environments. Populations with high average inbreeding ( F   ≈  0.2) had population growth rates reduced by 71% compared with populations with no inbreeding. Our results show that inbreeding can have long-term demographic consequences even when environmental variation is large and deleterious alleles may have been purged during bottlenecks. Thus, efforts to guard against inbreeding effects in populations of endangered species have not been misplaced. Long-term data on 26 reintroduced Alpine ibex populations show that inbreeding reduces per capita population growth rates, especially in harsher environmental conditions. These results validate conservation efforts to reduce inbreeding in rare species.

A Correction to this paper has been published: https://doi.org/10.1038/s42003-021-01679-0.

1. When prevention of invasive species' introductions fails, society faces the challenge to manage invasive species in an effective and efficient way. The success of this depends on biological aspects and on cooperation between decision makers and scientists. Using the case of the round goby Neogobius melanostomus, one of Europe's \"worst invasive species\", we propose an approach guiding scientists to co-produce effective and efficient population control measures in collaboration with decision makers. 2. We surveyed the effectiveness, urgency and simplicity perceived by decision makers as well as the support of two population control options: removal of eggs and/or adults. Using a field study and a dynamical population model, we investigated the effectiveness and efficiency for both options in different population contexts. 3. Decision makers initially seemed to lack a clear preference for either control option. After being presented with preliminary field and modelling results, decision makers mostly approved measures being developed to implement the two control options. 4. Starting population control early after detecting the species requires in total fewer years for eradication than controlling an established population: to reach an eradication success rate of 95%, 13 years for early start vs. 18 years for late start are needed when removing eggs and adults; when removing adults only, 20 vs. 29 years are needed. Removing eggs and adults combined results in a yearly effort of 5.01 h/m², while removing adults only results in a yearly effort of 1.76 h/m². Thus, removing adults only proves to be the most efficient option to eradicate the population. Nonetheless, considerable effort is needed: when removing less than 57% of the adult population, eradication is not feasible, even assuming low survival and fecundity rates for the population. Furthermore, inflow of new propagules renders eradication efforts ineffective. 5. Synthesis and applications. Scientists who aim to support decision makers in finding an optimal control strategy for invasive species need to be able to provide scientific knowledge on effectiveness and efficiency of different options. For round goby and most non-native species, eradication is only feasible if started early in recently arrived populations and if inflow of new propagules can be prevented.

Emerging wildlife diseases are taking a heavy toll on animal and plant species worldwide. Mitigation, particularly in the initial epidemic phase, is hindered by uncertainty about the epidemiology and management of emerging diseases, but also by vague or poorly defined objectives. Here, we use a quantitative analysis to assess how the decision context of mitigation objectives, available strategies and practical constraints influences the decision of whether and how to respond to epidemics in wildlife. To illustrate our approach, we parametrized the model for European fire salamanders affected by Batrachochytrium salamandrivorans , and explored different combinations of conservation, containment and budgetary objectives. We found that in approximately half of those scenarios, host removal strategies perform equal to or worse than no management at all during a local outbreak, particularly where removal cannot exclusively target infected individuals. Moreover, the window for intervention shrinks rapidly if an outbreak is detected late or if a response is delayed. Clearly defining the decision context is, therefore, vital to plan meaningful responses to novel outbreaks. Explicitly stating objectives, strategies and constraints, if possible before an outbreak occurs, avoids wasting precious resources and creating false expectations about what can and cannot be achieved during the epidemic phase.

Mitigation of infectious wildlife diseases is especially challenging where pathogens affect communities of multiple host species. Although most ecological studies recognize the challenge posed by multiple-species pathogens, the implications for management are typically assessed only qualitatively. Translating the intuitive understanding that multiple host species are important into practice requires a quantitative assessment of whether and how secondary host species should also be targeted by management and the effort this will require. Using a multiple-species compartmental model, we determined analytically whether and how intensively secondary host species should be managed to prevent outbreaks in focal hosts based on the reproduction number of individual host species and between-species transmission rates. We applied the model to the invasive pathogenic fungus Batrachochytrium salamandrivorans in a 2-host system in northern Europe. Avoiding a disease outbreak in the focal host (fire salamanders [Salamandra salamandra]) was impossible unless management also heavily targeted the secondary host (alpine newts [Ichthyosaura alpestris]). Preventing an outbreak in the community required targeted removal of at least 80% of each species. This proportion increased to 90% in the presence of an environmental reservoir of B. salamandrivorans and when the proportion of individuals removed could not be adjusted for different host species (e.g., when using traps that are not species specific). We recommend the focus of disease-mitigation plans should shift from focal species to the community level and calculate explicitly the management efforts required on secondary host species to move beyond the simple intuitive understanding that multiple host species may all influence the system. Failure to do so may lead to underestimating the magnitude of the effort required and ultimately to suboptimal or futile management attempts. La mitigación de enfermedades infecciosas en fauna silvestre representa un reto especial cuando los patógenos afectan a comunidades de múltiples especies hospederas. Aunque la mayoría de los estudios ecológicos reconocen el reto que plantean los patógenos de múltiples especies, las implicaciones para el manejo comúnmente sólo se evalúan en el aspecto cualitativo. La traducción del entendimiento intuitivo hacia la práctica de que las múltiples especies hospederas son importantesrequiere unavaloración cuantitativa sobre si y cuán intensivamente se deberían considerar en el manejo las especies hospederas secundarias y los esfuerzos que esto requerirá. Determinamos analíticamente con un modelo compartimentado de múltiples especiessi ycuán intensivamente se deberían manejar las especies hospederas secundarias para prevenir brotes en los hospederos focales con base en el número de reproducción de las especies hospederas individuales y en las tasas de transmisión entre especies. Aplicamos el modelo al hongo patógeno invasivo Batrachochytrium salamandrivorans en un sistema de dos hospederos al norte de Europa. Fue imposible evitar un brote de enfermedad en el hospedero focal (la salamandra de fuego [Salamandra salamandra]) a menos que el manejo también se enfocara considerablemente en el hospedero secundario (el tritón alpino [Ichthyosaura alpestris]). Para prevenir un brote dentro de la comunidad se requirió delaextirpación de al menos el 80% de cada especie. Esta proporción incrementó al 90% con la presencia de un reservorio ambiental de B. salamandrivorans y cuando la proporción de individuos removidos no pudo ajustarse para diferentes especies (p. ej.: el uso de trampas que nos son específicas para una especie) Recomendamos que el foco de los planes para la mitigación de enfermedades cambie de una especie focal al nivel de comunidad y que calculen explícitamente los esfuerzos de manejo requeridos sobre las especies hospederas secundarias para avanzar más allá del simpleentendimiento intuitivo de que múltiples especies hospederas pueden todas influir sobre el sistema. Si se falla en esto, se podría subestimar la magnitud del esfuerzo requerido y finalmente podría resultar en intentos de manejo sub-óptimos o inútiles.

1. Conservation science can be most effective in its decision-support role when seeking answers to clearly formulated questions of direct management relevance. Emerging wildlife diseases, a driver of global biodiversity loss, illustrate the challenges of performing this role: in spite of considerable research, successful disease mitigation is uncommon. Decision analysis is increasingly advocated to guide mitigation planning, but its application remains rare. 2. Using an integral projection model, we explored potential mitigation actions for avoiding population declines and the ongoing spatial spread of the fungus Batrachochytrium salamandrivorans (Bsal). This fungus has recently caused severe amphibian declines in north-western Europe and currently threatens Palearctic salamander diversity. 3. Available evidence suggests that a Bsal outbreak in a fire salamander (Salamandra salamandra) population will lead to its rapid extirpation. Treatments such as antifungals or probiotics would need to effectively interrupt transmission (reduce probability of infection by nearly 90%) in order to reduce the risk of host extirpation and successfully eradicate the pathogen. 4. Improving the survival of infected hosts is most likely to be detrimental as it increases the potential for pathogen transmission and spread. Active removal of a large proportion of the host population has some potential to locally eradicate Bsal and interrupt its spread, depending on the presence of Bsal reservoirs and on the host's spatial dynamics, which should therefore represent research priorities. 5. Synthesis and applications. Mitigation of Batrachochytrium salamandrivorans epidemics in susceptible host species is highly challenging, requiring effective interruption of transmission and radical removal of host individuals. More generally, our study illustrates the advantages of framing conservation science directly in the management decision context, rather than adapting to it a posteriori.

Ecological and evolutionary predictions are being increasingly employed to inform decision-makers confronted with intensifying pressures menacing life on Earth. For these efforts to effectively guide conservation actions, knowing the limit of predictability is pivotal. In this study, we provide realistic expectations about the enterprise of predicting changes in ecological and evolutionary observations through time. We begin with an intuitive explanation of predictability (that is, the extent to which predictions are possible) employing an easy-to-use metric, predictive power PP(t). To illustrate the challenge of forecasting, we then show that among insects, birds, fishes, and mammals (i) 50% of the populations are predictable at most one year in advance, and (ii) the median one-year-ahead predictive power corresponds to a sobering prediction R2 of approximately 20%. Nonetheless, predictability is not an immutable property of ecological systems. For example, different harvesting strategies can impact the predictability of exploited populations to varying degrees. Moreover, considering multivariate time series, incorporating explanatory variables or accounting for time trends (environmental forcing) can enhance predictability. To effectively address the urgent challenge of biodiversity loss, researchers and practitioners must be aware of the predictive information within the available data and explore efficient ways to leverage this information for environmental stewardship.

Wildlife diseases figure prominently among the main causes of biodiversity loss worldwide. Especially fungal and fungus-like pathogens are on the rise, wreaking havoc across the tree of life by threatening species persistence and destabilizing ecosystems. A worrisome example are freshwater crayfish species in Eurasia and Oceania, facing the dual challenge of introduced competitive crayfish species and an introduced water mold (Aphanomyces astaci) causing crayfish plague. A. astaci locally extinguishes susceptible native crayfish populations, while non-native individuals (mostly from North America) remain largely unaffected. Despite its significant impact and its ∼150 years of presence in Europe, studies and disease management recommendations for crayfish plague that are firmly rooted in epidemiological theory are scarce. Here, we present a practical eco-epidemiological framework to understand how multi-species crayfish communities react to crayfish plague introductions. The framework is based on the observation that the dynamics of crayfish communities are mainly determined by life-history characteristics, within- and among-species competition, effects of generalist predators (including fishing), and host-pathogen interactions. From this ecological and epidemiological context, we derive fundamental epidemiological metrics, single-host species and community-level basic reproduction numbers (R0). We investigate how host species densities affect the likelihood of a disease outbreak in a crayfish community, and we demonstrate that a community’s R0 value is simply the sum of the community’s single-host species R0 values, adjusted for competition and predation. We further demonstrate how R0 can be used to guide preventative and mitigation actions for crayfish communities. For example, we show how R0 expressions – even without a detailed parametrization – can be used to construct regional risk rankings for different crayfish communities, for an effective allocation of resources to local conservation plans. Our eco-epidemiological framework will also be of interest to the management of other aquatic host-pathogen systems with water-borne pathogen transmission as the main route of pathogen spread.