Wild birds provide many ecosystem services that are economically, ecologically, and culturally important to humans . One especially important service is suppression of insect populations in agricultural systems . On a global scale, insectivorous birds consume an estimated 400–500 million tons of insects annually and have the capacity to decrease arthropod populations and increase crop yields of both temperate and tropical farms . While these beneficial effects are not always observed , attention has focused on promoting avian diversity and abundance on farms to leverage these benefits . The fact that birds consume agricultural pests does not ensure that they can control them, in the sense of substantially reducing densities of rapidly-growing pests. Here, we evaluate the capacity of birds to suppress agricultural pests, specifically the coffee berry borer, aninvasive pest found in almost every coffee-producing region worldwide. The coffee berry borer is one of the most economically significant pests of coffee worldwide , causing an estimated annual global loss of US $500 million . These small beetles damage coffee crops when a female bores into a coffee cherry and excavates chambers for larvae to grow, consuming the coffee bean. Control of CBB can be accomplished by spraying fungal bio-insecticide Beauvaria bassinia, increasing harvest frequency or continually removing, by hand, over-ripe and fallen cherries, tomato grow bag which serve as reservoirs for infestations .

The last, and most laborious, control method appears to be the most economically effective In addition to human-mediated control, natural predators such as ants, parasitoid wasps, and nematodes are being explored as potential bio-control agents . Birds have also been identified as a significant biological control agent of CBB . Field experiments in Central America have shown that CBB infestation dramatically decreases when birds are present . For example, Karp et al. reported that bird predation suppresses CBB infestation by 50% and saves farmers US $75– 310/ha per year; another estimate values bird predation at US $584/ha . Suppression is done by both resident foliage-gleaning insectivores, such as rufous-capped warblers , and Neotropical migrants like the yellow warbler . Similar to other agriculture systems, avian abundance is higher on farms with heterogenous landscapes in close proximity to native habitat , suggesting low-intensity shade coffee farms are better not only for supporting biodiversity, but also in providing pest mediating ecosystem services . Several lines of evidence support the notion that birds depredate CBB in coffee plantations, and that their effects are biologically significant. Firstly, we know that a variety of bird species consume CBB from assays of avian fecal and regurgitant samples , though the detection rate is quite low . Low detection rates might be due to low consumption rates; detectability of DNA in feces depends on number of CBB eaten, and time since feeding, as well as fecal mass . Secondly, bird and bat exclosure experiments are associated with greater CBB infestation within enclosures . At the same time, it is not clear how birds can effectively suppress CBB at most sites, and throughout the season. Exclosure experiments that report avian suppression appear to be at sites with relatively low CBB infestations , whereas coffee-producing regions with more recent introduction of CBB have infestations of up to 500,000 CBB in a season .

We also do not know whether suppression is effective throughout the reproductive cycle of the CBB, or just when abundances are relatively low. Finally, CBB field traps often capture large numbers of CBB, even in the presence of birds . Consequently, while there is clear evidence that birds consume CBB, the degree to which CBB populations can be suppressed is less clear, particularly because of the species’ population growth potential . Here, we use a CBB population growth model to assess the capacity of birds at naturally occurring densities to reduce CBB populations, as a function of a starting infestation size. We created an age-based population growth model for CBB using data from a life-stage transition matrix published by Mariño et al. . We converted their matrix into a female-only, daily time-step, deterministic Leslie matrix; we could not estimate population growth directly from the original matrix because it did not use a common time step . We incorporated a skewed adult sex ratio to mimic real populations , and added a life-stage for dispersing females, the stage at which CBB are vulnerable to predation by birds. Since the entire CBB life cycle occurs within the coffee cherry, CBB are vulnerable to predation by birds for a short time window when adult females disperse between plants and burrow into a new cherry . Birds do not eat coffee cherries, with the exception of the Jacu , which is found in southeastern South America. Consequently, we assumed that only adult CBB females are vulnerable to bird predation. With our Leslie matrix, we projected population growth for a closed population during a single CBB breeding season. We projected growth at three levels of initial starting populations of CBB , calculated from published estimates of CBB densities from alcohol lure traps in coffee farms from Colombia, Hawaii and Costa Rica. We then determined the degree to which dispersing female survival rate would have to be decreased to result in a 50% depression in the adult population size at the end of the coffee season at all three infestation levels.

Finally, we assessed the plausibility of this degree of CBB suppression by birds as a function of avian energy requirements, reported avian densities on coffee farms, prey composition of avian diets, estimated caloric value of CBB, and the starting population size of CBB females.Coffee phenology is directly related to rainfall patterns that differ among coffee producing regions, leading to distinct seasons, and timing of harvest. Our model assumes environmental conditions of Costa Rica, and thus describe the coffee phenology of this region. In regions of Costa Rica with marked seasonality, coffee flowering is triggered during the dry to wet season transition by the onset of acute precipitation . Areas with relatively consistent rain patterns have more continuous flowering events and a longer harvest season In the Central Valley of Costa Rica, flowering typically begins in March, with three flowering events spread over a month . Flowers are short-lived, lasting only a few days before fruit begin to develop. Maturation of coffee cherries is slow, with immature green cherries taking up to 240 days to develop into red, ripe fruit that is ready for harvest in mid-October through January . After harvest, coffee plants are left to recuperate until flowering is initiated again the following year by the next onset of rain.Following the coffee flowering period and initiation of cherry growth, grow bags garden adult female CBB emerge and disperse via flight in search of new cherries to colonize . Timing of emergence appears to be driven primarily by relative humidity and temperature, with dispersal peaks occurring around the end of the coffee harvest, from December through March . Females begin ovipositing in chambers carved out of the coffee endosperm roughly 120–150 days after coffee flowering, when the dry content of the seed is 20% or higher . It is this dispersal period, and subsequent drilling into the coffee cherry, when CBB are vulnerable to predation by birds, as the remainder of the CBB life cycle occurs within the coffee cherry. There are five main CBB developmental stages: egg, larva, pupa, juvenile, and adult. Females can oviposit daily for up to 40 days, averaging 1–2 eggs per day . After a week, eggs hatch and larva take 17 days to develop into pupa. Following pupation , juveniles emerge and reach sexual maturity after about 4 days . The length of the CBB life cycle can be slowed and accelerated depending on average temperature ; the developmental times used here are based on 25 C rearing conditions . Offspring sex ratio is skewed toward females, ranging from 1:5 to 1:494 . Since males are flightless, mating occurs between siblings within the natal cherry. Fertilized females then disperse to colonize other cherries, though multi-generational oviposition within the natal cherry is possible. The prolonged maturation of the coffee crop allows continual reproduction, with 2–8 CBB generations feasible in a single season if environmental conditions and food availability be favorable . With the removal of cherries during harvest, adult CBB will enter diapause in coffee cherries that remain on the plant or fall to the ground .Since birds do not eat coffee cherries, biocontrol by birds would only occur during the brief dispersal period when CBB are vulnerable. There is a rich bird community during this period of time as both resident and migratory birds are present . Neotropical migrants are potentially more abundant on coffee farms than resident species that may prefer forest habitat due to higher prey abundances .

Many migratory warbler species of the Setophaga genus that frequent coffee farms have been confirmed as CBB predators, as have resident bird species such as the rufous-capped warbler and common tody flycatcher  Overall, insectivorous birds are the most abundant on coffee farms and hold great potential as biocontrol of many insect pests . Details on bird densities on Costa Rica coffee farms used in the model are expanded on below .To our knowledge, there is little information about population densities of CBB in coffee plantations at the start of the growing season. The start of CBB reproduction commenced 120 days after coffee flowering and continued until 305 days after flowering, yielding a 185-day CBB breeding season. We confirmed CBB reproduction was possible within this period for Central Valley Costa Rica using degree day calculations from Jaramillo et al. based on CBB thermal tolerance. We then calculated how much the dispersing adult survival rate would have to be reduced to cause a 50% reduction in adult female borer population size on day 185. To determine how many CBB would need to be consumed by birds to achieve this goal, we found the difference between daily borer population sizes of unsuppressed and suppressed populations and summed the differences across the CBB reproductive season. We used sensitivity analysis to estimate the degree to which changes in each vital rate affects population growth rate . All models were implemented using the popbio package in R . R code for all analyses is provided in the Supporting Information . We also wanted our model to project CBB population growth that represented “low” and “high” infestations observed in the field. To start, we estimated probable CBB densities using data on the number of dispersing females collected in alcohol-lure traps. At peak dispersal, CBB numbers have been recorded as high as 1000–6120 CBB/trap/week to as low as 50–105 CBB/trap/week . Using these trap counts, we calculated potential CBB densities per hectare via reported trap densities and converted weekly capture estimates to the number of daily dispersers to complement our daily population model. We used a density independent model, a standard first step in many population models. However, note that we would need to divide CBB numbers by plant density to evaluate the impacts of CBB population growth on yield. We also would need empirical data on how the demography of CBB populations change with coffee-plant density to implement a revised model, and we are unaware of published data on this. Consequently, this analysis is beyond the scope of this paper . Using data from Aristizabal et al. , we selected a high peak dispersal count from farms with large infestations and a low peak dispersal count from farms with small infestations to represent peak dispersal on Day 185 in our model. We then back calculated the initial population sizes that would yield those ultimate densities. We used our calculated values of 269 and 5 as our “high” and “low” initial population sizes of gravid females at the start of the coffee season and used 100 CBB to represent “medium” initial population size.The mass, in dry weight, of a female adult CBB was determined from the weighted average of CBB using midpoint values for weight ranges from Moore et al. . We estimated the caloric content of a single CBB using the average energy value of Coleoptera species in the adult stage . Using our estimated CBB caloric content, we calculated the number of CBB required to make up 5% and 10% of an average bird’s daily diet .