Overall, insectivorous birds are the most abundant on coffee farms and hold great potential as bio-control 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. We first initialized the coffee berry borer population model with 100 dispersing females . 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, plastic square flower bucket 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 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.Parameters for our Leslie matrix for coffee berry borers are broadly consistent with expectations and general knowledge . For example, our conversion of fecundity to a daily value, F1 = 1.341, is consistent with published literature stating that 1–2 eggs are laid per day by CBB . Model projections showed that across a 185-day CBB breeding period starting at the point of first ovipositing, an initial population size of 100 female dispersers would produce 1.3 million offspring, resulting in a new adult population of 70,245 females . Assuming 99% of colonizing females successfully bore and oviposit in a coffee cherry on Day 0, the first generation of new dispersing females does not appear until day 37.
At Day 38, the adult population begins to increase, and continues to do so exponentially.The daily growth rate of this population converged on 1.042. Sensitivity analysis revealed that survival of adult females had the largest impact on overall population growth , followed by daily survival of pupa , juveniles , eggs and larvae and dispersing females . In addition to modeling growth with 100 initial colonists , we projected the population growth of low and high starting populations calculated from observed weekly alcohol-lure trap catches during peak dispersal . Comparing the three population projections, peak number of dispersers at Day 185 varied considerably, with 162, 3259, and 8768 daily dispersers for low, medium, and high colonizing populations, respectively. In the high population projection, the adult population toward the end of the growing season reached over 18,800 individuals. Note that because these are density-independent models, the number of CBB does not depend on plant density. However, the impacts of the CBB population on yield would depend on coffee plant density. To reduce the final adult population by 50%, the daily survival rate of dispersing females would have to be reduced from 0.99602 to 0.83202. This change represents a 16.4% reduction in daily survival when dispersing. The number of CBB that birds need to eat to reduce the adult population at this rate was driven by the initial population size as a straight line, y = 79.23 N0 . At medium starting population , birds need to consume 7628 CBB during the borer breeding season, while at high starting population , about 20,500 dispersing CBB must be consumed by birds. Daily consumption rates by birds would have to increase over time as the CBB population grows and could vary from 15 to 750 CBB being consumed a day, depending on starting population size . Overall, we calculated that for every female CBB in the initial colonization, birds need to consume 79 CBB to reduce the end of season population by half.We estimated that the caloric content of a 195 μg adult CBB to be 1.09 calories per gram dry weight, or 0.00109 kcal. At 5%–10% of a bird’s daily diet based on number of prey items, birds would consume <7 CBB per day. This represents 0.03%–0.05% of daily caloric requirements of our average insectivorous bird. At these feeding rates, our models suggest that by the time of peak dispersal, 4, 88, and 236 birds are required at low, medium, and high starting population sizes, respectively, to reduce CBB populations by 50% on day 185 .Our model suggests that avian predation is likely to be effective at reducing CBB populations by 50% only during small infestations , or during the early stages of larger infestations . Birds appear unable to successfully suppress medium and large infestations because the number of CBB that need to be eaten in a season requires higher bird densities than are reported in the literature. Karp et al. estimated 4–12 birds/ha of species that are confirmed or suspected CBB predators. Flocks of migratory birds on coffee farms are estimated at 19/ha and 24/ha , but these values are also short of our estimates of necessary densities for suppressing larger CBB outbreaks. One caveat to our conclusions is that our calculations were based on CBB accounting for 5%–10% of a bird’s daily diet . This assumption meant birds would only eat a set maximum of 7 CBB per day. Sherry et al. reported up to 116 CBB in the stomach contents of a single warbler, suggesting under certain circumstances in the field, birds eat more CBB. Generalist insectivores, particularly Neotropical migrants, have flexible foraging preferences and would likely feed opportunistically on CBB in response to dramatic dispersal peaks. Therefore, birds might be expected to increase feeding rates as CBB disperser abundances increase, though it may depend on the relative abundances of other prey. Better data on CBB consumption rates by birds under different circumstances would improve our estimates of the circumstances under which birds can control CBB populations.
A second caveat is that bird densities used in the model may not represent the potential for CBB control because bird densities depend on the structure of the agricultural landscape, which the current model does not consider. On coffee farms, plastic plant pot birds are more abundant when native tree cover is highest and natural forests are close by . Across tropical and temperate regions, the propensity for birds to forage on farms, and thus exert pressure on agricultural pests, is correlated with the physical complexity and diversity of the agroecosystem . For example, birds make more frequent foraging trips to apple orchards with high native tree coverage . In alfalfa fields, edge habitat complexity supports greater avian richness leading to lower pest abundances . Under some circumstances, the density of birds foraging in certain areas may be higher than average densities would imply, leading to greater control potential than our models suggest. More generally, our CBB population model is density independent and assumes environmental conditions and sufficient resources to allow CBB populations to increase without restriction. As a result, our model is limited, as it does not consider localized effects of weather and temperature fluctuations on CBB developmental time , nor characteristics of coffee farms that influence both CBB infestation and bird density. We assumed maximal capacity for CBB population growth and used estimates of bird densities from the literature that only included birds known to consume CBB, perhaps underestimating the potential for avian control. Models are an important tool for estimating population dynamics, but as with any species, the growth potential for CBB and availability of its predators, is context dependent. Our study echoes Kendall et al.’s conclusion that, even though errors in model construction are common, these seldom change qualitative conclusions. From our population matrix, CBB daily growth rate converged on λdaily = 1.042 around day 124, with an observed rate of population change across the entire coffee-growing season of 705 . Our λdaily is higher than Mariño et al.’s reported lambda of 1.32 over 50– 56 days, which corresponds to λdaily ≈ 1.006 . Part of this discrepancy may come from the fact that Marino et al. combined vital rates across life stages with different time steps. Nonetheless, both models are consistent in predicting rapidly growing populations. Observed CBB population growth rates are similar to ours: Baker, Barrera, & Rivas, calculated a 1.067 growth rate in wild populations and RuizC ardenas and Baker reported 1.047 in CBB reared in laboratory settings. In their sensitivity analysis, Mariño et al. reported that adult female survival, and transitions from larva to pupa and pupa to juvenile had high sensitivity in contributing to population growth rate, with adult survival the highest . We found a similar peak sensitivity value for female adult survival in our matrix , supporting the idea that CBB population growth is most sensitive to adult survival rate. Interestingly, dispersal survival from our matrix was estimated to have low impact on population growth , even though this life stage is when CBB are vulnerable to bird predation. Thus, our analysis superficially suggests that population control once CBB are established should focus on reducing adult survival rather than on trapping dispersing females , if the same impact on numbers could be achieved. However, dispersing females are much more accessible to control methods like spraying fungal bio-insecticide than are adult females, which are inside the coffee cherries, so despite the tremendous difference in sensitivity values, management of an established population is likely to be more cost effective by continuing to focus on dispersing females . Population models specific to CBB have been criticized for not being representative of wild populations, since more generations are estimated through modeling than are observed in field studies . We analyzed CBB population growth using a deterministic model, with an even distribution of dispersal and a fixed predation pressure. While CBB dispersal is continuous, there can be dramatic intraseasonal peaks in numbers that were not captured by our model . In addition, reported longevity of female CBB varies widely from 55 to 380 days, though some studies looked at CBB reared on artificial diet . Refinements of survival in natural settings would, therefore, improve models of CBB population growth, and the potential for control by birds. If field data on CBB vital rate stochasticity become available, and bird densities opportunistically increase during CBB peak numbers, it could affect our conclusions about the capacity of birds to control larger CBB outbreaks. Based on our analyses, there is a population density of CBB above which their capacity to produce more adults exceeds the ability of birds to control their numbers, at least to limit the population size by 50%.